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A proposal for the non-Abelian tensor multiplet: If one compactifies the Abelian $(1,0)$ tensor multiplet on a circle, one
finds 5d SYM for the zero modes. For the Kaluza-Klein modes one can likewise
find a Lagrangian description in 5d \cite{Bonetti:2012st}. Since in 5d we have
an ordinary YM gauge potential, one may look for a non-Abelian generalization
and indeed such a non-Abelian generalization was found in
\cite{Bonetti:2012st}. In this paper, we study this non-Abelian generalization
for the $(1,0)$ tensor multiplet in detail. We obtain the supersymmetry
variations that we close on-shell. This way we get the fermionic equation of
motion and a modified selfduality constraint.
|
Towards a categorification of scattering amplitudes: Categorification of scattering amplitudes for planar Feynman diagrams in
scalar field theories with a polynomial potential is reported. Amplitudes for
cubic theories are directly written down in terms of projectives of hearts of
intermediate $t$-structures restricted to the cluster category of quiver
representations, without recourse to geometry. It is shown that for theories
with $\phi^{m+2}$ potentials those corresponding to $m$-cluster categories are
to be used. The case of generic polynomial potentials is treated and our
results suggest the existence of a generalization of higher cluster categories
which we call pseudo-periodic categories. An algorithm to obtain the
projectives of hearts of intermediate $t$-structures for these types is
presented.
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Infinitely many conservation laws in self-dual Yang--Mills theory: Using a nonlocal field transformation for the gauge field known as
Cho--Faddeev--Niemi--Shabanov decomposition as well as ideas taken from
generalized integrability, we derive a new family of infinitely many conserved
currents in the self-dual sector of SU(2) Yang-Mills theory. These currents may
be related to the area preserving diffeomorphisms on the reduced target space.
The calculations are performed in a completely covariant manner and, therefore,
can be applied to the self-dual equations in any space-time dimension with
arbitrary signature.
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On non-abelian low energy effective action for D-branes: Connection between the partition function for the 2D sigma model with
boundary pertubations and the low energy effective action for massless fields
from in the open string theory is discussed. In the non-abelian case with a
stack of $N$ D-branes, the terms up to the order of $\alpha'^3$ are found
|
Subsystem Complexity and Holography: We study circuit complexity for spatial regions in holographic field
theories. We study analogues based on the entanglement wedge of the bulk
quantities appearing in the "complexity = volume" and "complexity = action"
conjectures. We calculate these quantities for one exterior region of an
eternal static neutral or charged black hole in general dimensions, dual to a
thermal state on one boundary with or without chemical potential respectively,
as well as for a shock wave geometry. We then define several analogues of
circuit complexity for mixed states, and use tensor networks to gain intuition
about them. We find a promising qualitative match between the holographic
action and what we call the purification complexity, the minimum number of
gates required to prepare an arbitrary purification of the given mixed state.
On the other hand, the holographic volume does not appear to match any of our
definitions of mixed-state complexity.
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A Note on Cosmic (p,q,r) Strings: The spectrum of $(p,q)$ bound states of F- and D-strings has a distinctive
square-root tension formula that is hoped to be a hallmark of fundamental
cosmic strings. We point out that the Bogomol'nyi-Prasad-Sommerfield (BPS)
bound for vortices in ${\cal N}=2$ supersymmetric Abelian-Higgs models also
takes the square-root form. In contrast to string theory, the most general
supersymmetric field theoretic model allows for $(p,q,r)$ strings, with three
classes of strings rather than two. Unfortunately, we find that there do not
exist BPS solutions except in the trivial case. The issue of whether there
exist non-BPS solutions which may closely resemble the square-root form is left
as an open question.
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D-brane Superpotentials: Geometric and Worldsheet Approaches: From the worldsheet perspective, the superpotential on a D-brane wrapping
internal cycles of a Calabi-Yau manifold is given as a generating functional
for disk correlation functions. On the other hand, from the geometric point of
view, D-brane superpotentials are captured by certain chain integrals. In this
work, we explicitly show for branes wrapping internal 2-cycles how these two
different approaches are related. More specifically, from the worldsheet point
of view, D-branes at the Landau-Ginzburg point have a convenient description in
terms of matrix factorizations. We use a formula derived by Kapustin and Li to
explicitly evaluate disk correlators for families of D2-branes. On the geometry
side, we then construct a three-chain whose period gives rise to the effective
superpotential and show that the two expressions coincide. Finally, as an
explicit example, we choose a particular compact Calabi-Yau hypersurface and
compute the effective D2-brane superpotential in different branches of the open
moduli space, in both geometric and worldsheet approaches.
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Topological Model for Domain Walls in (Super-)Yang-Mills Theories: We derive a topological action that describes the confining phase of
(Super-)Yang-Mills theories with gauge group $SU(N)$, similar to the work
recently carried out by Seiberg and collaborators. It encodes all the
Aharonov-Bohm phases of the possible non-local operators and phases generated
by the intersection of flux tubes. Within this topological framework we show
that the worldvolume theory of domain walls contains a Chern-Simons term at
level $N$ also seen in string theory constructions. The discussion can also
illuminate dynamical differences of domain walls in the supersymmetric and
non-supersymmetric framework. Two further analogies, to string theory and the
fractional quantum Hall effect might lead to additional possibilities to
investigate the dynamics.
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String Theory of the Regge Intercept: Using the Polchinski-Strominger effective string theory in covariant gauge,
we compute the mass of a rotating string in D dimensions with large angular
momenta J, in one or two planes, in fixed ratio, up to and including first
subleading order in the large J expansion. This constitutes a first-principles
calculation of the value for the order $J^0$ contribution to the mass-squared
of a meson on the leading Regge trajectory in planar QCD with bosonic quarks.
For open strings with Neumann boundary conditions, and for closed strings in
$D\geq 5$, the order $J^0$ term in the mass-squared is exactly calculated by
the semiclassical approximation. This term in the expansion is universal and
independent of the details of the theory, assuming only D-dimensional Poincare
invariance and the absence of other infinite-range excitations on the string
worldvolume, beyond the Nambu-Goldstone bosons.
|
Static and non-static quantum effects in two-dimensional dilaton gravity: We study backreaction effects in two-dimensional dilaton gravity. The
backreaction comes from an $R^2$ term which is a part of the one-loop effective
action arising from massive scalar field quantization in a certain
approximation. The peculiarity of this term is that it does not contribute to
the Hawking radiation of the classical black hole solution of the field
equations. In the static case we examine the horizon and the physical
singularity of the new black hole solutions. Studying the possibility of time
dependence we see the generation of a new singularity. The particular solution
found still has the structure of a black hole, indicating that non-thermal
effects cannot lead, at least in this approximation, to black hole evaporation.
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The black hole final state for the Dirac fields In Schwarzschild
spacetime: We show that the internal stationary state of a black hole for massless Dirac
fields can be represented by an entangled state of collapsing matter and
infalling Hawking radiation. This implies that the Horowitz-Maldacena
conjecture for the black hole final state originally proposed for the massless
scalar fields is also applicable to fermionic fields as well. For an initially
mixed state we find that the measure of mixedness is expected to decrease under
evaporation.
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Block-Structure Method for the Solution of the Matrix System of
Equations g{ij}g{jk}=delta{i}{k} in the N-dimensional Case: In this paper a new block-structure method is presented for the solution of
the well-known from gravity theory matrix system of equations
g{ij}g{jk}=delta{i}{k} (with respect to the unknown covariant components g{ij}
and by known contravariant ones g{jk}) by transforming this matrix system into
a linear algebraic system of equations in the general N-dimensional case.
Although powerful computer methods exist for the solution of this problem for a
given (fixed) dimension of the matrices g{ij} and especially for numerical
elements of g{ij}, the structure of the obtained linear algebraic system in the
general N-dimensional case and for arbitrary elements of g{ij} (functions) has
not been known.
The proposed new analytical block-structure method for the case of
symmetrical matrices g{ij} and g{jk} (the standard case in gravity theory) is
based on the construction of a block-structure matrix, whose "elements" are
again matrices. The method allows to obtain the structure of this linear system
in the general N-dimensional case, after multiplication (to the left) with the
transponed matrix.
Some arguments are given why the proposed method may be applied, after some
refinement and generalization for the case of non-symmetrical matrices g{ij}
and g{jk}, for finding the graviton modes in the Kaluza-Klein expansion in
theories with extra dimensions.
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General covariance, and supersymmetry without supersymmetry: An unusual four-dimensional generally covariant and supersymmetric SU(2)
gauge theory is described. The theory has propagating degrees of freedom, and
is invariant under a local (left-handed) chiral supersymmetry, which is half
the supersymmetry of supergravity. The Hamiltonian 3+1 decomposition of the
theory reveals the remarkable feature that the local supersymmetry is a
consequence of Yang-Mills symmetry, in a manner reminiscent of how general
coordinate invariance in Chern-Simons theory is a consequence of Yang-Mills
symmetry. It is possible to write down an infinite number of conserved
currents, which strongly suggests that the theory is classically integrable. A
possible scheme for non-perturbative quantization is outlined. This utilizes
ideas that have been developed and applied recently to the problem of
quantizing gravity.
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Inflation in $R^2$ supergravity with non-minimal superpotentials: We investigate the cosmological inflation in a class of supergravity models
that are generalizations of non-supersymmetric $R^2$ models. Although such
models have been extensively studied recently, especially after the launch of
the PLANCK and BICEP2 data, the class of models that can be constructed has not
been exhausted. In this note, working in a supergravity model that is a
generalization of Cecotti's model, we show that the appearance of new
superpotential terms, which are quadratic in the superfield $\, \Lambda$ that
couples to the Ricci supermultiplet, alters substantially the form of the
scalar potential. The arising potential has the form of the Starobinsky
potential times a factor that is exponential in the inflaton field and
dominates for large inflaton values. We show that the well-known Starobinsky
inflation scenario is maintained only for unnaturally small fine-tuned values
of the coupling describing the $\Lambda^2$ superpotential terms. A welcome
feature is the possible increase of the tensor to scalar ratio $r$, within the
limits set by the new Planck and BICEP2 data.
|
Virasoro blocks and quasimodular forms: We analyse Virasoro conformal blocks in the regime of heavy intermediate
exchange $(h_p \rightarrow \infty)$. For the 1-point block on the torus and the
4-point block on the sphere, we show that each order in the large-$h_p$
expansion can be written in closed form as polynomials in the Eisenstein
series. The appearance of this structure is explained using the fusion kernel
and, more markedly, by invoking the modular anomaly equations via the 2d/4d
correspondence. We observe that the existence of these constraints allows us to
develop a faster algorithm to recursively construct the blocks in this regime.
We then apply our results to find corrections to averaged heavy-heavy-light OPE
coefficients.
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A Generalization of Gauge Invariance: We consider perturbative quantum field theory in the causal framework. Gauge
invariance is, in this framework, an identity involving chronological products
of the interaction Lagrangian; it express the fact that the scattering matrix
must leave invariant the sub-space of physical states. We are interested in
generalizations of such identity involving Wick sub-monomials of the
interaction Lagrangian. The analysis can be performed by direct computation in
the lower orders of perturbation theory; guided by these computations we
conjecture a generalization for arbitrary orders.
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The Coulomb Branch of 3d $\mathcal{N}=4$ Theories: We propose a construction of the quantum-corrected Coulomb branch of a
general 3d gauge theory with $\mathcal{N}=4$ supersymmetry, in terms of local
coordinates associated with an abelianized theory. In a fixed complex
structure, the holomorphic functions on the Coulomb branch are given by
expectation values of chiral monopole operators. We construct the chiral ring
of such operators, using equivariant integration over BPS moduli spaces. We
also quantize the chiral ring, which corresponds to placing the 3d theory in a
2d Omega background. Then, by unifying all complex structures in a twistor
space, we encode the full hyperk\"ahler metric on the Coulomb branch. We verify
our proposals in a multitude of examples, including SQCD and linear quiver
gauge theories, whose Coulomb branches have alternative descriptions as
solutions to the Bogomolnyi and/or Nahm equations.
|
Loop quantum gravity and light propagation: Within loop quantum gravity we construct a coarse-grained approximation for
the Einstein-Maxwell theory that yields effective Maxwell equations in flat
spacetime comprising Planck scale corrections.
The corresponding Hamiltonian is defined as the expectation value of the
electromagnetic term in the Einstein-Maxwell Hamiltonian constraint,
regularized a la Thiemann, with respect to a would-be semiclassical state. The
resulting energy dispersion relations entail Planck scale corrections to those
in flat spacetime. Both the helicity dependent contribution of Gambini and
Pullin [GP] and, for a value of a parameter of our approximation, that of Ellis
et. al. [ELLISETAL] are recovered. The electric/magnetic asymmetry in the
regularization procedure yields nonlinearities only in the magnetic sector
which are briefly discussed. Observations of cosmological Gamma Ray Bursts
might eventually lead to the needed accuracy to study some of these quantum
gravity effects.
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Regge trajectories of the charged string in a magnetic background: The set of Casimir operators associated with the global symmetries of a
charged string in a constant magnetic background are found. It is shown that
the string rest energy can be expressed as a combination of these invariants.
Using this result, the Regge trajectories of the system are derived. The first
Regge trajectory is given by a family of infinitely many parallel
straight-lines, one for each spin projection along the magnetic field.
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Evidence for Non-perturbative String Symmetries: String theory appears to admit a group of discrete field transformations --
called $S$ dualities -- as exact non-perturbative quantum symmetries.
Mathematically, they are rather analogous to the better-known $T$ duality
symmetries, which hold perturbatively. In this talk the evidence for $S$
duality is reviewed and some speculations are presented.
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Inhomogeneous Jacobi equation and Holographic subregion complexity: We derive a general expression for obtaining Holographic subregion complexity
for asymptotically $AdS$ spacetimes, pertubatively around pure $AdS$ using a
variational technique. An essential step in finding subregion complexity is to
identify the bulk minimal surface of the entangling subregion. Our method
therefore heavily relies on solutions of an inhomogeneous version of Jacobi
equation, used to study deformations of the entangling surface for
perturbations of the bulk metric. Using this method we have obtained the change
in complexity for a strip and a circular disk like subsystem for \emph{boosted}
black brane like perturbations over pure $AdS_4$. As a corollary, we find that
for spherical subsytems in $3+1$ dimensional bulk, the linear change of
subregion complexity for \emph{boosted} black brane like perturbations over
pure $AdS_4$ , vanishes.
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D-type Conformal Matter and SU/USp Quivers: We discuss the four dimensional models obtained by compactifying a single M5
brane probing $D_{N}$ singularity (minimal D-type $(1,0)$ conformal matter in
six dimensions) on a torus with flux for abelian subgroups of the $SO(4N)$
flavor symmetry. We derive the resulting quiver field theories in four
dimensions by first compactifying on a circle and relating the flux to duality
domain walls in five dimensions. This leads to novel ${\cal N}=1$ dualities in
4 dimensions which arise from distinct five dimensional realizations of the
circle compactifications of the D-type conformal matter.
|
Precision Cosmology and the Landscape: After reviewing the cosmological constant problem - why is Lambda not huge? -
I outline the two basic approaches that had emerged by the late 1980s, and note
that each made a clear prediction. Precision cosmological experiments now
indicate that the cosmological constant is nonzero. This result strongly favors
the environmental approach, in which vacuum energy can vary discretely among
widely separated regions in the universe. The need to explain this variation
from first principles constitutes an observational constraint on fundamental
theory. I review arguments that string theory satisfies this constraint, as it
contains a dense discretuum of metastable vacua. The enormous landscape of
vacua calls for novel, statistical methods of deriving predictions, and it
prompts us to reexamine our description of spacetime on the largest scales. I
discuss the effects of cosmological dynamics, and I speculate that weighting
vacua by their entropy production may allow for prior-free predictions that do
not resort to explicitly anthropic arguments.
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Anomalous dimensions of spinning operators from conformal symmetry: We compute, to the first non-trivial order in the $\epsilon$-expansion of a
perturbed scalar field theory, the anomalous dimensions of an infinite class of
primary operators with arbitrary spin $\ell=0,1,..$, including as a particular
case the weakly broken higher-spin currents, using only constraints from
conformal symmetry. Following the bootstrap philosophy, no reference is made to
any Lagrangian, equations of motion or coupling constants. Even the space
dimensions d are left free. The interaction is implicitly turned on through the
local operators by letting them acquire anomalous dimensions. When matching
certain four-point and five-point functions with the corresponding quantities
of the free field theory in the $\epsilon\to 0$ limit, no free parameter
remains. It turns out that only the expected discrete d values are permitted
and the ensuing anomalous dimensions reproduce known results for the weakly
broken higher-spin currents and provide new results for the other spinning
operators.
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M Theory and P-Branes: Ten dimensional type IIA and IIB theories with p-branes are compactified to
8-dimensions. It is shown that resulting branes can be classified according to
the representations of $\bf {SL(3,Z) \times SL(2,Z)}$. These p-branes can also
be obtained by compactification of M theory on three torus and various
wrappings of membrane and five brane of the eleven dimensional theory. It is
argued that there is evidence for bound states of the branes in eight
dimensions as is the case in the interpretation of $\bf {SL(2,Z)}$ family of
string solutions obtained by Schwarz.
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Exploring quark-gluon plasma on the loop space: Langevin equation describing soft modes in the quark-gluon plasma is
reformulated on the loop space. The Cauchy problem for the resulting loop
equation is solved for the case when the nonvanishing components of the gauge
potential correspond to the Cartan generators of the SU(N)-group and are
proportional to a constant unit vector in the Cartan subalgebra. The
regularized form of the loop equation with an arbitrary gauge potential is
found, and perturbation theory in powers of the 't Hooft coupling is discussed.
|
$CP^2$ soliton scattering: The collective coordinate approximation: The $CP^2$ model, with and without a generalized Hopf term, is studied using
the collective coordinate approximation. In the spirit of this approximation,
an ansatz is given which in previous numerical studies was seen to give a good
parameterization of the numerical solution. The equations of motion for the
collective coordinates are then solved analytically, for solitons close
together and for solitons far apart. The solutions show how the generalized
Hopf term changes the scattering angle which in its absence is $90^{\circ}$.
|
Quantum Bound States with Zero Binding Energy: After reviewing the general properties of zero-energy quantum states, we give
the explicit solutions of the \seq with $E=0$ for the class of potentials
$V=-|\gamma|/r^{\nu}$, where $-\infty < \nu < \infty$. For $\nu > 2$, these
solutions are normalizable and correspond to bound states, if the angular
momentum quantum number $l>0$. [These states are normalizable, even for $l=0$,
if we increase the space dimension, $D$, beyond 4; i.e. for $D>4$.] For $\nu
<-2$ the above solutions, although unbound, are normalizable. This is true even
though the corresponding potentials are repulsive for all $r$. We discuss the
physics of these unusual effects.
