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Topological invariants for holographic semimetals: We study the behavior of fermion spectral functions for the holographic
topological Weyl and nodal line semimetals. We calculate the topological
invariants from the Green functions of both holographic semimetals using the
topological Hamiltonian method, which calculates topological invariants of
strongly interacting systems from an effective Hamiltonian system with the same
topological structure. Nontrivial topological invariants for both systems have
been obtained and the presence of nontrivial topological invariants further
supports the topological nature of the holographic semimetals. | Gravitational Corrections for Supersymmetric Gauge Theories with Flavors
via Matrix Models: We study the gravitational corrections to the F-term in four-dimensional N=1
U(N) gauge theories with flavors, using the Dijkgraaf-Vafa theory. We derive a
compact formula for the annulus contribution in terms of the prime form on the
matrix model curve. Remarkably, the full R^2 correction can be reproduced as a
special momentum sector of a single c=1 CFT correlator, which closely resembles
that in the bosonization of fermions on Riemann surfaces. The N=2 limit of the
torus contribution agrees with the multi-instanton calculations as well as the
topological A-model result. The planar contributions, on the other hand, have
no counterpart in the topological gauge theories, and we speculate about the
origin of these terms. |
Deriving the First Law of Black Hole Thermodynamics without Entanglement: In AdS/CFT, how is the bulk first law realized in the boundary CFT? Recently,
Faulkner et al. showed that in certain holographic contexts, the bulk first law
has a precise microscopic interpretation as a first law of entanglement entropy
in the boundary theory. However, the bulk can also satisfy a first law when the
boundary density matrix is pure, i.e. in the absence of entanglement with other
degrees of freedom. In this note we argue that the bulk first law should
generally be understood in terms of a particular coarse-graining of the
boundary theory. We use geons, or single-exterior black holes, as a testing
ground for this idea. Our main result is that for a class of small
perturbations to these spacetimes the Wald entropy agrees to first order with
the one-point entropy, a coarse-grained entropy recently proposed by Kelly and
Wall. This result also extends the regime over which the one-point entropy is
known to be equal to the causal holographic information of Hubeny and
Rangamani. | Anomalies and nonperturbative results: We investigate nonperturbative effects in N=1 and N=2 supersymmetric theories
using a relation between perturbative and exact anomalies as a starting point.
For N=2 supersymmetric SU(n) Yang-Mills theory we derive the general structure
of the Picard-Fuchs equations; for N=1 supersymmetric Yang-Mills theories we
find holomorphic part of the superpotential (with gluino condensate) exactly. |
On the Associativity of Star Product in Systems with Nonlinear
Constraints: The noncommutative star product of phase space functions is, by construction,
associative for both non-degenerate and degenerate case (involving only second
class constraints) as has been shown by Berezin, Batalin and Tyutin. However,
for the latter case, the manifest associativity is lost if an arbitrary
coordinate system is used but can be restored by using an unconstrained
canonical set.
The existence of such a canonical transformation is guaranteed by a theorem
due to Maskawa and Nakajima. In terms of these new variables, the Kontsevich
series for the star product reduces to an exponential series which is
manifestly associative. We also show, using the star product formalism, that
the angular momentum of a particle moving on a circle is quantized. | General treatment of anomalies in (1,0) and (1,1) two-dimensional
super-gravity: In this paper we discuss the interplay among (~super-~)coordinate, Weyl and
\l\ anomaly both in chiral and non-chiral super-gravity represented by $(1,0)$
and $(1,1)$ two-dimensional models. It is shown that for this purpose two
regularization dependent parameters are needed in the effective action. We
discuss in {\it full generality} the regularization ambiguities of the induced
effective action and recover the corresponding general form of the anomalous
Ward Identities. Finally, we explain the difference between chiral and
non-chiral super-gravity models in terms of the free parameters and establish
relation between these two models by projecting $(1,1)$ into $(1,0)$
super-symmetry. |
Holographic duals of five-dimensional SCFTs on a Riemann surface: We study the twisted compactifications of five-dimensional Seiberg SCFTs,
with $SU_\mathcal{M}(2)\times E_{N_f+1}$ flavor symmetry, on a generic Riemann
surface that preserves four supercharges. The five-dimensional SCFTs are
obtained from the decoupling limit of $N$ D4-branes probing a geometry of
$N_f<8$ D8-branes and an O8-plane. In addition to the R-symmetry, we can also
twist the flavor symmetry by turning on background flux on the Riemann surface.