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Carrollian and celestial spaces at infinity: We show that the geometry of the asymptotic infinities of Minkowski spacetime
(in $d+1$ dimensions) is captured by homogeneous spaces of the Poincar\'e
group: the blow-ups of spatial (Spi) and timelike (Ti) infinities in the sense
of Ashtekar--Hansen and a novel space Ni fibering over $\mathscr{I}$. We embed
these spaces \`a la Penrose--Rindler into a pseudo-euclidean space of signature
$(d+1,2)$ as orbits of the same Poincar\'e subgroup of O$(d+1,2)$. We describe
the corresponding Klein pairs and determine their Poincar\'e-invariant
structures: a carrollian structure on Ti, a pseudo-carrollian structure on Spi
and a "doubly-carrollian" structure on Ni. We give additional geometric
characterisations of these spaces as grassmannians of affine hyperplanes in
Minkowski spacetime: Spi is the (double cover of the) grassmannian of affine
lorentzian hyperplanes; Ti is the grassmannian of affine spacelike hyperplanes
and Ni fibers over the grassmannian of affine null planes, which is
$\mathscr{I}$. We exhibit Ni as the fibred product of $\mathscr{I}$ and the
lightcone over the celestial sphere. We also show that Ni is the total space of
the bundle of scales of the conformal carrollian structure on $\mathscr{I}$ and
show that the symmetry algebra of its doubly-carrollian structure is isomorphic
to the symmetry algebra of the conformal carrollian structure on $\mathscr{I}$;
that is, the BMS algebra. We show how to reconstruct Minkowski spacetime from
any of its asymptotic geometries, by establishing that points in Minkowski
spacetime parametrise certain lightcone cuts in the asymptotic geometries. We
include an appendix comparing with (A)dS and observe that the de Sitter groups
have no homogeneous spaces which could play the r\^ole that the celestial
sphere plays in flat space holography.
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On Conformally Compactified Phase Space: Conformally compactified phase space is conceived as an automorphism space
for the global action of the extended conformal group. Space time and momentum
space appear then as conformally dual, that is conjugate with respect to
conformal reflections. If now the former, as generally agreed, is appropriate
for the description of classical mechanics in euclidean geometrical form, then
the latter results appropriate for the description of quantum mechanics in
spinor geometrical form. In such description, fermion multiplets will naturally
appear as consequence of higher symmetries and furthermore, the euclidean
geometry, bilinearly resulting from that of spinors, will a priori guarantee
the absence of ultraviolet divergences when dealing with quantum field
theories. Some further possible consequences of conformal reflections of
interest for physics, are briefly outlined.
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Hierarchical Axion Inflation: We propose a new field theory mechanism for generating an effective
trans-Planckian decay constant from sub-Planckian ones. Using the minimal two
axions and a hierarchy between two axion decay constants is sufficient for
realizing inflation through non-perturbative effects only and with minimal
tuning. The inflationary motion is kept entirely within a sub-Planckian domain.
We outline possible strategies of embedding the model in a string theory setup.
|
Scattering of conformal higher spin fields: We develop a formalism for describing the most general notion of tree-level
scattering amplitudes in 4d conformal higher spin theory. As conformal higher
spin fields obey higher-derivative equations of motion, there are many distinct
on-shell external states which may contribute to their scattering, some of
which grow polynomially with time, leading to ill-defined amplitudes. We
characterize the set of admissible scattering states which produce finite tree
amplitudes, noting that there are more such states than just standard massless
higher spins obeying two-derivative equations of motion. We use conformal
gravity as a prime example, where the set of scattering states includes the
usual Einstein graviton and a `ghost' massless spin 1 particle. An extension of
the usual spinor helicity formalism allows us to encode these scattering states
efficiently in terms of `twistor-spinors'. This leads to compact momentum space
expressions for all finite tree-level 3-point amplitudes of conformal higher
spin theory. While some of these 3-point amplitudes vanish (including all those
with only standard two-derivative higher spin external states), there are many
others which are non-vanishing. We also comment on the generalization to
scattering of conformal higher spins in AdS$_4$.
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Hidden Beauty in Multiloop Amplitudes: Planar L-loop maximally helicity violating amplitudes in N = 4 supersymmetric
Yang-Mills theory are believed to possess the remarkable property of satisfying
iteration relations in L. We propose a simple new method for studying the
iteration relations for four-particle amplitudes which involves the use of
certain linear differential operators and eliminates the need to fully evaluate
any loop integrals. We carry out this procedure in explicit detail for the
two-loop amplitude and argue that this method can be used to prove the
iteration relations to all loops up to polynomials in logarithms.
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Anti-De Sitter BPS Black Holes in N=2 Gauged Supergravity: Electrically charged solutions breaking half of the supersymmetry in Anti-De
Sitter four dimensional N=2 supergravity coupled to vector supermultiplets are
constructed. These static black holes live in an asymptotic $AdS_4$ space-time.
The Killing spinor, i. e., the spinor for supersymmetry variation is explicitly
constructed for these solutions.
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N=4 SYM on S^3 with Near Critical Chemical Potentials: We study the N = 4 theory at weak coupling, on a three sphere in the grand
canonical ensemble with R symmetry chemical potentials. We focus attention on
near critical values for the chemical potentials, above which the classical
theory has no ground state. By computing a one loop effective potential for the
light degrees of freedom in this regime, we show the existence of flat
directions of complex dimension N, 2N and 3N for one, two and three critical
chemical potentials respectively; these correspond to one half, one quarter and
one-eighth BPS states becoming light respectively at the critical values. At
small finite temperature we show that the chemical potentials can be continued
beyond their classical limiting values to yield a deconfined metastable phase
with lifetime diverging in the large N limit. Our low temperaure analysis
complements the high temperature metastability found by Yamada and Yaffe. The
resulting phase diagram at weak coupling bears a striking resemblance to the
strong coupling phase diagram for charged AdS black holes. Our analysis also
reveals subtle qualitative differences between the two regimes.
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A new approach for computing the geometry of the moduli spaces for a
Calabi-Yau manifold: It is known that moduli spaces of Calabi-Yau (CY) manifolds are special
K\"ahler manifolds. This structure determines the corresponding low-energy
effective theory which arises in superstring compactifications on CY manifolds.
In the case, where CY manifold is given as a hypersurface in the weighted
projective space, we propose a new procedure for computing the K\"ahler
potential of the moduli space. Our method is based on the fact that the moduli
space of CY manifolds is a marginal subspace of the Frobenius manifold which
arises on the deformation space of the corresponding Landau--Ginzburg
superpotential.
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The AdS/CFT Correspondence and Logarithmic Corrections to Braneworld
Cosmology and the Cardy-Verlinde Formula: The AdS/CFT correspondence is employed to derive logarithmic corrections to
the Cardy-Verlinde formula when thermal fluctuations in the Anti-de Sitter
black hole are accounted for. The qualitative effect of these corrections on
the braneworld cosmology is investigated. The role of such terms in enabling a
contracting universe to undergo a bounce is demonstrated. Their influence on
the stability of black holes in AdS space and the Hawking-Page-Witten phase
transitions is also discussed.
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Remarks on a Lorentz-breaking 4D chiral gauge theory: We investigate a Lorentz-violating chiral model composed by two fermions, a
complex scalar field and a gauge field. We show that by convenientely adjusting
the parameters of the model, it is possible to generate an unambiguous
Carroll-Field-Jackiw term and, at the same time, provide the cancelation of the
chiral anomaly. The renormalizability of the model is investigated and it is
shown that the same counterterms needed in the symmetric phase also renormalize
the model with broken symmetry.
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Airy Equation for the Topological String Partition Function in a Scaling
Limit: We use the polynomial formulation of the holomorphic anomaly equations
governing perturbative topological string theory to derive the free energies in
a scaling limit to all orders in perturbation theory for any Calabi-Yau
threefold. The partition function in this limit satisfies an Airy differential
equation in a rescaled topological string coupling. One of the two solutions of
this equation gives the perturbative expansion and the other solution provides
geometric hints of the non-perturbative structure of topological string theory.
Both solutions can be expanded naturally around strong coupling.
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Deconstructing Supersymmetry: Two supersymmetric classical mechanical systems are discussed. Concrete
realizations are obtained by supposing that the dynamical variables take values
in a Grassmann algebra with two generators. The equations of motion are
explicitly solved.
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Determinant representations of scalar products for the open XXZ chain
with non-diagonal boundary terms: With the help of the F-basis provided by the Drinfeld twist or factorizing
F-matrix for the open XXZ spin chain with non-diagonal boundary terms, we
obtain the determinant representations of the scalar products of Bethe states
of the model.
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Closed string symmetries in open string field theory: tachyon vacuum as
sine-square deformation: We revisit the identity-based solutions for tachyon condensation in open
bosonic string field theory (SFT) from the viewpoint of the sine-square
deformation (SSD). The string Hamiltonian derived from the simplest solution
includes the sine-square factor, which is the same as that of an open system
with SSD in the context of condensed matter physics. We show that the open
string system with SSD or its generalization exhibits decoupling of the left
and right moving modes and so it behaves like a system with a periodic boundary
condition. With a method developed by Ishibashi and Tada, we construct pairs of
Virasoro generators in this system, which represent symmetries for a closed
string system. Moreover, we find that the modified BRST operator in the open
SFT at the identity-based tachyon vacuum decomposes to holomorphic and
antiholomorphic parts, and these reflect closed string symmetries in the open
SFT. On the basis of SSD and these decomposed operators, we construct
holomorphic and antiholomorphic continuous Virasoro algebras at the tachyon
vacuum. These results imply that it is possible to formulate a pure closed
string theory in terms of the open SFT at the identity-based tachyon vacuum.
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Dirac Neutrino Masses in NCG: Several models in NCG with mild changes to the standard model(SM)are
introduced to discuss the neutrino mass problem. We use two constraints,
Poincar$\acute{e}$ duality and gauge anomaly free, to discuss the possibility
of containing right-handed neutrinos in them. Our work shows that no model in
this paper, with each generation containing a right-handed neutrino, can
satisfy these two constraints in the same time. So, to consist with neutrino
oscillation experiment results, maybe fundamental changes to the present
version of NCG are usually needed to include Dirac massive neutrinos.
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Power Spectrum and Non-Gaussianities in Anisotropic Inflation: We study the planar regime of curvature perturbations for single field
inflationary models in an axially symmetric Bianchi I background. In a theory
with standard scalar field action, the power spectrum for such modes has a pole
as the planarity parameter goes to zero. We show that constraints from back
reaction lead to a strong lower bound on the planarity parameter for
high-momentum planar modes and use this bound to calculate the signal-to-noise
ratio of the anisotropic power spectrum in the CMB, which in turn places an
upper bound on the Hubble scale during inflation allowed in our model. We find
that non-Gaussianities for these planar modes are enhanced for the flattened
triangle and the squeezed triangle configurations, but show that the estimated
values of the f_NL parameters remain well below the experimental bounds from
the CMB for generic planar modes (other, more promising signatures are also
discussed). For a standard action, f_NL from the squeezed configuration turns
out to be larger compared to that from the flattened triangle configuration in
the planar regime. However, in a theory with higher derivative operators,
non-Gaussianities from the flattened triangle can become larger than the
squeezed configuration in a certain limit of the planarity parameter.
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Muti-instanton Amplitudes in Type IIB String Theory: We compute the normalization of the multiple D-instanton amplitudes in type
IIB string theory and show that the result agrees with the prediction of
S-duality due to Green and Gutperle.
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Hamiltonian approach to QCD in Coulomb gauge - a survey of recent
results: I report on recent results obtained within the Hamiltonian approach to QCD in
Coulomb gauge. Furthermore this approach is compared to recent lattice data,
which were obtained by an alternative gauge fixing method and which show an
improved agreement with the continuum results. By relating the Gribov
confinement scenario to the center vortex picture of confinement it is shown
that the Coulomb string tension is tied to the spatial string tension. For the
quark sector a vacuum wave functional is used which explicitly contains the
coupling of the quarks to the transverse gluons and which results in
variational equations which are free of ultraviolet divergences. The
variational approach is extended to finite temperatures by compactifying a
spatial dimension. The effective potential of the Polyakov loop is evaluated
from the zero-temperature variational solution. For pure Yang--Mills theory,
the deconfinement phase transition is found to be second order for SU(2) and
first order for SU(3), in agreement with the lattice results. The corresponding
critical temperatures are found to be $275 \, \mathrm{MeV}$ and $280 \,
\mathrm{MeV}$, respectively. When quarks are included, the deconfinement
transition turns into a cross-over. From the dual and chiral quark condensate
one finds pseudo-critical temperatures of $198 \, \mathrm{MeV}$ and $170 \,
\mathrm{MeV}$, respectively, for the deconfinement and chiral transition.
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Toward the Universal Theory of Strings: We show that the $N=2$ superstrings may be viewed as a special class of the
$N=4$ superstrings and demonstrate their equivalence. This allows us to realize
all known string theories based on linear algebras and with $N<4$
supersymmetries as special choices of the vacua in the $N=4$ superstring.
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Charged Dilatonic AdS Black Holes and Magnetic AdS_{D-2} x R^2 Vacua: We consider D-dimensional Einstein gravity coupled to two U(1) fields and a
dilaton with a scalar potential. We derive the condition that the analytical
AdS black holes with two independent charges can be constructed. Turning off
the cosmological constant, the extremal Reissner-Nordstrom black hole emerges
as the harmonic superposition of the two U(1) building blocks. With the
non-vanishing cosmological constant, our extremal solutions contain the
near-horizon geometry of AdS_2 x R^{D-2} with or without a hyperscaling. We
also obtain the magnetic AdS_{D-2} x Y^2 vacua where Y^2 can be R^2, S^2 or
hyperbolic 2-space. These vacua arise as the fix points of some super
potentials and recover the known supersymmetric vacua when the theory can be
embedded in gauged supergravities. The AdS_{D-2} x R^2 vacua are of particular
interest since they are dual to some quantum field theories at the lowest
Landau level. By studying the embedding of some of these solutions in the
string and M-theory, we find that the M2/M5-system with the equal M2 and M5
charges can intersect with another such M2/M5 on to a dyonic black hole.
Analogous intersection rule applies also to the D1/D5-system. The intersections
are non-supersymmetric but in the manner of harmonic superpositions.
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Classical Velocity in kappa-deformed Poincare Algebra and a Maximum
Acceleration: We study the commutators of the kappa-deformed Poincare Algebra (kappaPA) in
an arbitrary basis. It is known that the two recently studied doubly special
relativity theories correspond to different choices of kappaPA bases. We
present another such example. We consider the classical limit of kappaPA and
calculate particle velocity in an arbitrary basis. It has standard properties
and its expression takes a simple form in terms of the variables in the Snyder
basis. We then study the particle trajectory explicitly for the case of a
constant force. Assuming that the spacetime continuum, velocity, acceleration,
etc. can be defined only at length scales greater than x_{min} ne 0, we show
that the acceleration has a finite maximum.
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RG analysis of magnetic catalysis in Dynamical symmetry breaking: We perform the renormalization group analysis on the dynamical symmetry
breaking under strong external magnetic field, studied recently by Gusynin,
Miransky and Shovkovy. We find that any attractive four-Fermi interaction
becomes strong in the low energy, thus leading to dynamical symmetry breaking.
When the four-Fermi interaction is absent, the $\beta$-function for the
electromagnetic coupling vanishes in the leading order in $1/N$. By solving the
Schwinger-Dyson equation for the fermion propagator, we show that in $1/N$
expansion, for any electromagnetic coupling, dynamical symmetry breaking occurs
due to the presence of Landau energy gap by the external magnetic field.
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Thermodynamic Bethe ansatz for non-equilibrium steady states: exact
energy current and fluctuations in integrable QFT: We evaluate the exact energy current and scaled cumulant generating function
(related to the large-deviation function) in non-equilibrium steady states with
energy flow, in any integrable model of relativistic quantum field theory
(IQFT) with diagonal scattering. Our derivations are based on various recent
results of D. Bernard and B. Doyon. The steady states are built by connecting
homogeneously two infinite halves of the system thermalized at different
temperatures $T_l$, $T_r$, and waiting for a long time. We evaluate the current
$J(T_l,T_r)$ using the exact QFT density matrix describing these
non-equilibrium steady states and using Al.B. Zamolodchikov's method of the
thermodynamic Bethe ansatz (TBA). The scaled cumulant generating function is
obtained from the extended fluctuation relations which hold in integrable
models. We verify our formula in particular by showing that the conformal field
theory (CFT) result is obtained in the high-temperature limit. We analyze
numerically our non-equilibrium steady-state TBA equations for three models:
the sinh-Gordon model, the roaming trajectories model, and the sine-Gordon
model at a particular reflectionless point. Based on the numerics, we
conjecture that an infinite family of non-equilibrium $c$-functions, associated
to the scaled cumulants, can be defined, which we interpret physically. We
study the full scaled distribution function and find that it can be described
by a set of independent Poisson processes. Finally, we show that the
"additivity" property of the current, which is known to hold in CFT and was
proposed to hold more generally, does not hold in general IQFT, that is
$J(T_l,T_r)$ is not of the form $f(T_l)-f(T_r)$.