In particular, in the string theory construction of the five-dimensional SCFTs,
the background flux for the $SU_\mathcal{M}(2)$ has a geometric origin, similar
to the topological twist of the R-symmetry. We argue that the resulting
low-energy three-dimensional theories describe the dynamics on the world-volume
of the $N$ D4-branes wrapped on the Riemann surface in the O8/D8 background.
The Riemann surface can be described as a curve in a Calabi-Yau three-fold that
is a sum of two line bundles over it. This allows for an explicit construction
of $AdS_4$ solutions in massive IIA supergravity dual to the world-volume
theories, thereby providing strong evidence that the three-dimensional SCFTs
exist in the low-energy limit of the compactification of the five-dimensional
SCFTs. We compute observables such as the free energy and the scaling
dimensions of operators dual to D2-brane probes; these have non-trivial
dependence on the twist parameter for the $U(1)$ in $SU_\mathcal{M}(2)$. The
free energy exhibits the $N^{5/2}$ scaling that is emblematic of
five-dimensional SCFTs. | Holographic Superconductors: It has been shown that a gravitational dual to a superconductor can be
obtained by coupling anti-de Sitter gravity to a Maxwell field and charged
scalar. We review our earlier analysis of this theory and extend it in two
directions. First, we consider all values for the charge of the scalar field.
Away from the large charge limit, backreaction on the spacetime metric is
important. While the qualitative behaviour of the dual superconductor is found
to be similar for all charges, in the limit of arbitrarily small charge a new
type of black hole instability is found. We go on to add a perpendicular
magnetic field B and obtain the London equation and magnetic penetration depth.
We show that these holographic superconductors are Type II, i.e., starting in a
normal phase at large B and low temperatures, they develop superconducting
droplets as B is reduced. |
Quantum tunneling and spectroscopy of noncommutative inspired Kerr black
hole: We discuss the thermodynamics of the noncommutative inspired Kerr black hole
by means of a reformulated Hamilton-Jacobi method and a dimensional reduction
technique. In order to investigate the effect of the angular momentum of the
tunneling particle, we calculate the wave function to the first order of the
WKB ansatz. Then, using a density matrix technique we derive the radiation
spectrum from which the radiation temperature can be read out. Our results show
that the radiation of this noncommutative inspired black hole corresponds to a
modified temperature which involves the effect of noncommutativity. However,
the angular momentum of the tunneling particle has no influence on the
radiation temperature. Moreover, we analyze the entropy spectrum and verify
that its quantization is modified neither by the noncommutativity of spacetime
nor by the quantum correction of wave functions. | Cosmological Particle Creation and Dynamical Casimir Effect: In this paper we have considered the particle creation in the spatially
closed Robertson-Walker space-time. We considered a real massive scalar field
which conformally coupled to the Robertson-Walker background. With the
dependence of the scale factor on time, the case under consideration is a
dynamical Casimir effect with moving boundaries. |
A relation between moduli space of D-branes on orbifolds and Ising model: We study D-branes transverse to an abelian orbifold C^3/Z_n Z_n. The moduli
space of the gauge theory on the D-branes is analyzed by combinatorial
calculation based on toric geometry. It is shown that the calculation is
related to a problemto count the number of ground states of an
antiferromagnetic Ising model. The lattice on which the Ising model is defined
is a triangular one defined on the McKay quiver of the orbifold. | The supersymmetric version of the Green--Schwarz anomaly cancellation
mechanism: The $N=1$, $D=10$ Supergravity--Super--Yang--Mills (SUGRA-SYM) theory is
plagued by ABBJ gauge and Lorentz anomalies which are cancelled via the
Green-Schwarz anomaly cancellation mechanism. Due to the fact that the ABBJ
anomalies are not invariant under supersymmetry (SUSY) transformations one
concludes that the theory is plagued also by a SUSY anomaly. For the gauge
groups $SO(32)$ and $E_8\times E_8$ we compute this SUSY anomaly, by solving a
coupled cohomology problem, and we show that it can be cancelled by subtracting
from the action the known Green--Schwarz counterterm, the same which cancels
also the ABBJ anomaly, the expected result. Finally, we argue that the
corresponding mechanism does not apply in the dual SUGRA-SYM, related to the
heterotic five-brane. |
Momentum-space conformal blocks on the light cone: We study the momentum-space 4-point correlation function of identical scalar
operators in conformal field theory. Working specifically with null momenta, we