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Instantons on Calabi-Yau and hyper-Kähler cones: The instanton equations on vector bundles over Calabi-Yau and hyper-K\"ahler
cones can be reduced to matrix equations resembling Nahm's equations. We
complement the discussion of Hermitian Yang-Mills (HYM) equations on Calabi-Yau
cones, based on regular semi-simple elements, by a new set of (singular)
boundary conditions which have a known instanton solution in one direction.
This approach extends the classic results of Kronheimer by probing a relation
between generalised Nahm's equations and nilpotent pairs/tuples. Moreover, we
consider quaternionic instantons on hyper-K\"ahler cones over generic
3-Sasakian manifolds and study the HYM moduli spaces arising in this set-up,
using the fact that their analysis can be traced back to the intersection of
three Hermitian Yang-Mills conditions.
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Nonvanishing Finite Scalar Mass in Flux Compactification: We study possibilities to realize a nonvanishing finite Wilson line (WL)
scalar mass in flux compactification. Generalizing loop integrals in the
quantum correction to WL mass at one-loop, we derive the conditions for the
loop integrals and mode sums in one-loop corrections to WL scalar mass to be
finite. We further guess and classify the four-point and three-point
interaction terms satisfying these conditions. As an illustration, the
nonvanishing finite WL scalar mass is explicitly shown in a six dimensional
scalar QED by diagrammatic computation and effective potential analysis. This
is the first example of finite WL scalar mass in flux compactification.
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From phase space to multivector matrix models: Combining elements of twistor-space, phase space and Clifford algebras, we
propose a framework for the construction and quantization of certain (quadric)
varieties described by Lorentz-covariant multivector coordiantes. The
correspondent multivectors can be parametrized by second order polynomials in
the phase space. Thus the multivectors play a double role, as covariant objects
in $D=2,3,4 \texttt{ Mod } 8$ space-time dimensions, and as mechanical
observables of a non-relativistic system in $2^{[D/2]-1}$ euclidean dimensions.
The latter attribute permits a dual interpretation of concepts of
non-relativistic mechanics as applying to relativistic space-time geometry.
Introducing the Groenewold-Moyal *-product and Wigner distributions in phase
space induces Lorentz-covariant non-commutativity and it provides the spectra
of geometrical observables. We propose also new (multivector) matrix models,
interpreted as descending from the interaction term of a Yang-Mills theory with
minimally coupled massive fermions, in the large-$N$ limit, which serves as a
physical model containing the constructed multivector (fuzzy) geometries. We
also include a section on speculative aspects on a possible cosmological effect
and the origin of space-time entropy.
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Hawking radiation of scalar particles from accelerating and rotating
black holes: Hawking radiation of uncharged and charged scalars from accelerating and
rotating black holes is studied. We calculate the tunneling probabilities of
these particles from the rotation and acceleration horizons of these black
holes. Using the tunneling method we recover the correct Hawking temperature as
well.
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Coherent States in M-Theory: A Brane Scan using the Taub-NUT: The Taub-NUT geometry corresponds to the Kaluza-Klein monopole solution of
M-theory and on dimension reduction along the Taub-NUT circle direction it
becomes the D6 brane of type IIA string theory. We show that the Taub-NUT
geometry can be realised as a coherent state, or more appropriately as a
Glauber-Sudarshan state in M-theory, once we take the underlying resurgence
structure carefully. Using the duality chain it in turn implies that all
D-branes as well as NS5-branes can be realised as Glauber-Sudarshan states in
string theory. Our analysis also leads to an intriguing possibility of
realizing the gravity duals of certain non-conformal minimally-supersymmetric
gauge theories by deforming a class of Glauber-Sudarshan states.
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Remarks on Two-Loop Free Energy in N=4 Supersymmetric Yang-Mills Theory
at Finite Temperature: The strong coupling behavior of finite temperature free energy in N=4
supersymmetric SU(N) Yang-Mills theory has been recently discussed by Gubser,
Klebanov and Tseytlin in the context of AdS-SYM correspondence. In this note,
we focus on the weak coupling behavior. As a result of a two-loop computation
we obtain, in the large N 't Hooft limit, $F(g^2N\to 0)\approx
-\frac{\pi^2}{6}N^2V_3T^4(1-\frac{3}{2\pi^2}g^2N)$. Comparison with the strong
coupling expansion provides further indication that free energy is a smooth
monotonic function of the coupling constant.
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An involuted orbifold MSSM: A compactification of the E_8 x E_8 heterotic string on a Z_2 x Z_2 orbifold
equipped with an additional freely acting involution is presented. This model
reproduces the exact chiral MSSM spectrum with matter parity and a non-trivial
Yukawa structure. The key ingredient is a freely acting Wilson line associated
to the involution, breaking SU(5) to SU(3) x SU(2) x U(1)_Y. This work is based
on a talk given at the "9th Hellenic School and Workshop on Elementary Particle
Physics and Gravity" and reviews the results of a collaboration with M.
Blaszczyk, S. Groot Nibbelink, M. Ratz, F. Ruehle and M. Trapletti.
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Branes and the Kraft-Procesi transition: classical case: Moduli spaces of a large set of $3d$ $\mathcal{N}=4$ effective gauge theories
are known to be closures of nilpotent orbits. This set of theories has recently
acquired a special status, due to Namikawa's theorem. As a consequence of this
theorem, closures of nilpotent orbits are the simplest non-trivial moduli
spaces that can be found in three dimensional theories with eight supercharges.
In the early 80's mathematicians Hanspeter Kraft and Claudio Procesi
characterized an inclusion relation between nilpotent orbit closures of the
same classical Lie algebra. We recently showed a physical realization of their
work in terms of the motion of D3-branes on the Type IIB superstring embedding
of the effective gauge theories. This analysis is restricted to A-type Lie
algebras. The present note expands our previous discussion to the remaining
classical cases: orthogonal and symplectic algebras. In order to do so we
introduce O3-planes in the superstring description. We also find a brane
realization for the mathematical map between two partitions of the same integer
number known as "collapse". Another result is that basic Kraft-Procesi
transitions turn out to be described by the moduli space of orthosymplectic
quivers with varying boundary conditions.
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Baxter-Bazhanov Model, Frenkel-Moore Equation and the Braid Group: In this paper the three-dimensional vertex model is given, which is the
duality of the three-dimensional Baxter-Bazhanov (BB) model. The braid group
corresponding to Frenkel-Moore equation is constructed and the transformations
$R, I$ are found. These maps act on the group and denote the rotations of the
braids through the angles $\pi$ about some special axes. The weight function of
another three-dimensional vertex model related the 3D lattice integrable model
proposed by Boos, Mangazeev, Sergeev and Stroganov is presented also, which can
be interpreted as the deformation of the vertex model corresponding to the BB
model.
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Torsional Regularization of Self-Energy and Bare Mass of Electron: In the presence of spacetime torsion, the momentum components do not commute;
therefore, in quantum field theory, summation over the momentum eigenvalues
will replace integration over the momentum. In the Einstein--Cartan theory of
gravity, in which torsion is coupled to spin, the separation between the
eigenvalues increases with the magnitude of the momentum. Consequently, this
replacement regularizes divergent integrals in Feynman diagrams with loops by
turning them into convergent sums. In this article, we apply torsional
regularization to the self-energy of a charged lepton in quantum
electrodynamics. We show that this procedure eliminates the ultraviolet
divergence. We also show that torsion gives a photon a small nonzero mass,
which regularizes the infrared divergence. In the end, we calculate the finite
bare masses of the electron, muon, and tau lepton: $0.4329\,\mbox{MeV}$,
$90.95\,\mbox{MeV}$, and $1543\,\mbox{MeV}$, respectively. These values
constitute about $85\%$ of the observed, re-normalized masses.
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Schrödinger equations in constrained space with several initial
constraints: A general system constrained with {\it several} initial constraint conditions
is quantized based on the Dirac formalism and the Schr\"{o}dinger equation for
this system is obtained. These constraint conditions are now allowed to depend
not only on the coordinates but also on the velocities. It is shown that the
hermiticity for the observables of the system restricts the geometrical
structure of our world.
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Conformal symmetry and the Balitsky-Kovchegov equation: Solutions to the Balitsky-Kovchegov equation are considered which respect an
SO(3) subgroup of the conformal group. The symmetry dictates a specific
dependence of the saturation scale on the impact parameter. Applications to
deep inelastic scattering are considered.
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The Fully Quantized Axion and Dark Energy: This letter reviews the exact evolution equation for the axion effective
potential with the axion scale factor f and phenomenological consequences of
the flat effective potential solution are discussed. It is shown that the
corresponding vacuum energy can be consistent with Dark Energy, and we compare
this result to other studies relating the axion and Dark Energy.
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Superalgebras in Many Types of M-Brane Backgrounds and Various
Supersymmetric Brane Configurations: We derive superalgebras in many types of supersymmetric M-brane backgrounds.
The backgrounds examined here include the cases of the M-wave and the
M-Kaluza-Klein monopole. On the basis of the obtained algebras, we deduce all
the supersymmetric non-orthogonal intersections of the M-Kaluza-Klein monopole
and the M-5-brane at angles. In addition, we present a 1/4 supersymmetric
worldvolume 3-brane soliton on the M-5-brane in the M-5-brane background as an
extended solution of the 3-brane solitons of the M-5-brane by Howe, Lambert and
West. This soliton can be interpreted as a certain intersection of three
M-5-branes.
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Pythagoras' Theorem on a 2D-Lattice from a "Natural" Dirac Operator and
Connes' Distance Formula: One of the key ingredients of A. Connes' noncommutative geometry is a
generalized Dirac operator which induces a metric(Connes' distance) on the
state space. We generalize such a Dirac operator devised by A. Dimakis et al,
whose Connes' distance recovers the linear distance on a 1D lattice, into 2D
lattice. This Dirac operator being "naturally" defined has the so-called "local
eigenvalue property" and induces Euclidean distance on this 2D lattice. This
kind of Dirac operator can be generalized into any higher dimensional lattices.
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Minimal Supergravity Models of Inflation: We present a superconformal master action for a class of supergravity models
with one arbitrary function defining the Jordan frame. It leads to a
gauge-invariant action for a real vector multiplet, which upon gauge fixing
describes a massive vector multiplet, or to a dual formulation with a linear
multiplet and a massive tensor field. In both cases the models have one real
scalar, the inflaton, naturally suited for single-field inflation. Vectors and
tensors required by supersymmetry to complement a single real scalar do not
acquire vev's during inflation, so there is no need to stabilize the extra
scalars which are always present in the theories with chiral matter multiplets.
The new class of models can describe any inflaton potential which vanishes at
its minimum and grows monotonically away from the minimum. In this class of
supergravity models one can fit any desirable choice of inflationary parameters
n_s and r.
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sQGP as hCFT: We examine the proposal to make quantitative comparisons between the strongly
coupled quark-gluon plasma and holographic descriptions of conformal field
theory. In this note, we calculate corrections to certain transport
coefficients appearing in second-order hydrodynamics from higher curvature
terms to the dual gravity theory. We also clarify how these results might be
consistently applied in comparisons with the sQGP.
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Holographic n-partite Information in Hyperscaling Violating Geometry: The $n$-partite information (nI) is formulated as a measure of multi-partite
entanglement. Field theory computation revealed that the sign of nI is
indefinite for $n\geq 3$, while holographic studies conjectured a sign property
that holographic nI is non-negative/non-positive for even/odd $n$, with
tripartite information (TI, $n=3$) proved. We investigate the aspects of nI
with holographic duality in hyperscaling violating geometry. We confirm the
conjectured sign property for strips of equal length with equal separation
distance, and disprove this conjecture for $n>3$ with general configurations.
Therefore, nI in field theories and holography exhibits compatibility except
for $n=3$. We also discuss other properties of holographic nI with analytic
computation: the monotonicity, linearity, relation to hyperscaling violating
parameters, temperature and UV cutoff effects, and the physical implications.
It is doubtful that nI is an effective measure of entanglement considering the
indefinite sign, non-monotonicity, and quasi-linearity of its holographic dual.
In this respect, we propose constraints on the multi-partite entanglement
measures.
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Quantum Quivers and Hall/Hole Halos: Two pictures of BPS bound states in Calabi-Yau compactifications of type II
string theory exist, one as a set of particles at equilibrium separations from
each other, the other as a fusion of D-branes at a single point of space. We
show how quiver quantum mechanics smoothly interpolates between the two, and
use this, together with recent mathematical results on the cohomology of quiver
varieties, to solve some nontrivial ground state counting problems in
multi-particle quantum mechanics, including one arising in the setup of the
spherical quantum Hall effect, and to count ground state degeneracies of
certain dyons in supersymmetric Yang-Mills theories. A crucial ingredient is a
non-renormalization theorem in N=4 quantum mechanics for the first order part
of the Lagrangian in an expansion in powers of velocity.
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Atiyah-Hitchin in Five Dimensional Einstein-Maxwell Theory: We construct exact solutions to five-dimensional Einstein-Maxwell theory
based on Atiyah-Hitchin space. The solutions cannot be written explicitly in a
closed form, so their properties are investigated numerically. The
five-dimensional metric is regular everywhere except on the location of
original bolt in four-dimensional Atiyah-Hitchin base space. On each time-fixed
slices, the metric, asymptotically approaches an Euclidean Taub-NUT space.
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Massless picture, massive picture, and symmetry in the Gaussian
renormalization group: We consider renormalization groups of transformations composed of a Gaussian
convolution and a field dilatation. As an example, we consider perturbations of
a single component real Euclidean free field $\phi$ with covariance
$(-\bigtriangleup)^{-1+\frac{\epsilon}{2}}$. We show that the renormalization
group admits two equivalent formulations called massless picture and massive
picture respectively. We then show in the massive picture that the
renormalization group has a symmetry. The symmetry consists of global scale
transformations composed with certain Gaussian convolutions. We translate the
symmetry back to the massless picture. The relation between the symmetry and
the notion of an anomalous dimension is briefly discussed.
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Fokker-Type Confinement Models from Effective Lagrangian in Classical
Yang-Mills Theory: Abelian potentials of pointlike moving sources are obtained from the
nonstandard theory of Yang--Mills field. They are used for the construction of
the time-symmetric and time-asymmetric Fokker-type action integrals describing
the dynamics of two-particle system with confinement interaction. The
time-asymmetric model is reformulated in the framework of the Hamiltonian
formalism. The corresponding two-body problem is reduced to quadratures. The
behaviour of Regge trajectories is estimated within the semiclassical
consideration.
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Supersymmetric Q-balls and boson stars in (d+1) dimensions: We construct supersymmetric Q-balls and boson stars in (d+1) dimensions.
These non-topological solitons are solutions of a scalar field model with
global U(1) symmetry and a scalar field potential that appears in
gauge-mediated supersymmetry (SUSY) breaking in the minimal supersymmetric
extension of the Standard Model (MSSM). We are interested in both the
asymptotically flat as well as in the asymptotically Anti-de Sitter (AdS)
solutions. In particular, we show that for our choice of the potential
gravitating, asymptotically flat boson stars exist in (2+1) dimensions. We
observe that the behaviour of the mass and charge of the asymptotically flat
solutions at the approach of the maximal frequency depends strongly on the
number of spatial dimensions. For the asymptotically AdS solutions, the model
on the conformal boundary can be interpreted as describing d-dimensional
condensates of scalar glueballs.
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Robin conditions on the Euclidean ball: Techniques are presented for calculating directly the scalar functional
determinant on the Euclidean d-ball. General formulae are given for Dirichlet
and Robin boundary conditions. The method involves a large mass asymptotic
limit which is carried out in detail for d=2 and d=4 incidentally producing
some specific summations and identities. Extensive use is made of the
Watson-Kober summation formula.
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Holographic zero sound at finite temperature in the Sakai-Sugimoto model: In this paper, we study the fate of the holographic zero sound mode at finite
temperature and non-zero baryon density in the deconfined phase of the
Sakai-Sugimoto model of holographic QCD. We establish the existence of such a
mode for a wide range of temperatures and investigate the dispersion relation,
quasi-normal modes, and spectral functions of the collective excitations in
four different regimes, namely, the collisionless quantum, collisionless
thermal, and two distinct hydrodynamic regimes. For sufficiently high
temperatures, the zero sound completely disappears, and the low energy physics
is dominated by an emergent diffusive mode. We compare our findings to
Landau-Fermi liquid theory and to other holographic models.
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A Kaluza-Klein Model with Spontaneous Symmetry Breaking: Light-Particle
Effective Action and its Compactification Scale Dependence: We investigate decoupling of heavy Kaluza-Klein modes in an Abelian Higgs
model with space-time topologies $\mathbb{R}^{3,1} \times S^{1}$ and
$\mathbb{R}^{3,1} \times S^{1}/\mathbb{Z}_{2}$. After integrating out heavy KK
modes we find the effective action for the zero mode fields. We find that in
the $\mathbb{R}^{3,1} \times S^{1}$ topology the heavy modes do not decouple in
the effective action, due to the zero mode of the 5-th component of the 5-d
gauge field $A_{5}$. Because $A_{5}$ is a scalar under 4-d Lorentz
transformations, there is no gauge symmetry protecting it from getting mass and
$A_{5}^{4}$ interaction terms after loop corrections. In addition, after
symmetry breaking, we find new divergences in the $A_{5}$ mass that did not
appear in the symmetric phase. The new divergences are traced back to the
gauge-goldstone mixing that occurs after symmetry breaking. The relevance of
these new divergences to Symanzik's theorem is discussed. In order to get a
more sensible theory we investigate the $S^{1}/\mathbb{Z}_{2}$
compactification. With this kind of compact topology, the $A_{5}$ zero mode
disappears. With no $A_{5}$, there are no new divergences and the heavy modes
decouple. We also discuss the dependence of the couplings and masses on the
compactification scale. We derive a set of RG-like equations for the running of
the effective couplings with respect to the compactification scale. It is found
that magnitudes of both couplings decrease as the scale $M$ increases. The
effective masses are also shown to decrease with increasing compactification
scale. All of this opens up the possibility of placing constraints on the size
of extra dimensions.