show that its imaginary part admits an expansion in conformal blocks. The
blocks are polynomials in the cosine of the scattering angle, with degree
$\ell$ corresponding to the spin of the intermediate operator. The coefficients
of these polynomials are obtained in a closed-form expression for arbitrary
spacetime dimension $d > 2$. If the scaling dimension of the intermediate
operator is large, the conformal block reduces to a Gegenbauer polynomial
$\mathcal{C}_\ell^{(d-2)/2}$. If on the contrary the scaling dimension
saturates the unitarity bound, the block is different Gegenbauer polynomial
$\mathcal{C}_\ell^{(d-3)/2}$. These results are then used as an inversion
formula to compute OPE coefficients in a free theory example. | Yang-Mills Duality and the Generation Puzzle: The fermion generation puzzle has survived into this century as one of the
great mysteries in particle physics. We consider here a possible solution
within the Standard Model framework based on a nonabelian generalization of
electric-magnetic duality. First, by constructing in loop space a nonabelian
generalization of the abelian dual transform (Hodge *), one finds that a
``magnetic'' symmetry exists also in classical Yang-Mills theory dual to the
original (``electric'') gauge symmetry. Secondly, from a result of 't Hooft's,
one obtains that for confined colour SU(3), the dual symmetry
$\widetilde{SU}(3)$ is spontaneously broken and can play the role of the
``horizontal symmetry'' for generations. Thirdly, such an identification not
only offers an explanation why there should be three and apparently only three
generations of fermions with the remarkable mass and mixing patterns seen in
experiment, but allows even a calculation of the relevant parameters giving
very sensible results. Other testible predictions follow ranging from rare
hadron decays to cosmic ray air showers. |
Asymmetric Orbifolds and Higher Level Models: I introduce a class of string constructions based on asymmetric orbifolds
leading to level two models. In particular, I derive in detail various models
with gauge groups $E_6$ and SO(10), including a four generation $E_6$ model
with two adjoint representations. The occurrence of multiple adjoint
representations is a generic feature of the construction. In the course of
describing this approach, I will address the problem of twist phases in higher
twisted sectors of asymmetric orbifolds. | Populating the Whole Landscape: Every de Sitter vacuum can transition to every other de Sitter vacuum despite
any obstacle, despite intervening anti-de Sitter sinks, despite not being
connected by an instanton. Eternal inflation populates the whole landscape. |
On the general action of boundary (super)string field theory: We reconstruct boundary superstring field theory via boundary states. After a
minor modification of the fermionic two-form, all the equations needed for
Batalin-Vilkovisky formulation are simply represented by closed string
oscillators and the proof of gauge invariance is drastically simplified. The
general form of the action of boundary superstring field theory is also
obtained without any assumption and found to take exactly the same form as the
bosonic one. As a special case of this action, we revisit the conjecture that
the action is simply given by the disk partition function when matter and
ghosts are completely decoupled. | BPS States, String Duality, and Nodal Curves on K3: We describe the counting of BPS states of Type II strings on K3 by relating
the supersymmetric cycles of genus $g$ to the number of rational curves with
$g$ double points on K3. The generating function for the number of such curves
is the left-moving partition function of the bosonic string. |
Fradkin-Bacry-Ruegg-Souriau vector in kappa-deformed space-time: We study presence of an additional symmetry of a generic central potential in
the $\kappa$-space-time. An explicit construction of Fradkin and Bacry, Ruegg,
Souriau (FBRS) for a central potential is carried out and the piece-wise
conserved nature of the vector is established. We also extend the study to
Kepler systems with a drag term, particularly Gorringe-Leach equation is
generalized to the $\kappa$-deformed space. The possibility of mapping
Gorringe-Leach equation to an equation with out drag term is exploited in
associating a similar conserved vector to system with a drag term. An extension
of duality between two class of central potential is introduced in the
$\kappa$-deformed space and is used to investigate the duality existing between
two class of Gorringe-Leach equations. All the results obtained can be retraced
to the correct commutative limit as we let $a \rightarrow 0$. | The Second Law in 4D Einstein-Gauss-Bonnet Gravity: The topological contribution to black hole entropy of a Gauss-Bonnet term in
four dimensions opens up the possibility of a violation of the second law of
thermodynamics in black hole mergers. We show, however, that the second law is