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Heavy-Light Mesons from the AdS/CFT Correspondence: We propose a holographic description of heavy-light mesons, i.e. of mesons
containing a light and a heavy quark. In the semi-classical string limit, we
look at the dynamics of strings tied between two D7 branes. We consider this
setup both in an AdS background and in the non-supersymmetric Constable-Myers
geometry which induces chiral symmetry breaking. We compute the meson masses in
each case. Finally we discuss the relevance of this result for phenomenological
comparison to the physical b-quark sector.
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Four flavours, triality and bimodular forms: We consider $\mathcal{N}=2$ supersymmetric $\text{SU}(2)$ gauge theory with
$N_f=4$ massive hypermultiplets. The duality group of this theory contains
transformations acting on the UV-coupling $\tau_{\text{UV}}$ as well as on the
running coupling $\tau$. We establish that subgroups of the duality group act
separately on $\tau_{\text{UV}}$ and $\tau$, while a larger group acts
simultaneously on $\tau_{\text{UV}}$ and $\tau$. For special choices of the
masses, we find that the duality groups can be identified with congruence
subgroups of $\text{SL}(2,\mathbb Z)$. We demonstrate that in such cases, the
order parameters are instances of bimodular forms with arguments $\tau$ and
$\tau_{\text{UV}}$. Since the UV duality group of the theory contains the
triality group of outer automorphisms of the flavour symmetry $\text{SO}(8)$,
the duality action gives rise to an orbit of mass configurations. Consequently,
the corresponding order parameters combine to vector-valued bimodular forms
with $\text{SL}(2,\mathbb Z)$ acting simultaneously on the two couplings.
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The effect of a topological gauge field on Bose-Einstein condensation: We show that Bose-Einstein condensation of charged scalar fields interacting
with a topological gauge field at finite temperature is inhibited except for
special values of the topological field. We also show that fermions interacting
with this topological gauge field can condense for some values of the gauge
field.
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Effective Action in a General Chiral Model: Next to Leading Order
Derivative Expansion in the Worldline Method: We present a formalism to determine the imaginary part of a general chiral
model in the derivative expansion. Our formalism is based on the worldline path
integral for the covariant current that can be given in an explicit chiral and
gauge covariant form. The effective action is then obtained by integrating the
covariant current, taking account of the anomaly.
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Boundary fermion currents and subleading order chiral anomaly in the
AdS/CFT correspondence: We construct a wave-functional whose argument couples to boundary fermion
currents in the AdS/CFT correspondence. Using this we calculate the
contributions from bulk fermions to the chiral anomaly that give the subleading
order term in the exact $N$-dependence of the chiral anomaly of ${\cal N}=4$
SYM. The result agrees with the calculation of Bilal & Chu.
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The thermodynamic quantities of a black hole with an $f(R)$ global
monopole: The thermodynamic quantities such as the local temperature, heat capacity,
off-shell free energy and the stability of a black hole involving a global
monopole within or outside the $f(R)$ gravity are examined. We compare the two
classes of results to show the influence from the generalization of the general
relativity. It is found that the $f(R)$ theory will modify the thermodynamic
properties of black holes, but the shapes of curves for thermodynamic
quantities with respect to the horizon are similar to the results within the
frame of general relativity. In both cases there will exist a small black hole
which will decay and a large stable black hole in the case that the
temperatures are higher than their own critical temperature.
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Soliton Creation with a Twist: We consider soliton creation when there are "twist" degrees of freedom
present in the model in addition to those that make up the soliton.
Specifically we consider a deformed O(3) sigma model in 1+1 dimensions, which
reduces to the sine-Gordon model in the zero twist sector. We study the
scattering of two or more breather solutions as a function of twist, and find
soliton creation for a range of parameters. We speculate on the application of
these ideas, in particular on the possible role of magnetic helicity, to the
production of magnetic monopoles, and the violation of baryon number in nuclear
scattering experiments.
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OPEs and 3-point correlators of protected operators in N=4 SYM: Two- and three-point correlation functions of arbitrary protected operators
are constructed in N=4 SYM using analytic superspace methods. The OPEs of two
chiral primary multiplets are given. It is shown that the $n$-point functions
of protected operators for $n\leq4$ are invariant under $U(1)_Y$ and it is
argued that this implies that the two- and three-point functions are not
renormalised. It is shown explicitly how unprotected operators can be
accommodated in the analytic superspace formalism in a way which is fully
compatible with analyticity. Some new extremal correlators are exhibited.
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The Role of Möbius Constants and Scattering Functions in CHY Scalar
Amplitudes: The integrations leading to the Cachazo-He-Yuan (CHY) double-color $n$-point
massless scalar amplitude are carried out one integral at a time. M\"obius
invariance dictates the final amplitude to be independent of the three M\"obius
constants $\sigma_r, \sigma_s, \sigma_t$, but their choice affects integrations
and the intermediate results. The effect of the M\"obius constants, the two
colors, and the scattering functions on each integration is investigated. A
systematic way to carry out the $n-3$ integrations is explained, each exposing
one of the $n-3$ propagators of the Feynman diagrams. Two detailed examples are
shown to illustrate the procedure, one a five-point amplitude, and the other a
nine-point amplitude.
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Bulk Viscosity in Holographic Lifshitz Hydrodynamics: We compute the bulk viscosity in holographic models dual to theories with
Lifshitz scaling and/or hyperscaling violation, using a generalization of the
bulk viscosity formula derived in arXiv:1103.1657 from the null focusing
equation. We find that only a class of models with massive vector fields are
truly Lifshitz scale invariant, and have a vanishing bulk viscosity. For other
holographic models with scalars and/or massless vector fields we find a
universal formula in terms of the dynamical exponent and the hyperscaling
violation exponent.
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On the Taxonomy of Flux Vacua: We investigate several predictions about the properties of IIB flux vacua on
Calabi-Yau orientifolds, by constructing and characterizing a very large set of
vacua in a specific example, an orientifold of the Calabi-Yau hypersurface in
$WP^{4}_{1,1,1,1,4}$. We find support for the prediction of Ashok and Douglas
that the density of vacua on moduli space is governed by ${\rm det}(-R -
\omega)$ where $R$ and $\omega$ are curvature and K\"ahler forms on the moduli
space. The conifold point $\psi=1$ on moduli space therefore serves as an
attractor, with a significant fraction of the flux vacua contained in a small
neighborhood surrounding $\psi=1$. We also study the functional dependence of
the number of flux vacua on the D3 charge in the fluxes, finding simple power
law growth.
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A domain wall and chiral edge current in holographic chiral phase
transitions: We investigate spatially inhomogeneous solutions in a top-down holographic
model: the D3/D7 model which provides a holographic description of the chiral
phase transition for a finite external magnetic field, chemical potential, and
temperature. We numerically find a domain wall (or kink) solution in the three
dimensional space, which incorporates between the chiral symmetry broken phase
at the spatial infinity, under the homogeneous sources. Along with the
inhomogeneity of the chiral condensate, the charge density is also spatially
modulated. The modulated charge density and finite magnetic field lead to the
chiral edge current close to the domain wall. We explore the dependences of
those profiles on the chemical potential and temperature near the first and
second order phase transition points. Our results indicate that the
inhomogeneous solutions we found are in good agreement with those obtained by
the Ginzburg--Landau theory in the vicinity of the transition points.
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Dangerous Angular KK/Glueball Relics in String Theory Cosmology: The presence of Kaluza-Klein particles in the universe is a potential
manifestation of string theory cosmology. In general, they can be present in
the high temperature bath of the early universe. In particular examples, string
theory inflation often ends with brane-antibrane annihilation followed by the
energy cascading through massive closed string loops to KK modes which then
decay into lighter standard model particles. However, massive KK modes in the
early universe may become dangerous cosmological relics if the inner manifold
contains warped throat(s) with approximate isometries. In the complimentary
picture, in the AdS/CFT dual gauge theory with extra symmetries, massive
glueballs of various spins become the dangerous cosmological relics. The decay
of these angular KK modes/glueballs, located around the tip of the throat, is
caused by isometry breaking which results from gluing the throat to the compact
CY manifold. We address the problem of these angular KK particles/glueballs,
studying their interactions and decay channels, from the theory side, and the
resulting cosmological constraints on the warped compactification parameters,
from the phenomenology side. The abundance and decay time of the long-lived
non-relativistic angular KK modes depend strongly on the parameters of the
warped geometry, so that observational constraints rule out a significant
fraction of the parameter space. In particular, the coupling of the angular KK
particles can be weaker than gravitational.
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The supersymmetric standard model from the Z_6' orientifold?: We construct N=1 supersymmetric fractional branes on the Z_6' orientifold.
Intersecting stacks of such branes are needed to build a supersymmetric
standard model. If a,b are the stacks that generate the SU(3)_c and SU(2)_L
gauge particles, then, in order to obtain just the chiral spectrum of the
(supersymmetric) standard model (with non-zero Yukawa couplings to the Higgs
multiplets), it is necessary that the number of intersections a \circ b of the
stacks a and b, and the number of intersections a \circ b' of a with the
orientifold image b' of b satisfy (a \circ b, a \circ b')=\pm(2,1) or \pm(1,2).
It is also necessary that there is no matter in symmetric representations of
the gauge group, and not too much matter in antisymmetric representations, on
either stack. We provide a number of examples having these properties.
Different lattices give different solutions and different physics.
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Solitons in an effective theory of CP violation: We study an effective field theory describing CP-violation in a scalar meson
sector. We write the simplest interaction that we can imagine, $${\cal L}\sim
\epsilon_{i_1\cdots
i_5}\epsilon^{\mu_1\cdots\mu_4}\phi_{i_1}\partial_{\mu_1}\phi_{i_2}\partial_{\mu_2}\phi_{i_3}\partial_{\mu_3}\phi_{i_4}\partial_{\mu_4}\phi_{i_5}$$
which involves 5 scalar fields. The theory describes CP-violation only when it
contains scalar fields representing mesons such as the $K^*_0$, sigma, $f_0$ or
$a_0$. If the fields represent pseudo-scalar mesons, such as B, K and $\pi$
mesons then the Lagrangian describes anomalous processes such as $KK\to
\pi\pi\pi$. We speculate that the field theory contains long lived excitations
corresponding to $Q$-ball type domain walls expanding through space-time. In an
1+1 dimensional, analogous, field theory we find an exact, analytic solution
corresponding to such solitons. The solitons have a U(1) charge $Q$, which can
be arbitrarily high, but oddly, the energy behaves as $Q^{2/3}$ for large
charge, thus the configurations are stable under disintegration into elementary
charged particles of mass $m$ with $Q=1$. We also find analytic complex
instanton solutions which have finite, positive Euclidean action.
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On the Hagedorn Behaviour of PP-wave Strings and N=4 SYM Theory at
Finite R-Charge Density: We discuss the high temperature behaviour of IIB strings in the maximally
symmetric plane wave background, and show that there is a Hagedorn temperature.
We discuss the map between strings in the pp-wave background and the dual
superconformal field theory in the thermal domain. The Hagedorn bound describes
a curve in the R-charge chemical potential versus temperature phase diagram of
the dual Yang-Mills theory and the theory manifestly exists on both sides.
Using a recent observation of Brower, Lowe, and Tan, we update our earlier
calculation to reflect that the pp-wave string exists on both sides of the
Hagedorn bound as well.
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Supersymmetric Duality in Deformed Superloop Space: In this paper, we will analyse the superloop space formalism for a four
dimensional supersymmetric Yang-Mills theory in deformed superspace. We will
deform the $\mathcal{N} =1$ superspace by imposing non-anticommutativity. This
non-anticommutative deformation of the superspace will break half the
supersymmetry of the original theory. So, this theory will have $\mathcal{N}
=1/2$ supersymmetry. We will analyse the superloop space duality for this
deformed supersymmetric Yang-Mills theory using the $\mathcal{N} =1/2$
superspace formalism. We will demonstrate that the sources in the original
theory will become monopoles in the dual theory, and the monopoles in the
original theory will become sources in the dual theory.
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Microstates and statistical entropy of observed black holes: We propose an ideal building of microscopic configurations for observed black
holes from the compactification of Einstein gravity plus a positive
cosmological constant in five dimensions on a circle and then compute their
statistical entropy. To compute the statistical entropy in this work is applied
to general black holes independent of the symmetries of the black hole solution
such as the spherical symmetry and going beyond the class of special black
holes that are supersymmetric and (near-)extremal as well as have exotic
charges. The statistical entropy of black holes includes the Bekenstein-Hawking
area term at leading order and sub-leading exponential corrections. We find a
new exponential correction which is more meaningful than that found previously
in the literature.
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E$_9$ exceptional field theory I. The potential: We construct the scalar potential for the exceptional field theory based on
the affine symmetry group E$_9$. The fields appearing in this potential live
formally on an infinite-dimensional extended spacetime and transform under
E$_9$ generalised diffeomorphisms. In addition to the scalar fields expected
from D=2 maximal supergravity, the invariance of the potential requires the
introduction of new constrained scalar fields. Other essential ingredients in
the construction include the Virasoro algebra and indecomposable
representations of E$_9$. Upon solving the section constraint, the potential
reproduces the dynamics of either eleven-dimensional or type IIB supergravity
in the presence of two isometries.
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Loops from Cuts: We derive novel recursion relations for all loop amplitude integrands of
planar, maximally supersymmetric Yang-Mills theory in terms of unitarity-like
`cuts' obtained via sequences of BCFW deformations in momentum-twistor space.
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Typicality and thermality in 2d CFT: We identify typical high energy eigenstates in two-dimensional conformal
field theories at finite $c$ and establish that correlation functions of the
stress tensor in such states are accurately thermal as defined by the standard
canonical ensemble. Typical states of dimension $h$ are shown to be typical
level $h/c$ descendants. In the AdS$_3$/CFT$_2$ correspondence, it is such
states that should be compared to black holes in the bulk. We also discuss the
discrepancy between thermal correlators and those computed in high energy
primary states: the latter are reproduced instead by a generalized Gibbs
ensemble with extreme values chosen for the chemical potentials conjugate to
the KdV charges.
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Quark-antiquark pair production in space-time dependent fields: Fermion-antifermion pair-production in the presence of classical fields is
described based on the retarded and advanced fermion propagators. They are
obtained by solving the equation of motion for the Dirac Green's functions with
the respective boundary conditions to all orders in the field. Subsequently,
various approximation schemes fit for different field configurations are
explained. This includes longitudinally boost-invariant forms. Those occur
frequently in the description of ultrarelativistic heavy-ion collisions in the
semiclassical limit. As a next step, the gauge invariance of the expression for
the expectation value of the number of produced fermion-antifermion pairs as a
functional of said propagators is investigated in detail. Finally, the
calculations are carried out for a longitudinally boost-invariant model-field,
taking care of the last issue, especially.
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Liouville Field Theory on an Unoriented Surface: Liouville field theory on an unoriented surface is investigated, in
particular, the one point function on a RP^2 is calculated. The constraint of
the one point function is obtained by using the crossing symmetry of the two
point function. There are many solutions of the constraint and we can choose
one of them by considering the modular bootstrap.
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Testing the membrane paradigm with holography: One version of the membrane paradigm states that as far as outside observers
are concerned, black holes can be replaced by a dissipative membrane with
simple physical properties located at the stretched horizon. We demonstrate
that such a membrane paradigm is incomplete in several aspects. We argue that
it generically fails to capture the massive quasinormal modes, unless we
replace the stretched horizon by the exact event horizon, and illustrate this
with a scalar field in a BTZ black hole background. We also consider as a
concrete example linearized metric perturbations of a five-dimensional
AdS-Schwarzschild black brane and show that a spurious excitation appears in
the long-wavelength response that is only removed from the spectrum when the
membrane paradigm is replaced by ingoing boundary conditions at the event
horizon. We interpret this excitation in terms of an additional Goldstone boson
that appears due to symmetry breaking by the classical solution ending on the
stretched horizon rather than the event horizon.
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Massless Lifshitz Field Theory for Arbitrary $z$: By using the notion of fractional derivatives, we introduce a class of
massless Lifshitz scalar field theory in (1+1)-dimension with an arbitrary
anisotropy index $z$. The Lifshitz scale invariant ground state of the theory
is constructed explicitly and takes the form of Rokhsar-Kivelson (RK). We show
that there is a continuous family of ground states with degeneracy
parameterized by the choice of solution to the equation of motion of an
auxiliary classical system. The quantum mechanical path integral establishes a
2d/1d correspondence with the equal time correlation functions of the Lifshitz
scalar field theory. We study the entanglement properties of the Lifshitz
theory for arbitrary $z$ using the path integral representation. We find that
the Lifshitz vacuum at $z=1$ is insensitive to any subdivision of the system.
The entanglement measures are expressed in terms of certain cross ratio
functions we specify, and satisfy the $c$-function monotonicity theorems. We
also consider the holographic description of the Lifshitz theory. In order to
match with the field theory result for the entanglement entropy, we propose a
$z$-dependent radius scale for the Lifshitz background. This relation is
consistent with the $z$-dependent scaling symmetry respected by the Lifshitz
vacuum. Furthermore, the time-like entanglement entropy is determined using
holography. Our result suggests that there should exist a fundamental
definition of time-like entanglement other than employing analytic continuation
as performed in relativistic field theory.
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Cosmic F- and D-strings: Macroscopic fundamental and Dirichlet strings have several potential
instabilities: breakage, tachyon decays, and confinement by axion domain walls.
We investigate the conditions under which metastable strings can exist, and we
find that such strings are present in many models. There are various
possibilities, the most notable being a network of (p,q) strings. Cosmic
strings give a potentially large window into string physics.
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Trace anomaly in the field-antifield formalism: The field-antifield quantization method is used to calculate the trace
anomaly for a massless scalar field in a curved background, by means of the
zeta function regularization procedure.
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On Squeezed Limits in Single-Field Inflation - Part I: The n-point correlation functions in single-field inflation obey a set of
consistency conditions in the exact squeezed limit which are not present in
multi-field models, and thus are powerful tools to distinguish between the two.
However, these consistency conditions may be violated for a finite range of
scales in single-field models, for example by departures from the Bunch-Davies
state. These it excited states may be the consequence of interactions during
inflation, or may be a remnant of the era that preceded inflation. In this
paper we analyze the bispectrum, and show that in the regime of theoretical
control the resulting signal in the squeezed limit remains undetectably small
in all known models which continuously excite the state. We also show that the
signal remains undetectably small if the initial state is related to the
Bunch-Davies state by a Bogoliubov transformation and the energy density in the
state is small enough so that the usual slow-roll conditions are obeyed.
Bogoliubov states that lead to violations of the slow-roll conditions, as well
as more general excited states, require more careful treatment and will be
discussed in a separate publication.
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BPS Spectrum of Supersymmetric CP(N-1) Theory with Z_N Twisted Masses: We revisit the BPS spectrum of the supersymmetric CP(N-1) two-dimensional
model with Z_N-symmetric twisted masses m_l (l=0,1, ..., N-1). A related issue
we address is that of the curves of marginal stability (CMS) in this theory.
Previous analyses were incomplete. We close the gap by exploiting a number of
consistency conditions. In particular, we amend the Dorey formula for the BPS
spectrum. Our analysis is based on the exact Veneziano--Yankielowicz-type
superpotential and on the strong-coupling spectrum of the theory found from the
mirror representation at small masses, |m_l| << \Lambda . We show that at weak
coupling the spectrum, with necessity, must include N-1 BPS towers of states,
instead of just one, as was thought before. Only one of the towers is seen in
the quasiclassical limit. We find the corresponding CMS for these towers, and
argue that in the large-N limit they become circles, filling out a band on the
plane of a single mass parameter of the model at hand. Inside the CMS, N-1
towers collapse into N stable states.
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Gopakumar-Vafa Invariants and the Emergent String Conjecture: The Emergent String Conjecture of Lee, Lerche, and Weigand holds that every
infinite-distance limit in the moduli space of a quantum gravity represents
either a decompactification limit or an emergent string limit in some duality
frame. Within the context of 5d supergravities coming from M-theory
compactifications on Calabi-Yau threefolds, we find evidence for this
conjecture by studying (a) the gauge couplings and (b) the BPS spectrum, which
is encoded in the Gopakumar-Vafa invariants of the threefold. In the process,
we derive a testable geometric consequence of the Emergent String Conjecture,
and we verify that it is satisfied in all complete intersection Calabi-Yau
threefolds in products of projective spaces (CICYs).
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Racetrack inflation and assisted moduli stabilisation: We present a model of inflation based on a racetrack model without flux
stabilization. The initial conditions are set automatically through topological
inflation. This ensures that the dilaton is not swept to weak coupling through
either thermal effects or fast roll. Including the effect of non-dilaton fields
we find that moduli provide natural candidates for the inflaton. The resulting
potential generates slow-roll inflation without the need to fine tune
parameters. The energy scale of inflation must be near the GUT scale and the
scalar density perturbation generated has a spectrum consistent with WMAP data.
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Emergent Gravity from Vanishing Energy-Momentum Tensor: A constraint of vanishing energy-momentum tensor is motivated by a variety of
perspectives on quantum gravity. We demonstrate in a concrete example how this
constraint leads to a metric-independent theory in which quantum gravity
emerges as a nonperturbative artifact of regularization-scale physics. We
analyze a scalar theory similar to the Dirac-Born-Infeld (DBI) theory with
vanishing gauge fields, with the DBI Lagrangian modulated by a scalar
potential. In the limit of a large number of scalars, we explicitly demonstrate
the existence of a composite massless spin-2 graviton in the spectrum that
couples to matter as in Einstein gravity. We comment on the cosmological
constant problem and the generalization to theories with fermions and gauge
fields.
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Algebraic Solution of the Supersymmetric Hydrogen Atom in d Dimensions: In this paper the N=2 supersymmetric extension of the Schroedinger
Hamiltonian with 1/r-potential in arbitrary space-dimensions is constructed.
The supersymmetric hydrogen atom admits a conserved Laplace-Runge-Lenz vector
which extends the rotational symmetry SO(d) to a hidden SO(d+1) symmetry. This
symmetry of the system is used to determine the discrete eigenvalues with their
degeneracies and the corresponding bound state wave functions.
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Holographic Josephson Junction in 3+1 dimensions: In arXiv:1101.3326[hep-th], a (2+1)-dimensional holographic Josephson
junction was constructed, and it was shown that the DC Josephson current is
proportional to the sine of the phase difference across the junction. In this
paper, we extend this study to a holographic description for the
(3+1)-dimensional holographic DC Josephson junction. By solving numerically the
coupled differential equations, we also obtain the familiar characteristics of
Josephson junctions.
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Quantum Structure of Field Theory and Standard Model Based on
Infinity-free Loop Regularization/Renormalization: To understand better the quantum structure of field theory and standard model
in particle physics, it is necessary to investigate carefully the divergence
structure in quantum field theories (QFTs) and work out a consistent framework
to avoid infinities. The divergence has got us into trouble since developing
quantum electrodynamics in 1930s, its treatment via the renormalization scheme
is satisfied not by all physicists, like Dirac and Feynman who have made
serious criticisms. The renormalization group analysis reveals that QFTs can in
general be defined fundamentally with the meaningful energy scale that has some
physical significance, which motivates us to develop a new symmetry-preserving
and infinity-free regularization scheme called loop regularization (LORE). A
simple regularization prescription in LORE is realized based on a manifest
postulation that a loop divergence with a power counting dimension larger than
or equal to the space-time dimension must vanish. The LORE method is achieved
without modifying original theory and leads the divergent Feynman loop
integrals well-defined to maintain the divergence structure and meanwhile
preserve basic symmetries of original theory. The crucial point in LORE is the
presence of two intrinsic energy scales which play the roles of ultraviolet
cut-off $M_c$ and infrared cut-off $\mu_s$ to avoid infinities. The key concept
in LORE is the introduction of irreducible loop integrals (ILIs) on which the
regularization prescription acts, which leads to a set of gauge invariance
consistency conditions between the regularized tensor-type and scalar-type
ILIs. The evaluation of ILIs with ultraviolet-divergence-preserving (UVDP)
parametrization naturally leads to Bjorken-Drell's analogy between Feynman
diagrams and electric circuits. The LORE method has been shown to be applicable
to both underlying and effective QFTs.
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Gauge Invariant Variational Approach with Fermions: the Schwinger Model: We extend the gauge invariant variational approach of Phys. Rev. D52 (1995)
3719, hep-th/9408081, to theories with fermions. As the simplest example we
consider the massless Schwinger model in 1+1 dimensions. We show that in this
solvable model the simple variational calculation gives exact results.
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Investigation of anomalous axial QED: Although axial QED suffers from a gauge anomaly, gauge invariance may be
maintained by the addition of a nonlocal counterterm. Such nonlocal
conterterms, however, are expected to ruin unitarity of the theory. We
explicitly investigate some relevant Feynman diagrams and show that, indeed,
unitarity is violated, contrary to recent claims.
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On the Chiral WZNW Phase Space, Exchange r-Matrices and Poisson-Lie
Groupoids: This is a review of recent work on the chiral extensions of the WZNW phase
space describing both the extensions based on fields with generic monodromy as
well as those using Bloch waves with diagonal monodromy. The symplectic form on
the extended phase space is inverted in both cases and the chiral WZNW fields
are found to satisfy quadratic Poisson bracket relations characterized by
monodromy dependent exchange r-matrices. Explicit expressions for the exchange
r-matrices in terms of the arbitrary monodromy dependent 2-form appearing in
the chiral WZNW symplectic form are given. The exchange r-matrices in the
general case are shown to satisfy a new dynamical generalization of the
classical modified Yang-Baxter (YB) equation and Poisson-Lie (PL) groupoids are
constructed that encode this equation analogously as PL groups encode the
classical YB equation. For an arbitrary simple Lie group $G$, exchange
r-matrices are exhibited that are in one-to-one correspondence with the
possible PL structures on $G$ and admit them as PL symmetries.
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Finiteness of the triple gauge-ghost vertices in ${\cal N}=1$
supersymmetric gauge theories: the two-loop verification: By an explicit calculation we demonstrate that the triple gauge-ghost
vertices in a general renormalizable ${\cal N}=1$ supersymmetric gauge theory
are UV finite in the two-loop approximation. For this purpose we calculate the
two-loop divergent contribution to the $\bar c^+ V c$-vertex proportional to
$(C_2)^2$ and use the finiteness of the two-loop contribution proportional to
$C_2 T(R)$ which has been checked earlier. The theory under consideration is
regularized by higher covariant derivatives and quantized in a manifestly
${\cal N}=1$ supersymmetric way with the help of ${\cal N}=1$ superspace. The
two-loop finiteness of the vertices with one external line of the quantum gauge
superfield and two external lines of the Faddeev--Popov ghosts has been
verified for a general $\xi$-gauge. This result agrees with the
nonrenormalization theorem proved earlier in all orders, which is an important
step for the all-loop derivation of the exact NSVZ $\beta$-function.
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Geometric phase and chiral anomaly; their basic differences: All the geometric phases are shown to be topologically trivial by using the
second quantized formulation. The exact hidden local symmetry in the
Schr\"{o}dinger equation, which was hitherto unrecognized, controls the
holonomy associated with both of the adiabatic and non-adiabatic geometric
phases. The second quantized formulation is located in between the first
quantized formulation and the field theory, and thus it is convenient to
compare the geometric phase with the chiral anomaly in field theory. It is
shown that these two notions are completely different.
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N=4 super Yang-Mills matrix integrals for almost all simple gauge groups: In this paper the partition function of N=4 D=0 super Yang-Mills matrix
theory with arbitrary simple gauge group is discussed. We explicitly computed
its value for all classical groups of rank up to 11 and for the exceptional
groups G_2, F_4 and E_6. In the case of classical groups of arbitrary rank we
conjecture general formulas for the B_r, C_r and D_r series in addition to the
known result for the A_r series. Also, the relevant boundary term contributing
to the Witten index of the corresponding supersymmetric quantum mechanics has
been explicitly computed as a simple function of rank for the orthogonal and
symplectic groups SO(2N+1), Sp(2N), SO(2N).
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Integrable systems connected with black holes: This work is devoted to the study of some important questions in general
relativity. They include topics related to astrophysical shock waves, impulsive
signals, gravitational memory effect, black hole geometries and integrable
systems connected with them.
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Predictive description of Planck-scale-induced spacetime fuzziness: Several approaches to the quantum-gravity problem predict that spacetime
should be "fuzzy", but have been so far unable to provide a crisp physical
characterization of this notion. An intuitive picture of spacetime fuzziness
has been proposed on the basis of semi-heuristic arguments, and in particular
involves an irreducible Planck-scale contribution to the uncertainty of the
energy of a particle. These arguments also inspired a rather active
phenomenological programme looking for blurring of images of distant
astrophysical sources that would result from such energy uncertainties. We here
report the first ever physical characterization of spacetime fuzziness derived
constructively within a quantum picture of spacetime, the one provided by
spacetime noncommutativity. Our results confirm earlier heuristic arguments
suggesting that spacetime fuzziness, while irrelevantly small on terrestrial
scales, could be observably large for propagation of particles over
cosmological distances. However, we find no Planck-scale-induced lower bound on
the uncertainty of the energy of particles, and we observe that this changes
how we should picture a quantum spacetime and also imposes a reanalysis of the
associated phenomenology.
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Topology and phase transition for EPYM AdS black hole in thermal
potential: As we all know the local topological properties of thermodynamical systems
can be expressed by the winding numbers as the defects. The topological number
that is the sum of all winding numbers can be used to classify the global
topological nature of thermodynamical systems. In this paper, we construct a
kind of thermal potential and then put the Einstein-power-Yang-Mills AdS black
hole in it. Through the analysis of the geometric characteristics of the
thermal potential based on the complex analysis we find the topological number
is an invariant that is same as shown in the way of the Duan's $\phi$-mapping
topological current [Sci. Sin. 9, 1072 (1979)]. Furthermore, we adopt the
Kramer's escape rate method to investigate the intensity of the first-order
phase transition.
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Diluting Cosmological Constant via Large Distance Modification of
Gravity: We review a solution of the cosmological constant problem in a brane-world
model with infinite-volume extra dimensions. The solution is based on a
nonlinear generally covariant theory of a metastable graviton that leads to a
large-distance modification of gravity.
From the extra-dimensional standpoint the problem is solved due to the fact
that the four-dimensional vacuum energy curves mostly the extra space. The
four-dimensional curvature is small, being inversely proportional to a positive
power of the vacuum energy. The effects of infinite-volume extra dimensions are
seen by a brane-world observer as nonlocal operators.
From the four-dimensional perspective the problem is solved because the
zero-mode graviton is extremely weakly coupled to localized four-dimensional
sources. The observable gravity is mediated not by zero mode but, instead, by a
metastable graviton with a lifetime of the order of the present-day Hubble
scale. Therefore, laws of gravity are modified in the infrared above the Hubble
scale. Large wave-length sources, such as the vacuum energy, feel only the
zero-mode interaction and, as a result, curve space very mildly. Shorter
wave-length sources interact predominantly via exchange of the metastable
graviton. Because of this, all standard properties of early cosmology,
including inflation, are intact.
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Arrows of Time in the Bouncing Universes of the No-boundary Quantum
State: We derive the arrows of time of our universe that follow from the no-boundary
theory of its quantum state (NBWF) in a minisuperspace model. Arrows of time
are viewed four-dimensionally as properties of the four-dimensional Lorentzian
histories of the universe. Probabilities for these histories are predicted by
the NBWF. For histories with a regular `bounce' at a minimum radius we find
that fluctuations are small at the bounce and grow in the direction of
expansion on either side. For recollapsing classical histories with big bang
and big crunch singularities we find that the fluctuations are small near one
singularity and grow through the expansion and recontraction to the other
singularity. The arrow of time defined by the growth in fluctuations thus
points in one direction over the whole of a recollapsing spacetime but is
bidirectional in a bouncing spacetime. We argue that the electromagnetic,
thermodynamic, and psychological arrows of time are aligned with the
fluctuation arrow. The implications of a bidirectional arrow of time for
causality are discussed.
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Lessons from conformally reduced quantum gravity: In this work we study a significantly enlarged truncation of conformally
reduced quantum gravity in the context of Asymptotic Safety, including all
operators that can be resolved in such a truncation including up to the sixth
order in derivatives. A fixed point analysis suggests that there is no
asymptotically safe fixed point in this system once one goes beyond an
Einstein-Hilbert approximation. We will put these findings into context and
discuss some lessons that can be learned from these results for general
non-perturbative renormalisation group flows.
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Higher Spin Double Field Theory : A Proposal: We construct a double field theory coupled to the fields present in
Vasiliev's equations. Employing the "semi-covariant" differential geometry, we
spell a functional in which each term is completely covariant with respect to
$\mathbf{O}(4,4)$ T-duality, doubled diffeomorphisms, $\mathbf{Spin}(1,3)$
local Lorentz symmetry and, separately, $\mathbf{HS}(4)$ higher spin gauge
symmetry. We identify a minimal set of BPS-like conditions whose solutions
automatically satisfy the full Euler-Lagrange equations. As such a solution, we
derive a linear dilaton vacuum. With extra algebraic constraints further
supplemented, the BPS-like conditions reduce to the bosonic Vasiliev equations.
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Russian Doll Renormalization Group, Kosterlitz-Thouless Flows, and the
Cyclic sine-Gordon model: We investigate the previously proposed cyclic regime of the
Kosterlitz-Thouless renormalization group (RG) flows. The period of one cycle
is computed in terms of the RG invariant. Using bosonization, we show that the
theory has $U_q (\hat{sl(2)})$ quantum affine symmetry, with $q$ {\it real}.
Based on this symmetry, we study two possible S-matrices for the theory,
differing only by overall scalar factors. We argue that one S-matrix
corresponds to a continuum limit of the XXZ spin chain in the
anti-ferromagnetic domain $\Delta < -1$. The latter S-matrix has a periodicity
in energy consistent with the cyclicity of the RG. We conjecture that this
S-matrix describes the cyclic regime of the Kosterlitz-Thouless flows.
The other S-matrix we investigate is an analytic continuation of the usual
sine-Gordon one. It has an infinite number of resonances with masses that have
a Russian doll scaling behavior that is also consistent with the period of the
RG cycles computed from the beta-function. Closure of the bootstrap for this
S-matrix leads to an infinite number of particles of higher spin with a mass
formula suggestive of a string theory.
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The Asymptotically Safe Standard Model: From quantum gravity to
dynamical chiral symmetry breaking: We present a comprehensive non-perturbative study of the phase structure of
the asymptotically safe Standard Model. The physics scales included range from
the asymptotically safe trans-Planckian regime in the ultraviolet, the
intermediate high-energy regime with electroweak symmetry breaking to strongly
correlated QCD in the infrared. All flows are computed with a self-consistent
functional renormalisation group approach, using a vertex expansion in the
fluctuation fields. In particular, this approach takes care of all physical
threshold effects and the respective decoupling of ultraviolet degrees of
freedom. Standard Model and gravity couplings and masses are fixed by their
experimental low energy values. Importantly, we accommodate for the difference
between the top pole mass and its Euclidean analogue. Both, the correct mass
determination and the threshold effects have a significant impact on the
qualitative properties, and in particular on the stability properties of the
specific ultraviolet-infrared trajectory with experimental Standard Model
physics in the infrared. We show that in the present rather advanced
approximation the matter part of the asymptotically safe Standard Model has the
same number of relevant parameters as the Standard Model, and is asymptotically
free. This result is based on the novel UV fixed point found in the present
work: the fixed point Higgs potential is flat but has two relevant directions.
These results and their analysis are accompanied by a thorough discussion of
the systematic error of the present truncation, also important for systematic
improvements.
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The SU(n)_1 WZW Models: Spinon Decomposition and Yangian Structure: We present a `spinon formulation' of the $SU(n)_1$ Wess-Zumino-Witten models.