not violated in the regime where Einstein-Gauss-Bonnet holds as an effective
theory and black holes can be treated thermodynamically. For mergers of AdS
black holes, the second law appears to be violated even in Einstein gravity; we
argue, however, that the second law holds when gravitational potential energy
is taken into account. |
A Note on Inflation with Tachyon Rolling on the Gauss-Bonnet Brane: In this paper we study the tachyonic inflation in brane world cosmology with
Gauss-Bonnet term in the bulk. We obtain the exact solution of slow roll
equations in case of exponential potential. We attempt to implement the
proposal of Lidsey and Nunes, astro-ph/0303168, for the tachyon condensate
rolling on the Gauss-Bonnet brane and discuss the difficulties associated with
the proposal. | Spectral Flow in 3D Flat Spacetimes: In this paper we investigate spectral flow symmetry in asymptotically flat
spacetimes both from a gravity as well as a putative dual quantum field theory
perspective. On the gravity side we consider models in Einstein gravity and
supergravity as well as their "reloaded" versions, present suitable boundary
conditions, determine the respective asymptotic symmetry algebras and the
thermal entropy of cosmological solutions in each of these models. On the
quantum field theory side we identify the spectral flow symmetry as
automorphisms of the underlying symmetry algebra of the theory. Using spectral
flow invariance we then determine the thermal entropy of these quantum field
theories and find perfect agreement with the results from the gravity side. In
addition we determine logarithmic corrections to the thermal entropy. |
Mass Gap in Quantum Chromodynamics: We present a heuristic argument in support of the assertion that QCD will
exhibit a mass gap, if the Callan-Symanzik function \beta(g) obeys the
inequality \beta(g) < 0, for all g > 0. | Analytical study of critical magnetic field in a holographic
superconductor: We analytically sutdy the effect of external magnetic field in a Holographic
superconductor by using Sturm-Liouville method. We estimate the coefficient of
proportionality at critical temperature and find its denpendence on external
magnetic field. By exploring phase diagrams of critical temperature and
magnetic field for various condensates, we conclude that a Meissner-like effect
is a general feature in Holographic superconductors. We also study the quantum
phase transition at zero temperature and find that critical charge density
increases linearly with the condensate dimension. |
Spectroscopy of a canonically quantized horizon: Deviations from Hawking's thermal black hole spectrum, observable for
macroscopic black holes, are derived from a model of a quantum horizon in loop
quantum gravity. These arise from additional area eigenstates present in
quantum surfaces excluded by the classical isolated horizon boundary
conditions. The complete spectrum of area unexpectedly exhibits evenly spaced
symmetry. This leads to an enhancement of some spectral lines on top of the
thermal spectrum. This can imprint characteristic features into the spectra of
black hole systems. It most notably gives the signature of quantum gravity
observability in radiation from primordial black holes, and makes it possible
to test loop quantum gravity with black holes well above Planck scale. | Screening length and the direction of plasma winds: We study the screening length of a heavy quark-antiquark pair in strongly
coupled gauge theory plasmas flowing at velocity v following a proposal by Liu,
Rajagopal, and Wiedemann. We analyze the screening length as the direction of
the plasma winds vary. To leading order in v, this angle-dependence can be
studied analytically for many theories by extending our previous formalism. We
show that the screening length is locally a minimum (maximum) when the pair is
perpendicular (parallel) to the plasma winds, which has been observed for the
N=4 plasma. Also, we compare AdS/CFT results with weak coupling ones, and we
discuss the subleading dependence on v for the Dp-brane. |
Conformal blocks for highly disparate scaling dimensions: We show that conformal blocks simplify greatly when there is a large
difference between two of the scaling dimensions for external operators. In
particular the spacetime dimension only appears in an overall constant which we
determine via recurrence relations. Connections to the conformal bootstrap
program and the AdS / CFT correspondence are also discussed. | Quantum Observables of Quantized Fluxes: While it has become widely appreciated that defining (higher) gauge theories
requires, in addition to ordinary phase space data, also "flux quantization"
laws in generalized differential cohomology, there has been little discussion
of the general rules, if any, for lifting Poisson-brackets of
(flux-)observables and their quantization from traditional phase spaces to the
resulting higher moduli stacks of flux-quantized gauge fields.