Central to this approach are a set of massless quasi-particles, called
`spinons', which transform in the representation ${\bf \bar{n}}$ of $su(n)$ and
carry fractional statistics of angle $\theta = \pi/n$. Multi-spinon states are
grouped into irreducible representations of the yangian $Y(sl_n)$. We give
explicit results for the $su(n)$ content of these yangian representations and
present $N$-spinon cuts of the WZW character formulas. As a by-product, we
obtain closed expressions for characters of the $su(n)$ Haldane-Shastry spin
chains.
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Forward-Backward Squeezing Propagator: I show that a usual propagator cannot be defined for the pseudo-diffusion
equation of the Q-functions. Instead, a forward-backward propagator is defined,
which motivated a generalization of Cahill-Glauber interpolating operator. Our
generalized operator ${\bf Q}(p,q;\sigma_p^{-1},\sigma_q)$ depends on two
squeezing parameters $\sigma_p$ and $\sigma_q$, and is shown to obey a
generalized pseudo-diffusion equation or a diffusion equation, depending on the
curve $(\sigma_p(\mu),\sigma_q(\mu))$ along which one moves in the
$(\sigma_p,\sigma_q)$ plane. An algorithm is also given for squeezing Q
functions directly, using one-dimensional diffusion propagators.
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Non-Minimally Coupled Massive Scalar Field in a 2D Black Hole: Exactly
Solvable Model: We study a nonminimal massive scalar field in a 2-dimensional black hole
spacetime. We consider the black hole which is the solution of the 2d dilaton
gravity derived from string-theoretical models. We found an explicit solution
in a closed form for all modes and the Green function of the scalar field with
an arbitrary mass and a nonminimal coupling to the curvature. Greybody factors,
the Hawking radiation, and $ < \phi^2 >^{ren} $ are calculated explicitly for
this exactly solvable model.
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Euclidean scalar Green functions near the black hole and black brane
horizons: We discuss approximations of the Riemannian geometry near the horizon. If a
D+1 dimensional manifold N has a bifurcate Killing horizon then we approximate
N by a product of the two-dimensional Rindler space and a D-1 dimensional
Riemannian manifold M. We obtain approximate formulas for scalar Green
functions. We study the behaviour of the Green functions near the horizon and
their dimensional reduction. We show that if M is compact then the Green
function near the horizon can be approximated by the Green function of a
two-dimensional quantum field theory. The correction term is exponentially
small away from the horizon. We extend the results to black brane solutions of
supergravity in 10 and 11 dimensions. The near horizon geometry can be
approximated by N=AdS_p x S_q. We discuss Euclidean Green functions on N and
their behaviour near the horizon.
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Hybrid compactifications and brane gravity in six dimensions: We consider a six-dimensional axisymmetric Einstein-Maxwell model of warped
braneworlds. The bulk is bounded by two branes, one of which is a conical
3-brane and the other is a 4-brane wrapped around the axis of symmetry. The
latter brane is assumed to be our universe. If the tension of the 3-brane is
fine-tuned, it folds the internal two-dimensional space in a narrow cone,
making sufficiently small the Kaluza-Klein circle of the 4-brane. An arbitrary
energy-momentum tensor can be accommodated on this ring-like 4-brane. We study
linear perturbations sourced by matter on the brane, and show that weak gravity
is apparently described by a four-dimensional scalar-tensor theory. The extra
scalar degree of freedom can be interpreted as the fluctuation of the internal
space volume (or that of the circumference of the ring), the effect of which
turns out to be suppressed at long distances. Consequently, four-dimensional
Einstein gravity is reproduced on the brane. We point out that as in the
Randall-Sundrum model, the brane bending mode is crucial for recovering the
four-dimensional tensor structure in this setup.
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Strings on a Cone and Black Hole Entropy: String propagation on a cone with deficit angle $2\pi (1- \frac{1}{N} ) $ is
described by constructing a non-compact orbifold of a plane by a $Z_{N}$
subgroup of rotations. It is modular invariant and has tachyons in the twisted
sectors that are localized to the tip of the cone. A possible connection with
the quantum corrections to the black hole entropy is outlined. The entropy
computed by analytically continuing in N would receive contribution only from
the twisted sectors and be naturally proportional to the area of the event
horizon. Evidence is presented for a new duality for these orbifolds similar to
the ${\scriptstyle R} \rightarrow {1\over R} $ duality.
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Isolated States and the Classical Phase Spase of 2-d String Theory: We investigate the classical phase space of 2-d string theory. We derive the
linearised covariant equations for the spacetime fields by considering the most
general deformation of the energy-momentum tensor which describes $c=1$ matter
system coupled to 2-d gravity and by demanding that it respect conformal
invariance. We derive the gauge invariances of the theory, and so investigate
the classical phase space, defined as the space of all solutions to the
equations of motion modulo gauge transformations. We thus clarify the origins
of two classes of isolated states.
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Hyperfine Splitting and the Zeeman Effect in Holographic Heavy-Light
Mesons: We inspect the mass spectrum of heavy-light mesons in deformed N=2 super
Yang-Mills theory using the AdS/CFT correspondence. We demonstrate how some of
the degeneracies of the supersymmetric meson spectrum can be removed upon
breaking the supersymmetry, thus leading to the emergence of hyperfine
structure. The explicit SUSY breaking scenarios we consider involve on one hand
tilting one of the two fundamental D7 branes inside the internal R^6 space, and
on the other hand applying an external magnetic field on the (untilted) branes.
The latter scenario leads to the well-known Zeeman effect, which we inspect for
both weak and strong magnetic fields.
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Non-linear charged planar black holes in four-dimensional
Scalar-Gauss-Bonnet theories: In this work, we consider the recently proposed well-defined theory that
permits a healthy $D\to 4$ limit of the Einstein-Gauss-Bonnet combination,
which requires the addition of a scalar degree of freedom. We continue the
construction of exact, hairy black hole solutions in this theory in the
presence of matter sources, by considering a nonlinear electrodynamics source,
constructed through the Pleba\'nski tensor and a precise structural function
$\mathcal{H}(P)$. Computing the thermodynamic quantities with the Wald
formalism, we identify a region in parameter space where the hairy black holes
posses well-defined, non-vanishing, finite thermodynamic quantities, in spite
of the relaxed asymptotic approach to planar AdS. We test its local stability
under thermal and electrical fluctuations and we also show that a Smarr
relation is satisfied for these black hole configurations.
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Infrared divergences, mass shell singularities and gauge dependence of
the dynamical fermion mass: We study the behavior of the dynamical fermion mass when infrared divergences
and mass shell singularities are present in a gauge theory. In particular, in
the massive Schwinger model in covariant gauges we find that the pole of the
fermion propagator is divergent and gauge dependent at one loop, but the
leading singularities cancel in the quenched rainbow approximation. On the
other hand, in physical gauges, we find that the dynamical fermion mass is
finite and gauge independent at least up to one loop.
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Quantumgroups in the Higgs Phase: In the Higgs phase we may be left with a residual finite symmetry group H of
the condensate. The topological interactions between the magnetic- and electric
excitations in these so-called discrete H gauge theories are completely
described by the Hopf algebra or quantumgroup D(H). In 2+1 dimensional space
time we may add a Chern-Simons term to such a model. This deforms the
underlying Hopf algebra D(H) into a quasi-Hopf algebra by means of a 3-cocycle
H. Consequently, the finite number of physically inequivalent discrete H gauge
theories obtained in this way are labelled by the elements of the cohomology
group H^3(H,U(1)). We briefly review the above results in these notes. Special
attention is given to the Coulomb screening mechanism operational in the Higgs
phase. This mechanism screens the Coulomb interactions, but not the
Aharonov-Bohm interactions. (Invited talk given by Mark de Wild Propitius at
`The III International Conference on Mathematical Physics, String Theory and
Quantum Gravity', Alushta, Ukraine, June 13-24, 1993. To be published in Theor.
Math. Phys.)
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Induced gravity and gauge interactions revisited: It has been shown that the primary, old-fashioned idea of Sakharov's induced
gravity and gauge interactions, in the "one-loop dominance" version, works
astonishingly well yielding phenomenologically reasonable results. As a
byproduct, the issue of the role of the UV cutoff in the context of the induced
gravity has been reexamined (an idea of self-cutoff induced gravity). As an
additional check, the black hole entropy has been used in the place of the
action. Finally, it has been explicitly shown that the induced coupling
constants of gauge interactions of the standard model assume qualitatively
realistic values.
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Multi-centered AdS$_3$ solutions from Virasoro conformal blocks: We revisit the construction of multi-centered solutions in three-dimensional
anti-de Sitter gravity in the light of the recently discovered connection
between particle worldlines and classical Virasoro conformal blocks. We focus
on multi-centered solutions which represent the backreaction of point masses
moving on helical geodesics in global AdS$_3$, and argue that their
construction reduces to a problem in Liouville theory on the disk with
Zamolodchikov-Zamolodchikov boundary condition. In order to construct the
solution one needs to solve a certain monodromy problem which we argue is
solved by a vacuum classical conformal block on the sphere in a particular
channel. In this way we construct multi-centered gravity solutions by using
conformal blocks special functions. We show that our solutions represent
left-right asymmetric configurations of operator insertions in the dual CFT. We
also provide a check of our arguments in an example and comment on other types
of solutions.
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Massive Neutrinos and (Heterotic) String Theory: String theories in principle address the origin and values of the quark and
lepton masses. Perhaps the small values of neutrino masses could be explained
generically in string theory even if it is more difficult to calculate
individual values, or perhaps some string constructions could be favored by
generating small neutrino masses. We examine this issue in the context of the
well-known three-family standard-like Z_3 heterotic orbifolds, where the theory
is well enough known to construct the corresponding operators allowed by string
selection rules, and analyze the D- and F-flatness conditions. Surprisingly, we
find that a simple see-saw mechanism does not arise. It is not clear whether
this is a property of this construction, or of orbifolds more generally, or of
string theory itself. Extended see-saw mechanisms may be allowed; more analysis
will be needed to settle that issue. We briefly speculate on their form if
allowed and on the possibility of alternatives, such as small Dirac masses and
triplet see-saws. The smallness of neutrino masses may be a powerful probe of
string constructions in general. We also find further evidence that there are
only 20 inequivalent models in this class, which affects the counting of string
vacua.
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Full Lagrangian and Hamiltonian for quantum strings on AdS_4 x CP^3 in a
near plane wave limit: We find the full interacting Lagrangian and Hamiltonian for quantum strings
in a near plane wave limit of AdS_4 x CP^3. The leading curvature corrections
give rise to cubic and quartic terms in the Lagrangian and Hamiltonian that we
compute in full. The Lagrangian is found as the type IIA Green-Schwarz
superstring in the light-cone gauge employing a superspace construction with 32
grassmann-odd coordinates. The light-cone gauge for the fermions is non-trivial
since it should commute with the supersymmetry condition. We provide a
prescription to properly fix the kappa-symmetry gauge condition to make it
consistent with light-cone gauge. We use fermionic field redefinitions to find
a simpler Lagrangian. To construct the Hamiltonian a Dirac procedure is needed
in order to properly keep into account the fermionic second class constraints.
We combine the field redefinition with a shift of the fermionic phase space
variables that reduces Dirac brackets to Poisson brackets. This results in a
completely well-defined and explicit expression for the full interacting
Hamiltonian up to and including terms quartic in the number of fields.
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Hawking temperature and the bound on greybody factors in $D = 4$ double
field theory: We investigate the basic properties of Hawking radiation for spherical
solutions in $D = 4$ double field theory. We give the expression of the Hawking
temperature for the solution and then discuss the results of various limits. We
find that for all these limits only Schwarzschild solution and F-JNW solution
can generate Hawking radiation. Moreover, we obtain the lower bound on greybody
factors $\sigma_l(\omega)$ for the spherical solutions in $D = 4$ double field
theory. In particular, we calculate the bound on greybody factors
$\sigma_l(\omega)$ for F-JNW solution. For F-JNW solution, $\sigma_l(\omega)$
monotonically increases with the increase of $a(b)$ for fixed $b(a)$.
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Thermalization in backgrounds with hyperscaling violating factor: We present an analytic solution of a Vaidya-charged black hole with a
hyperscaling violating factor in an Einstein-Maxwell-dilaton model, where the
scalar potential plays a key role in the existence of the solution. By making
use of this result, we study the process of thermalization after a global
quench in a theory which its gravitational description is provided by the
resultant solution in the case of zero charge. In particular, we probe the
system by entanglement entropy and show that it exhibits certain scaling
behaviors during the process.
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Two-dimensional gravity with an invariant energy scale: We investigate the gauging of a two-dimensional deformation of the Poincare
algebra, which accounts for the existence of an invariant energy scale. The
model describes 2D dilaton gravity with torsion. We obtain explicit solutions
of the field equations and discuss their physical properties.
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On Tensorial Spaces and BCFW Recursion Relations for Higher Spin Fields: In this short review we briefly consider two topics in the higher spin gauge
theory: the method of "tensorial (super) spaces" and application of BCFW
recursion relations to higher spin fields.
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Polynomial Fermionic Forms for the Branching Functions of the Rational
Coset Conformal Field Theories $\widehat{su}(2)_{M}\times
\widehat{su}(2)_{N}/\widehat{su}(2)_{M+N}$}: General fermionic expressions for the branching functions of the rational
coset conformal field theories $\widehat{su}(2)_{M}\times
\widehat{su}(2)_N/\widehat{su}(2)_{M+N}$ are given. The equality of the bosonic
and fermionic representations for the branching functions is proven by
introducing polynomial truncations of these branching functions which are the
configuration sums of the RSOS models in regime III. The path space
interpretation of the RSOS models provides recursion relations for the
configuration sums. The proof of the recursion relations for the fermionic
expressions is given by using telescopic expansion techniques. The
configuration sums of the RSOS model in regime II which correspond to the
branching functions of the $Z_{M+N}$-parafermion conformal field theory are
obtained by the duality transformation $q\rightarrow q^{-1}$.
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Holographic Entanglement negativity in flat space generalized minimal
massive gravity: In this paper we study the application of holographic entanglement negativity
proposal for bipartite states in the 2d Galilean conformal field theory
($GCFT_2$) dual to bulk asymptotically flat spacetimes in the context of
generalized minimal massive gravity (GMMG) model. $GCFT_2$ is considered on the
boundary side of the duality and the bulk gravity is described by GMMG that is
asymptotically symmetric under the Galilean conformal transformations. In this
paper, the replica technique, based on the two-point and the four-point twist
correlators, is utilized and the entanglement entropy and the entanglement
negativity are obtained in the bipartite configurations of the system in the
boundary.
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Classical {\it vs.}\ Landau-Ginzburg Geometry of Compactification: We consider superstring compactifications where both the classical
description, in terms of a Calabi-Yau manifold, and also the quantum theory is
known in terms of a Landau-Ginzburg orbifold model. In particular, we study
(smooth) Calabi-Yau examples in which there are obstructions to parametrizing
all of the complex structure cohomology by polynomial deformations thus
requiring the analysis based on exact and spectral sequences. General arguments
ensure that the Landau-Ginzburg chiral ring copes with such a situation by
having a nontrivial contribution from twisted sectors. Beyond the expected
final agreement between the mathematical and physical approaches, we find a
direct correspondence between the analysis of each, thus giving a more complete
mathematical understanding of twisted sectors. Furthermore, this approach shows
that physical reasoning based upon spectral flow arguments for determining the
spectrum of Landau-Ginzburg orbifold models finds direct mathematical
justification in Koszul complex calculations and also that careful point- field
analysis continues to recover suprisingly much of the stringy features.
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Computing the Effective Action with the Functional Renormalization Group: The "exact" or "functional" renormalization group equation describes the
renormalization group flow of the effective average action $\Gamma_k$. The
ordinary effective action $\Gamma_0$ can be obtained by integrating the flow
equation from an ultraviolet scale $k=\Lambda$ down to $k=0$. We give several
examples of such calculations at one-loop, both in renormalizable and in
effective field theories. We use the results of Barvinsky, Vilkovisky and
Avramidi on the non-local heat kernel coefficients to reproduce the four point
scattering amplitude in the case of a real scalar field theory with quartic
potential and in the case of the pion chiral lagrangian. In the case of gauge
theories, we reproduce the vacuum polarization of QED and of Yang-Mills theory.
We also compute the two point functions for scalars and gravitons in the
effective field theory of scalar fields minimally coupled to gravity.
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Black holes in $ω$-defomed gauged $N=8$ supergravity: Motivated by the recently found 4-dimensional omega-deformed gauge
supergravity, we investigate the black hole solutions within all the single
scalar field consistent truncations of this theory. We construct black hole
solutions that have spherical, toroidal, and hyperbolic horizon topology. The
scalar field is regular everywhere outside the curvature singularity and the
stress-energy tensor satisfies the null energy condition. When the parameter
omega does not vanish, there is a degeneracy in the spectrum of black hole
solutions for boundary conditions that preserve the asymptotic Anti-de Sitter
symmetries. These boundary conditions correspond to multi-trace deformations in
the dual field theory.
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Inhomogeneous Anisotropic Cosmology: In homogeneous and isotropic Friedmann-Robertson-Walker cosmology, the
topology of the universe determines its ultimate fate. If the Weak Energy
Condition is satisfied, open and flat universes must expand forever, while
closed cosmologies can recollapse to a Big Crunch. A similar statement holds
for homogeneous but anisotropic (Bianchi) universes. Here, we prove that
$arbitrarily$ inhomogeneous and anisotropic cosmologies with "flat" (including
toroidal) and "open" (including compact hyperbolic) spatial topology that are
initially expanding must continue to expand forever at least in some region at
a rate bounded from below by a positive number, despite the presence of
arbitrarily large density fluctuations and/or the formation of black holes.
Because the set of 3-manifold topologies is countable, a single integer
determines the ultimate fate of the universe, and, in a specific sense, most
3-manifolds are "flat" or "open". Our result has important implications for
inflation: if there is a positive cosmological constant (or suitable
inflationary potential) and initial conditions for the inflaton, cosmologies
with "flat" or "open" topology must expand forever in some region at least as
fast as de Sitter space, and are therefore very likely to begin inflationary
expansion eventually, regardless of the scale of the inflationary energy or the
spectrum and amplitude of initial inhomogeneities and gravitational waves. Our
result is also significant for numerical general relativity, which often makes
use of periodic (toroidal) boundary conditions.