In this short note, we present a systematic analysis of (i) the canonical
quantization of flux observables in Yang-Mills theory and (ii) of valid flux
quantization laws in abelian Yang-Mills, observing (iii) that the resulting
topological quantum observables form the homology Pontrjagin algebra of the
loop space of the moduli space of flux-quantized gauge fields.
This is remarkable because the homology Ponrjagin algebra on loops of moduli
makes immediate sense in broad generality for higher and non-abelian
(non-linearly coupled) gauge fields, such as for the C-field in 11d
supergravity, where it recovers the quantum effects previously discussed in the
context of "Hypothesis H". |
Holographic Abrikosov lattice: vortex matter from black hole: The AdS/CFT correspondence provides a unique way to study the vortex matter
phases in superconductors. We solved the nonlinear equations of motion for the
Abelain-Higgs theory living on the AdS$_4$ black hole boundary that is dual to
a two dimensional strongly coupled type II superconductor at temperature $T$
with a perpendicular external uniform magnetic field $B_0$. We found the
associated two critical magnetic fields, $B_{c1}(T)$ and $B_{c2}(T)$. For $B_0
< B_{c1}(T)$ the magnetic field will be expelled out by the superconductor
resembling the Meissner effect and the superconductivity will be destroyed when
$B_0 > B_{c2}(T)$. The Abrikosov lattice appears in the range $B_{c1}(T) < B_0
< B_{c2}(T)$ including, due to the finite size and boundary effect, several
kinds of configurations such as hexagonal, square and slightly irregular square
lattices, when the magnetic field is increased. The upper and lower critical
fields behave as inverse squares of coherence length and magnetic penetration
depth respectively which matches the well known consensus. | Standard-like Models with Broken Supersymmetry from Type I String Vacua: We construct D=4 Type I vacua with massless content remarkably close to that
of the standard model of particle physics. They are tachyon-free
non-supersymmetric models which are obtained starting with a standard D=4, N=1
compact Type IIB orientifold and adding the same number of Dp-branes and
anti-Dp-branes distributed at different points of the underlying orbifold.
Supersymmetry-breaking is felt by the observable world either directly, by
gravity mediation or gauge mediation, depending on the brane configuration. We
construct several simple three generation examples with the gauge group of the
standard model or its left-right symmetric extensions. The models contain a
number of U(1) gauge groups whose anomalies are cancelled by a generalized
Green-Schwarz mechanism. These U(1)'s are broken but may survive as global
symmetries providing for a flavour structure to the models. The value of the
string scale may be lowered down to the intermediate scale (as required in the
gravity mediation case) or down to 1-100 TeV for the non-SUSY models. Thus the
present models are the first semirealistic string vacua realizing the
possibility of a low string scale. The unbalanced force between the pairs of
Dp- and anti-Dp-branes provides for an effect which tends to compactify some of
the extra dimensions but no others. This could provide a new mechanism for
radius stabilization. |
Extensions of a scale-separated AdS$_4$ solution and their mass spectrum: We consider two extensions of the so-called DGKT solution, a 4d
scale-separated anti-de Sitter (AdS) solution obtained as a compactification on
a 6d torus orbifold. Each extension consists in a specific large $n$ expansion
beyond the DGKT solution, where $n$ is the unbounded $F_4$-flux parameter. One
of the extensions considered generalizes the known warped, partially
backreacted solution. We analyse the two extensions in 10d massive type IIA
supergravity as well as in a 4d effective theory, using a general warped
compactification formalism, including axions. On top of known corrections to
DGKT, we mainly get new ones from $F_4$; other fluxes are very constrained by
flux quantization. In each extension, one would expect corresponding
corrections to the mass spectrum, before reaching contributions from
$\alpha'$-corrections. But the mass spectrum turns out to be robust, and
conformal dimensions remain unchanged. | Aspects of the QCD $θ$-vacuum: This paper addresses two aspects concerning the $\theta$-vacuum of Quantum
Chromodynamics. First, large-$N_c$ chiral perturbation theory is used to
calculate the first two non-trivial cumulants of the distribution of the
winding number, i.\,e. the topological susceptibility, $\chi_\mathrm{top}$, and
the fourth cumulant, $c_4$, up to next-to-leading order. Their large-$N_c$
scaling is discussed, and compared to lattice results. It is found that