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On Cardy states in the (2,2,2,2) Gepner model: We study Cardy states in the (2,2,2,2) Gepner model from the algebraic and
geometric sides. We present the full list of primaries of this model together
with their characters. The effects of fixed point resolution are analyzed.
Annulus partition function between various Cardy states are calculated. Using
the equivalent description in terms of $T^4/Z_4$ the corresponding geometrical
realization is partially found.
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Analytic and exponentially localized brane-world
Reissner-Nordström-AdS solution: a top-down approach: In this work, we construct a five-dimensional spherically-symmetric, charged
and asymptotically Anti-de Sitter black hole with its singularity being
point-like and strictly localised on our brane. In addition, the induced brane
geometry is described by a Reissner-Nordstr\"{o}m-(A)dS line-element. We
perform a careful classification of the horizons, and demonstrate that all of
them are exponentially localised close to the brane thus exhibiting a pancake
shape. The bulk gravitational background is everywhere regular, and reduces to
an AdS$_5$ spacetime right outside the black-hole event horizon. This geometry
is supported by an anisotropic fluid with only two independent components, the
energy density $\rho_E$ and tangential pressure $p_2$. All energy conditions
are respected close to and on our brane, but a local violation takes place
within the event horizon regime in the bulk. A tensor-vector-scalar
field-theory model is built in an attempt to realise the necessary bulk matter,
however, in order to do so, both gauge and scalar degrees of freedom need to
turn phantom-like at the bulk boundary. The study of the junction conditions
reveals that no additional matter needs to be introduced on the brane for its
consistent embedding in the bulk geometry apart from its constant, positive
tension. We finally compute the effective gravitational equations on the brane,
and demonstrate that the Reissner-Nordstr\"{o}m-(A)dS geometry on our brane is
caused by the combined effect of the five-dimensional geometry and bulk matter
with its charge being in fact a tidal charge.
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Black Hole Horizon Edge Partition Functions: We extend a formula for 1-loop black hole determinants by Denef, Hartnoll,
and Sachdev (DHS) to spinning fields on any $(d+1)$-dimensional static
spherically symmetric black hole. By carefully analyzing the regularity
condition imposed on the Euclidean eigenfunctions, we reveal an unambiguous
bulk-edge split in the 1-loop Euclidean partition function for tensor fields of
arbitrary integer spin: the bulk part captures the "renormalized" thermal
canonical partition function recently discussed in arXiv:2207.07024; the edge
part is related to quasinormal modes (QNMs) that fail to analytically continue
to a subset of Euclidean modes with enhanced fall-offs near the origin. Since
the edge part takes the form of a path integral on $S^{d-1}$, this suggests
that these are associated with degrees of freedom living on the bifurcation
surface in the Lorentzian two-sided black hole geometry. For massive higher
spin on static BTZ and massive vector on Nariai black holes, we find that the
edge partition function is related to the QNMs with lowest overtone numbers.
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Spontaneous Supersymmetry Breaking in Inhomogeneous Supersymmetric Field
Theories and BPS Vacua: We study spontaneous supersymmetry breaking in inhomogeneous extensions of
${\cal N}=1$ supersymmetric field theory models in 4-dimensions. The ${\cal
N}=1$ Abelian Higgs model with the inhomogeneous mass parameter and the FI
coefficient that are dependent on spatial coordinates, as well as the
O'Raifeartaigh model with all its parameters being dependent on spatial
coordinates, are studied in detail. In the presence of inhomogeneous
parameters, half supersymmetry can be preserved by adding appropriate
inhomogeneous deformations to the original Lagrangians. The inhomogeneous
deformations often break the R-symmetry explicitly. In cases where the
inhomogeneous deformations do not break the R-symmetry explicitly, we
demonstrate that spontaneous breaking of the R-symmetry is infeasible. We argue
that those models can not be spontaneous supersymmetry breaking models,
according to the Nelson-Seiberg argument. We comment on this issue in the
context of a generic ${\cal N}=1$ supersymmetric model as well.
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Superstring Scattering from D-Branes Bound States: We derive fully covariant expressions for disk scattering amplitudes of any
two massless closed strings in which mixed Neumann and Dirichlet world-sheet
boundary conditions are included. From the two-point amplitudes, we derive the
long range background fields and verify that they correspond to D$p$-brane
bound state. Also, from the scattering amplitudes, we calculate the linear
coupling of closed string fields to D-brane world-volume and show that they are
consistent with Born-Infeld and Chern-Simons actions in the presence of a
background field.
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Weyl Anomaly Induced Stress Tensors in General Manifolds: Considering arbitrary conformal field theories in general (non-conformally
flat) backgrounds, we adopt a dimensional regularization approach to obtain
stress tensors from Weyl anomalies. The results of type A anomaly-induced
stress tensors in four and six-dimensions generalize the previous results
calculated in a conformally flat background. On the other hand, regulators are
needed to have well-defined type B anomaly-induced stress tensors. We also
discuss ambiguities related to type D anomalies, Weyl invariants and order of
limit issues.
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The Interior of a Unitarily Evaporating Black Hole: We study microscopic operators describing the experience of an observer
falling into the horizon of a unitarily evaporating black hole. For a young
black hole, these operators can be taken to act only on the degrees of freedom
in the black hole region: the soft---or stretched horizon---modes as well as
the semiclassical modes in the zone region. On the other hand, for an old black
hole, the operators must also involve radiation emitted earlier; the difference
between the two cases comes from statistics associated with the coarse-graining
performed to obtain the effective theory of the interior. We find that the
operators relevant for the interior theory can be defined globally as standard
linear operators throughout the microstates, which obey the correct algebra up
to corrections exponentially suppressed in the ratio of excitation energy to
the Hawking temperature. We conjecture that the existence of such global
operators is required for the emergence of the semiclassical picture. We also
elucidate relation between the present construction and entanglement wedge
reconstruction of the interior.
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Anomaly and Cobordism Constraints Beyond the Standard Model: Topological
Force: Standard lore uses local anomalies to check the kinematic consistency of
gauge theories coupled to chiral fermions, e.g. Standard Models (SM). Based on
a systematic cobordism classification, we examine constraints from invertible
quantum anomalies (including all perturbative local and nonperturbative global
anomalies) for gauge theories. We also clarify the different uses of these
anomalies: including (1) anomaly cancellations of dynamical gauge fields, (2)
't Hooft anomaly matching conditions of background fields of global symmetries,
and others. We apply several 4d $\mathbb{Z}_{n}$ anomaly constraints of
$n=16,4,2$ classes, beyond the familiar Feynman-graph perturbative $\mathbb{Z}$
class local anomalies. As an application, for
(SU(3)$\times$SU(2)$\times$U(1))/$\mathbb{Z}_q$ SM (with $q=1,2,3,6$) and SU(5)
Grand Unification with 15n chiral Weyl fermions and with a discrete baryon
minus lepton number $X=5({\bf B}- {\bf L})-4Y$ preserved, we discover a new
hidden gapped sector previously unknown to the SM and Georgi-Glashow model. The
gapped sector at low energy contains either (1) 4d non-invertible topological
quantum field theory (TQFT, above the energy gap with heavy fractionalized
anyon excitations from 1d particle worldline and 2d string worldsheet,
inaccessible directly from Dirac or Majorana mass gap of the 16th Weyl fermions
[i.e., right-handed neutrinos], but accessible via a topological quantum phase
transition), or (2) 5d invertible TQFT in extra dimensions. Above a higher
energy scale, the discrete $X$ becomes dynamically gauged, the entangled
Universe in 4d and 5d is mediated by Topological Force. Our model potentially
resolves puzzles, surmounting sterile neutrinos and dark matter, in fundamental
physics.
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Cosmological Solutions of Horava-Witten Theory: We discuss simple cosmological solutions of Horava-Witten theory describing
the strongly coupled heterotic string. At energies below the grand-unified
scale, the effective theory is five- not four-dimensional, where the additional
coordinate parameterizes a S^1/Z_2 orbifold. Furthermore, it admits no
homogeneous solutions. Rather, the vacuum state, appropriate for a reduction to
four-dimensional supersymmetric models, is a BPS domain wall. Relevant
cosmological solutions are those associated with this BPS state. In particular,
such solutions must be inhomogeneous, depending on the orbifold coordinate as
well as on time. We present two examples of this new type of cosmological
solution, obtained by separation of variables rather that by exchange of time
and radius coordinate applied to a brane solution, as in previous work. The
first example represents the analog of a rolling radii solution with the radii
specifying the geometry of the domain wall. This is generalized in the second
example to include a nontrivial ``Ramond-Ramond'' scalar.
|
Knots and Preons: It is shown that the four trefoil solitons that are described by the
irreducible representations D^{3/2}_{mm'} of the quantum algebra SL_q(2) (and
that may be identified with the four families of elementary fermions
(e,\mu,\tau;\nu_e\nu_\mu\nu_\tau;d,s,b;u,c,t) may be built out of three preons,
chosen from two charged preons with charges (1/3,-1/3) and two neutral preons.
These preons are Lorentz spinors and are described by the D^{1/2}_{mm'}
representation of SL_q(2). There are also four bosonic preons described by the
D^1_{mm'} and D^0_{00} representations of SL_q(2). The knotted standard theory
may be replicated at the preon level and the conjectured particles are in
principle indirectly observable.
|
Asymptotic safety goes on shell: It is well known in quantum field theory that the off-shell effective action
depends on the gauge choice and field parametrization used in calculating it.
Nevertheless, the typical scheme in which the scenario of asymptotically safe
gravity is investigated is an off-shell version of the functional
renormalization group equation. Working with the Einstein-Hilbert truncation as
a test bed, we develop a new scheme for the analysis of asymptotically safe
gravity in which the on-shell part of the effective action is singled out and
we show that the beta function for the essential coupling has no explicit
gauge-dependence. In order to reach our goal, we introduce several technical
novelties, including a different decomposition of the metric fluctuations, a
new implementation of the ghost sector, and a new cut-off scheme. We find a
non-trivial fixed point, with a value of the cosmological constant which is
independent of the gauge-fixing parameters.
|
Hypergeometric functions, their epsilon expansions and Feynman diagrams: We review the hypergeometric function approach to Feynman diagrams. Special
consideration is given to the construction of the Laurent expansion. As an
illustration, we describe a collection of physically important one-loop vertex
diagrams for which this approach is useful.
|
Classical probes for 1/16 SUSY operators: We consider 1/16 SUSY solutions in AdS/CFT. On the gravity side, Gutowski and
Reall showed them to be charged, rotating black holes in AdS. On the CFT side,
an initial construction for 1/16 SUSY operators in N=4 SYM has been suggested
by Berkooz et al., with a Fermi-sea operator describing the extremal state. In
this work we analyze particle trajectories in the 1/16 SUSY black hole
background, and show the analysis to be sensitive to the Fermi-level of the
operator in the CFT.
|
Exts and the AGT relations: We prove the connection between the Nekrasov partition function of N=2
super-symmetric U(2) gauge theory with adjoint matter and conformal blocks for
the Virasoro algebra, as predicted by the Alday-Gaiotto-Tachikawa relations.
Mathematically, this is achieved by relating the Carlsson-Okounkov Ext vector
bundle on the moduli space of rank 2 sheaves with Liouville vertex
operators.Our approach is geometric in nature, and uses a new method for
intersection-theoretic computations of the Ext operator.
|
A Proposal for the Vector State in Vacuum String Field Theory: A previous calculation on the tachyon state arising as fluctuations of a $D$
brane in vacuum string field theory is extended to include the vector state. We
use the boundary conformal field theory approach of Rastelli, Sen and Zwiebach
to construct a vector state. It is shown that the vector field satisfies the
linearized equations of motion provided the two conditions $k^2=0$ and $k^\mu
A_\mu=0$ are satisfied. Earlier calculations using Fock space techniques by
Hata and Kawano have found massless vector states that are not necessarily
transverse.
|
The Negative Energy of Gravitation as Stabilizational Factor in Field
Theory and Cosmology: This paper has been withdrawn by the author due to inconsistency of the
considered working hypothesis. The consistent treatment is presented in the
last publications of the author.
|
Radiation reaction in various dimensions: We discuss the radiation reaction problem for an electric charge moving in
flat space-time of arbitrary dimensions. It is shown that four is the unique
dimension where a local differential equation exists accounting for the
radiation reaction and admitting a consistent mass-renormalization (the
Dirac-Lorentz equation). In odd dimensions the Huygens principle does not hold;
as a result, the radiation reaction force depends on the whole past history of
a charge (radiative tail). We show that the divergence in the tail integral can
be removed by the mass renormalization only in the 2+1 theory. In even
dimensions higher than four, divergences can not be removed by a
renormalization.
|
Arguments for F-theory: After a brief review of string and $M$-Theory we point out some deficiencies.
Partly to cure them, we present several arguments for ``$F$-Theory'', enlarging
spacetime to $(2, 10)$ signature, following the original suggestion of C. Vafa.
We introduce a suggestive Supersymmetric 27-plet of particles, associated to
the exceptional symmetric hermitian space $E_{6}/Spin^{c}(10)$. Several
possible future directions, including using projective rather than metric
geometry, are mentioned. We should emphasize that $F$-Theory is yet just a very
provisional attempt, lacking clear dynamical principles.
|
Conserved Quantities and the Algebra of Braid Excitations in Quantum
Gravity: We derive conservation laws from interactions of braid-like excitations of
embedded framed spin networks in Quantum Gravity. We also demonstrate that the
set of stable braid-like excitations form a noncommutative algebra under braid
interaction, in which the set of actively-interacting braids is a subalgebra.
|
Holographic Walking Technicolor and Stability of Techni-Branes: Techni-fermions are added as stacks of D7-anti-D7 techni-branes within the
framework of a holographic technicolor model that has been proposed as a
realization of walking technicolor. The stability of the embedding of these
branes is determined. When a sufficiently low bulk cut-off is provided the
fluctuations remain small. For a longer walking region, as would be required in
any realistic model of electroweak symmetry breaking, a larger bulk cut-off is
needed and in this case the oscillations destabilize.
|
On the ultraviolet finiteness of parity-preserving $U(1) \times U(1)$
massive QED$_3$: The parity-preserving $U_A(1)\times U_a(1)$ massive QED$_3$ is ultraviolet
finiteness -- exhibits vanishing $\beta$-functions, associated to the gauge
coupling constants (electric and pseudochiral charges) and the Chern-Simons
mass parameter, and all the anomalous dimensions of the fields -- as well as is
parity and gauge anomaly free at all orders in perturbation theory. The proof
is independent of any regularization scheme and it is based on the quantum
action principle in combination with general theorems of perturbative quantum
field theory by adopting the Becchi-Rouet-Stora (BRS) algebraic renormalization
method in the framework of Bogoliubov-Parasiuk-Hepp-Zimmermann (BPHZ)
subtraction scheme.
|
N=2 structures on solvable Lie algebras: the c=9 classification: Let G be a finite-dimensional Lie algebra (not necessarily semisimple). It is
known that if G is self-dual (that is, if it possesses an invariant metric)
then there is a canonical N=1 superconformal algebra associated to its N=1
affinization---that is, it admits an N=1 (affine) Sugawara construction. Under
certain additional hypotheses, this N=1 structure admits an N=2 extension. If
this is the case, G is said to possess an N=2 structure. It is also known that
an N=2 structure on a self-dual Lie algebra G is equivalent to a vector space
decomposition G = G_+ \oplus G_- where G_\pm are isotropic Lie subalgebras. In
other words, N=2 structures on G are in one-to-one correspondence with Manin
triples (G,G_+,G_-). In this paper we exploit this correspondence to obtain a
classification of the c=9 N=2 structures on self-dual solvable Lie algebras. In
the process we also give some simple proofs for a variety of Lie algebraic
results concerning self-dual Lie algebras admitting symplectic or K\"ahler
structures.
|
Chern-Simons term at finite density: The Chern-Simons topological term coefficient is derived at arbitrary finite
density. As it occures that $\mu^2 = m^2$ is the crucial point for
Chern-Simons. So when $\mu^2 < m^2 \mu$--influence disappears and we get the
usual Chern-Simons term. On the other hand when $\mu^2 > m^2$ the Chern-Simons
term vanishes because of non-zero density of background fermions. In particular
for massless case parity anomaly is absent at any finite density. This result
holds in any odd dimension as in abelian so as in nonabelian cases.
|
Dual D-Brane Actions on $AdS^5 \times S^5$: Utilizing coset superspace approach, dual actions of super D1-and D3-branes
on $AdS_5 \times S^5$ are constructed by carrying out duality transformation of
world-volume U(1) gauge field. Resulting world-volume actions are shown to
possess expected SL(2,{\bf Z}) properties. Crucial ingredient for deriving
SL(2, {\bf Z}) transformation property of the D-brane actions is covariance of
SU(2,2|4) coset superspace algebra under SO(2) rotation between two
ten-dimensional Type IIB Majorana-Weyl spinors.
|
Conformal Bootstrap Approach to O(N) Fixed Points in Five Dimensions: Whether O(N)-invariant conformal field theory exists in five dimensions with
its implication to higher-spin holography was much debated. We find an
affirmative result on this question by utilizing conformal bootstrap approach.
In solving for the crossing symmetry condition, we propose a new approach based
on specification for the low-lying spectrum distribution. We find the
traditional one-gap bootstrapping is not suited since the nontrivial fixed
point expected from large-N expansion sits at deep interior (not at boundary or
kink) of allowed solution region. We propose two-gap bootstrapping that
specifies scaling dimension of two lowest scalar operators. The approach carves
out vast region of lower scaling dimensions and universally features two tips.