$\chi_\mathrm{top}=\mathcal{O}(N_c^0)$, as known before, and
$c_4=\mathcal{O}(N_c^{-3})$, correcting the assumption of
$\mathcal{O}(N_c^{-2})$ in the literature. Second, we discuss the properties of
QCD at $\theta\sim\pi$ using chiral perturbation theory for the case of $2+1$
light flavors, i.\,e. by taking the strange quark mass heavier than the
degenerate up and down quark masses. It is shown that --- in accordance with
previous findings for $N_f=2$ and $N_f=3$ mass-degenerate flavors --- in the
region $\theta\sim\pi$ two vacuum states coexist, which become degenerate at
$\theta=\pi$. The wall tension of the energy barrier between these degenerate
vacua is determined as well as the decay rate of a false vacuum. |
A characterization of the differential in semi-infinite cohomology: Semi-infinite cohomology is constructed from scratch as the proper
generalization of finite dimensional Lie algebra cohomology. The differential d
and other operators are realized as universal inner deri- vations of a
completed algebra, which acts on any appropriate semi-infinite complex. In
particular, d is shown to be the unique derivation satisfying the "Cartan
identity" and certain natural degree conditions. The proof that d is
square-zero may well be the shortest (arguably, the only) one in print. | Perturbative Expansion around the Gaussian Effective Potential of the
Fermion Field Theory: We have extended the perturbative expansion method around the Gaussian
effective action to the fermionic field theory, by taking the 2-dimensional
Gross-Neveu model as an example. We have computed both the zero temperature and
the finite temperature effective potentials of the Gross-Neveu model up to the
first perturbative correction terms, and have found that the critical
temperature, at which dynamically broken symmetry is restored, is significantly
improved for small value of the flavour number. |
The Two-Dimensional Stringy Black-Hole: A New Approach and a Pathology: The string propagation in the two-dimensional stringy black-hole is
investigated from a new approach. We completely solve the classical and quantum
string dynamics in the lorentzian and euclidean regimes. In the lorentzian case
all the physics reduces to a massless scalar particle described by a
Klein-Gordon type equation with a singular effective potential. The scattering
matrix is found and it reproduces the results obtained by coset CFT techniques.
It factorizes into two pieces : an elastic coulombian amplitude and an
absorption part. In both parts, an infinite sequence of imaginary poles in the
energy appear. The generic features of string propagation in curved
D-dimensional backgrounds (string stretching, fall into spacetime
singularities) are analyzed in the present case. A new physical phenomenon
specific to the present black-hole is found : the quantum renormalization of
the speed of light. We find $c_{quantum} = \sqrt{{k\o{k-2}}}~c_{classical}$,
where $k$ is the integer in front of the WZW action. This feature is, however,
a pathology. Only for $ k \to \infty$ the pathology disappears (although the
conformal anomaly is present). We analyze all the classical euclidean string
solutions and exactly compute the quantum partition function. No critical
Hagedorn temperature appears here. | Toward an Effective Field Theory Approach to Reheating: We investigate whether Effective Field Theory (EFT) approaches, which have
been useful in examining inflation and dark energy, can also be used to
establish a systematic approach to inflationary reheating. We consider two
methods. First, we extend Weinberg's background EFT to the end of inflation and
reheating. We establish when parametric resonance and decay of the inflaton
occurs, but also find intrinsic theoretical limitations, which make it
difficult to capture some reheating models. This motivates us to next consider
Cheung, et. al.'s EFT approach, which instead focuses on perturbations and the
symmetry breaking induced by the cosmological background. Adapting the latter
approach to reheating implies some new and important differences compared to
the EFT of Inflation. In particular, there are new hierarchical scales, and we
must account for inflaton oscillations during reheating, which lead to discrete
symmetry breaking. Guided by the fundamental symmetries, we construct the EFT
of reheating, and as an example of its usefulness we establish a new class of
reheating models and the corresponding predictions for gravity wave
observations. In this paper we primarily focus on the first stages of
preheating. We conclude by discussing challenges for the approach and future
directions. This paper builds on ideas first proposed in the note
arXiv:1507.06651. |
Rationalizing roots: an algorithmic approach: In the computation of Feynman integrals which evaluate to multiple