We find that the sought-for nontrivial fixed point now sits at one of the tips,
while the Gaussian fixed point sits at the other tip. The scaling dimensions of
scalar operators fit well with expectation based on large-N expansion. We also
find indication that the fixed point persist for lower values of N all the way
down to N=1. This suggests that interacting unitary conformal field theory
exists in five dimensions for all nonzero N.
|
Hamiltonian Formulation of Jackiw--Pi 3-Dimensional Gauge Theories: A 3-dimensional non-abelian gauge theory was proposed by Jackiw and Pi to
create mass for the gauge fields. However, the quadratic action obtained by
switching off the non-abelian interactions possesses more gauge symmetries than
the original one, causing some difficulties in quantization. Jackiw and Pi
proposed another action by introducing new fields, whose gauge symmetries are
consistent with the quadratic part. It is shown that all of these theories have
the same number of physical degrees of freedom in the hamiltonian framework.
Hence, as far as the physical states are considered there is no inconsistency.
Nevertheless, perturbation expansion is still problematic. To cure this we
propose to modify one of the constraints of the non-abelian theory without
altering neither its canonical hamiltonian nor the number of physical states.
|
Six-Dimensional TQFTs and Twisted Supersymmetry: We describe a generalization of Yang--Mills topological field theory for
Abelian two-forms in six dimensions. The connection of this theory by a twist
to Poincar\'e supersymmetric theories is given. We also briefly consider
interactions and the case of self-dual three-forms in eight dimensions.
|
Effective Actions for Heterotic M-Theory: We discuss the moduli space approximation for heterotic M-theory, both for
the minimal case of two boundary branes only, and when a bulk brane is
included. The resulting effective actions may be used to describe the
cosmological dynamics in the regime where the branes are moving slowly, away
from singularities. We make use of the recently derived colliding branes
solution to determine the global structure of moduli space, finding a boundary
at which the trajectories undergo a hard wall reflection. This has important
consequences for the allowed moduli space trajectories, and for the behaviour
of cosmological perturbations in the model.
|
A diffeomorphism anomaly in every dimension: Field-theoretic pure gravitational anomalies only exist in $4k+2$ dimensions.
However, canonical quantization of non-field-theoretic systems may give rise to
diffeomorphism anomalies in any number of dimensions. I present a simple
example, where a higher-dimensional generalization of the Virasoro algebra
arises upon quantization.
|
Fano hypersurfaces and Calabi-Yau supermanifolds: In this paper, we study the geometrical interpretations associated with
Sethi's proposed general correspondence between N = 2 Landau-Ginzburg orbifolds
with integral \hat{c} and N = 2 nonlinear sigma models. We focus on the
supervarieties associated with \hat{c} = 3 Gepner models. In the process, we
test a conjecture regarding the superdimension of the singular locus of these
supervarieties. The supervarieties are defined by a hypersurface \widetilde{W}
= 0 in a weighted superprojective space and have vanishing super-first Chern
class. Here, \widetilde{W} is the modified superpotential obtained by adding as
necessary to the Gepner superpotential a boson mass term and/or fermion
bilinears so that the superdimension of the supervariety is equal to \hat{c}.
When Sethi's proposal calls for adding fermion bilinears, setting the bosonic
part of \widetilde{W} (denoted by \widetilde{W}_{bos}) equal to zero defines a
Fano hypersurface embedded in a weighted projective space. In this case, if the
Newton polytope of \widetilde{W}_{bos} admits a nef partition, then the
Landau-Ginzburg orbifold can be given a geometrical interpretation as a
nonlinear sigma model on a complete intersection Calabi-Yau manifold. The
complete intersection Calabi-Yau manifold should be equivalent to the
Calabi-Yau supermanifold prescribed by Sethi's proposal.
|
Note on $T\bar{T}$ deformed matrix models and JT supergravity duals: In this work we calculate the partition functions of $\mathcal{N}=1$ type 0A
and 0B JT supergravity (SJT) on 2D surfaces of arbitrary genus with multiple
finite cut-off boundaries, based on the $T\bar{T}$ deformed super-Schwarzian
theories. In terms of SJT/matrix model duality, we compute the corresponding
correlation functions in the $T\bar{T}$ deformed matrix model side by using
topological recursion relations as well as the transformation properties of
topological recursion relations under $T\bar{T}$ deformation. We check that the
partition functions finite cut-off 0A and 0B SJT on generic 2D surfaces match
the associated correlation functions in $T\bar{T}$ deformed matrix models
respectively.
|
Integrability of the AdS_5 x S^5 superstring and its deformations: This article reviews the application of integrability to the spectral problem
of strings on AdS_5 x S^5 and its deformations. We begin with a pedagogical
introduction to integrable field theories culminating in the description of
their finite-volume spectra through the thermodynamic Bethe ansatz. Next, we
apply these ideas to the AdS_5 x S^5 string and in later chapters discuss how
to account for particular integrable deformations. Through the AdS/CFT
correspondence this gives an exact description of anomalous scaling dimensions
of single trace operators in planar N=4 supersymmetry Yang-Mills theory, its
`orbifolds', and beta and gamma-deformed supersymmetric Yang-Mills theory. We
also touch upon some subtleties arising in these deformed theories.
Furthermore, we consider complex excited states (bound states) in the su(2)
sector and give their thermodynamic Bethe ansatz description. Finally we
discuss the thermodynamic Bethe ansatz for a quantum deformation of the AdS_5 x
S^5 superstring S-matrix, with close relations to among others Pohlmeyer
reduced string theory, and briefly indicate more recent developments in this
area.
|
Towards Spectral Geometry for Causal Sets: We show that the Feynman propagator (or the d'Alembertian) of a causal set
contains the complete information about the causal set. Intuitively, this is
because the Feynman propagator, being a correlator that decays with distance,
provides a measure for the invariant distance between pairs of events. Further,
we show that even the spectra alone (of the self-adjoint and anti-self-adjoint
parts) of the propagator(s) and d'Alembertian already carry large amounts of
geometric information about their causal set. This geometric information is
basis independent and also gauge invariant in the sense that it is relabeling
invariant (which is analogue to diffeomorphism invariance). We provide
numerical evidence that the associated spectral distance between causal sets
can serve as a measure for the geometric similarity between causal sets.
|
Entanglement Entropy for 2D Gauge Theories with Matters: We investigate the entanglement entropy in 1+1-dimensional $SU(N)$ gauge
theories with various matter fields using the lattice regularization. Here we
use extended Hilbert space definition for entanglement entropy, which contains
three contributions; (1) classical Shannon entropy associated with
superselection sector distribution, where sectors are labelled by irreducible
representations of boundary penetrating fluxes, (2) logarithm of the dimensions
of their representations, which is associated with "color entanglement", and
(3) EPR Bell pairs, which give "genuine" entanglement. We explicitly show that
entanglement entropies (1) and (2) above indeed appear for various multiple
"meson" states in gauge theories with matter fields. Furthermore, we employ
transfer matrix formalism for gauge theory with fundamental matter field and
analyze its ground state using hopping parameter expansion (HPE), where the
hopping parameter $K$ is roughly the inverse square of the mass for the matter.
We evaluate the entanglement entropy for the ground state and show that all
(1), (2), (3) above appear in the HPE, though the Bell pair part (3) appears in
higher order than (1) and (2) do. With these results, we discuss how the ground
state entanglement entropy in the continuum limit can be understood from the
lattice ground state obtained in the HPE.
|
Light-Front Dynamics of Chern-Simons Systems: Chern-Simons theory coupled to complex scalars is quantized on the light-
front in the local light-cone gauge by constructing the self-consistent
hamiltonian theory. It is shown that no inconsistency arises on using two local
gauge-fixing conditions in the Dirac procedure. The light-front Hamiltonian
turns out to be simple and the framework may be useful to construct
renormalized field theory of particles with fractional statistics ({\it
anyons}). The theory is shown to be relativistic and the extra term in the
transformation of the matter field under space rotations, interpreted in
previous works as anomaly, is argued to be gauge artefact.
|
Courant bracket as T-dual invariant extension of Lie bracket: We consider the symmetries of a closed bosonic string, starting with the
general coordinate transformations. Their generator takes vector components
$\xi^\mu$ as its parameter and its Poisson bracket algebra gives rise to the
Lie bracket of its parameters. We are going to extend this generator in order
for it to be invariant upon self T-duality, i.e. T-duality realized in the same
phase space. The new generator is a function of a $2D$ double symmetry
parameter $\Lambda$, that is a direct sum of vector components $\xi^\mu$, and
1-form components $\lambda_\mu$. The Poisson bracket algebra of a new generator
produces the Courant bracket in a same way that the algebra of the general
coordinate transformations produces Lie bracket. In that sense, the Courant
bracket is T-dual invariant extension of the Lie bracket. When the Kalb-Ramond
field is introduced to the model, the generator governing both general
coordinate and local gauge symmetries is constructed. It is no longer self
T-dual and its algebra gives rise to the $B$-twisted Courant bracket, while in
its self T-dual description, the relevant bracket becomes the $\theta$-twisted
Courant bracket. Next, we consider the T-duality and the symmetry parameters
that depend on both the initial coordinates $x^\mu$ and T-dual coordinates
$y_\mu$. The generator of these transformations is defined as an inner product
in a double space and its algebra gives rise to the C-bracket.
|
Causality and Superluminal Fields: The expression of causality depends on an underlying choice of chronology.
Since a chronology is provided by any Lorentzian metric in relativistic
theories, there are as many expressions of causality as there are
non-conformally related metrics over spacetime. Although tempting, a definitive
choice of a preferred metric to which one may refer to is not satisfying. It
would indeed be in great conflict with the spirit of general covariance.
Moreover, a theory which appear to be non causal with respect to (hereafter,
w.r.t) this metric, may well be causal w.r.t another metric. In a theory
involving fields that propagate at different speeds (e.g. due to some
spontaneous breaking of Lorentz invariance), spacetime is endowed with such a
finite set of non-conformally related metrics. In that case one must look for a
new notion of causality, such that 1. no particular metric is favored and 2.
there is an unique answer to the question : ``is the theory causal?''. This new
causality is unique and defined w.r.t the metric drawing the wider cone in the
tangent space of a given point of the manifold. Moreover, which metric defines
the wider cone may depend on the location on spacetime. In that sense,
superluminal fields are generically causal, provided that some other basic
requirements are met.
|
Relevant Deformations in Open String Field Theory: a Simple Solution for
Lumps: We propose a remarkably simple solution of cubic open string field theory
which describes inhomogeneous tachyon condensation. The solution is in
one-to-one correspondence with the IR fixed point of the RG-flow generated in
the two--dimensional world-sheet theory by integrating a relevant operator with
mild enough OPE on the boundary. It is shown how the closed string overlap
correctly captures the shift in the closed string one point function between
the UV and the IR limits of the flow. Examples of lumps in non-compact and
compact transverse directions are given.
|
Boundary entropy under ambient RG flow in the AdS/BCFT model: We discuss the change of the boundary entropy under an ambient
renormalization group flow. We use conformal perturbation theory to calculate
the change of the boundary entropy for $d$-dimensional BCFTs between two nearby
fixed points. We also use the AdS$_{d+1}$/BCFT$_d$ model to calculate the
boundary entropy. We show that the boundary entropy can increase under the
ambient RG flow both in conformal perturbation theory and the
AdS$_{d+1}$/BCFT$_d$ model. In a special case, the change of the boundary
entropy in the AdS$_{d+1}$/BCFT$_d$ model reduces to that of the conformal
perturbation theory.
|
Ectoplasm with an Edge: The construction of supersymmetric invariant actions on a spacetime manifold
with a boundary is carried out using the "ectoplasm" formalism for the
construction of closed forms in superspace. Non-trivial actions are obtained
from the pull-backs to the bosonic bodies of closed but non-exact forms in
superspace; finding supersymmetric invariants thus becomes a cohomology
problem. For a spacetime with a boundary, the appropriate mathematical language
changes to relative cohomology, which we use to give a general formulation of
off-shell supersymmetric invariants in the presence of boundaries. We also
relate this construction to the superembedding formalism for the construction
of brane actions, and we give examples with bulk spacetimes of dimension 3, 4
and 5. The closed superform in the 5D example needs to be constructed as a
Chern-Simons type of invariant, obtained from a closed 6-form displaying Weil
triviality.
|
A Universal w String Theory: It has been shown that there is a sequential embedding structure in a $w_N$\
string theory based on a linearized $W_N$\ algebra. The $w_N$\ string theory is
obtained as a special realization of the $w_{N+1}$\ string. The $w_{\infty}$\
string theory is a universal string theory in this sense. We have also shown
that there is a similar sequence for $N=1$\ string theory. The $N=1\ w_N$\
string can be given as a special case of the $N=1\ w_{N+1}$\ string. In
addition, we show that the $w_3$\ string theory is obtained as a special
realization of the $N=1\ w_3$\ string. We conjecture that the $w_N$\ string can
be obtained as a special $N=1\ w_N$\ string for general $w_N$. If this is the
case, $N=1\ w_{\infty}$\ string theory is more universal since it includes both
$N=0$\ and $N=1$\ $w_N$\ string theories.
|
Deformed oscillators algebra formulation of the Nonlinear Schrodinger
hierarchy and of its symmetry: We present a self-contained formulation of the Nonlinear Schrodinger
hierarchy and its Yangian symmetry in terms of deformed oscilator algebra (Z.F.
algebra). The link between Yangian Y(gl(N)) and finite W(gl(pN),N.gl(p))
algebras is also illustrated in this framework.
|
Holographic entanglement and causal information in coherent states: Scalar solitons in global AdS4 are holographically dual to coherent states
carrying a non-trivial condensate of a scalar operator. We study the
holographic information content of these states, focusing on a particular
spatial region, by examining the entanglement entropy and causal holographic
information. We show generically that whenever the dimension of the condensed
operator is sufficiently low (characterized by the double-trace operator
becoming relevant), such coherent states have lower entanglement and causal
holographic information than the vacuum state of the system, despite having
greater energy. We also use these geometries to illustrate the fact that causal
wedges associated with a simply-connected boundary region can have non-trivial
topology even in causally trivial spacetimes.
|
The Casimir effect for fermionic currents in conical rings with
applications to graphene ribbons: We investigate the combined effects of boundaries and topology on the vacuum
expectation values (VEVs) of the charge and current densities for a massive 2D
fermionic field confined on a conical ring threaded by a magnetic flux.
Different types of boundary conditions on the ring edges are considered for
fields realizing two inequivalent irreducible representations of the Clifford
algebra. The related bound states and zero energy fermionic modes are
discussed. The edge contributions to the VEVs of the charge and azimuthal
current densities are explicitly extracted and their behavior in various
asymptotic limits is considered. On the ring edges the azimuthal current
density is equal to the charge density or has an opposite sign. We show that
the absolute values of the charge and current densities increase with
increasing planar angle deficit. Depending on the boundary conditions, the VEVs
are continuous or discontinuous at half-integer values of the ratio of the
effective magnetic flux to the flux quantum. The discontinuity is related to
the presence of the zero energy mode. By combining the results for the fields
realizing the irreducible representations of the Clifford algebra, the charge
and current densities are studied in parity and time-reversal symmetric
fermionic models. If the boundary conditions and the phases in quasiperiodicity
conditions for separate fields are the same the total charge density vanishes.
Applications are given to graphitic cones with edges (conical ribbons).
|
Scalar and Spinor Field Actions on Fuzzy $S^4$: fuzzy $CP^3$ as a
$S^2_F$ bundle over $S^4_F$: We present a manifestly Spin(5) invariant construction of squashed fuzzy
$CP^3$ as a fuzzy $S^2$ bundle over fuzzy $S^4$. We develop the necessary
projectors and exhibit the squashing in terms of the radii of the $S^2$ and
$S^4$. Our analysis allows us give both scalar and spinor fuzzy action
functionals whose low lying modes are truncated versions of those of a
commutative $S^4$.
|
4d mirror-like dualities: We construct a family of $4d$ $\mathcal{N}=1$ theories that we call
$E^\sigma_\rho[USp(2N)]$ which exhibit a novel type of $4d$ IR duality very
reminiscent of the mirror duality enjoyed by the $3d$ $\mathcal{N}=4$
$T^\sigma_\rho[SU(N)]$ theories. We obtain the $E^\sigma_\rho[USp(2N)]$
theories from the recently introduced $E[USp(2N)]$ theory, by following the RG
flow initiated by vevs labelled by partitions $\rho$ and $\sigma$ for two
operators transforming in the antisymmetric representations of the $USp(2N)
\times USp(2N)$ IR symmetries of the $E[USp(2N)]$ theory. These vevs are the
$4d$ uplift of the ones we turn on for the moment maps of $T[SU(N)]$ to trigger
the flow to $T^\sigma_\rho[SU(N)]$. Indeed the $E[USp(2N)]$ theory, upon
dimensional reduction and suitable real mass deformations, reduces to the
$T[SU(N)]$ theory. In order to study the RG flows triggered by the vevs we
develop a new strategy based on the duality webs of the $T[SU(N)]$ and
$E[USp(2N)]$ theories.
|
Trace anomaly for Weyl fermions using the Breitenlohner-Maison scheme
for $γ_*$: We revisit the computation of the trace anomaly for Weyl fermions using
dimensional regularization. For a consistent treatment of the chiral gamma
matrix $\gamma_*$ in dimensional regularization, we work in $n$ dimensions from
the very beginning and use the Breitenlohner-Maison scheme to define
$\gamma_*$. We show that the parity-odd contribution to the trace anomaly
vanishes (for which the use of dimension-dependent identities is crucial), and
that the parity-even contribution is half the one of a Dirac fermion. To arrive
at this result, we compute the full renormalized expectation value of the
fermion stress tensor to second order in perturbations around Minkowski
spacetime, and also show that it is conserved.
|
Stability of Yang Mills Vacuum State: We examine the phenomena of the chromomagnetic gluon condensation in the
Yang-Mills theory and the problem of stability of the chromomagnetic vacuum
fields. The apparent instability of the chromomagnetic vacuum fields is a
result of quadratic approximation. The stability is restored when the nonlinear
interaction of negative/unstable modes is taken into account in the case of
chromomagnetic vacuum fields and the interaction of the zero modes in the case
of (anti)self-dual covariantly-constant vacuum fields. All these vacuum fields
are stable and indicate that the Yang-Mills vacuum is highly degenerate quantum
state.
|
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