polylogarithms one encounters quite often square roots. To express the Feynman
integral in terms of multiple polylogarithms, one seeks a transformation of
variables, which rationalizes the square roots. In this paper, we give an
algorithm for rationalizing roots. The algorithm is applicable whenever the
algebraic hypersurface associated with the root has a point of multiplicity
$(d-1)$, where $d$ is the degree of the algebraic hypersurface. We show that
one can use the algorithm iteratively to rationalize multiple roots
simultaneously. Several examples from high energy physics are discussed. | New Solvable Lattice Models from Conformal Field Theory: We build the trigonometric solutions of the Yang-Baxter equation that can not
be obtained from quantum groups in any direct way. The solution is obtained
using the construction suggested recently from the rational conformal field
theory corresponding to the WZW model on $SO(3)_{4 R}=SU(2)_{4 R} / Z_{2}$. We
also discuss the full elliptic solution to the Yang-Baxter equation whose
critical limit corresponds to the trigonometric solution found below. |
p,q-Duality and Hamiltonian Flows in the Space of Integrable Systems or
Integrable Systems as Canonical Transforms of the Free Ones: Variation of coupling constants of integrable system can be considered as
canonical transformation or, infinitesimally, a Hamiltonian flow in the space
of such systems. Any function $T(\vec p, \vec q)$ generates a one-parametric
family of integrable systems in vicinity of a single system: this gives an idea
of how many integrable systems there are in the space of coupling constants.
Inverse flow is generated by a dual "Hamiltonian", $\widetilde T(\vec p, \vec
q)$ associated with the dual integrable system. In vicinity of a self-dual
point the duality transformation just interchanges momenta and coordinates in
such a "Hamiltonian": $\widetilde T(\vec p, \vec q) = T(\vec q, \vec p)$. For
integrable system with several coupling constants the corresponding
"Hamiltonians" $T_i(\vec p, \vec q)$ satisfy Whitham equations and after
quantization (of the original system) become operators satisfying the
zero-curvature condition in the space of coupling constants: [ d/dg_a -
T_a(p,q), d/dg_b - T_b(p,q) ] = 0. Some explicit formulas are given for
harmonic oscillator and for Calogero-Ruijsenaars-Dell system. | Non-equilibrium Phase Transition from AdS/CFT: Using AdS/CFT correspondence we study non-equilibrium phase transition in the
presence of a constant external magnetic field. The transition occurs when the
sign of differential conductivity reverses. Utilizing numerical method we show
that the type of transition depends on the value of magnetic field as well as
the temperature of gauge theory. Moreover we show that this transition does not
depend on the supersymmetry and the subspace on which the fundamental matter
fields live. |
The boundary F-theorem for free fields: The boundary free energy, as defined by Gaiotto, is further analysed for free
scalars on a hemisphere and shown to be the same as the N-D determinant that
earlier occurred in a treatment of GJMS operators. It is also shown to be
identical, up to spin degeneracy, to the free energy for a spin-half field on
the hemisphere boundary. This is also true if the hemisphere is replaced by a
lune. The calculations are carried out in arbitrary dimensions. | Discrete symmetries of unitary minimal conformal theories: We classify the possible discrete (finite) symmetries of two--dimensional
critical models described by unitary minimal conformally invariant theories. We
find that all but six models have the group Z_2 as maximal symmetry. Among the
six exceptional theories, four have no symmetry at all, while the other two are
the familiar critical and tricritical 3--Potts models, which both have an S_3
symmetry. These symmetries are the expected ones, and coincide with the
automorphism groups of the Dynkin diagrams of simply--laced simple Lie algebras
ADE. We note that extended chiral algebras, when present, are almost never
preserved in the frustrated sectors. |
Complex structures for an S-matrix of Klein-Gordon theory on AdS
spacetimes: While the standard construction of the S-matrix fails on Anti-de Sitter (AdS)
spacetime, a generalized S-matrix makes sense, based on the hypercylinder
geometry induced by the boundary of AdS. In contrast to quantum field theory in
Minkowski spacetime, there is not yet a standard way to resolve the
quantization ambiguities arising in its construction. These ambiguities are
conveniently encoded in the choice of a complex structure. We explore in this
paper the space of complex structures for real scalar Klein-Gordon theory based
on a number of criteria. These are: invariance under AdS isometries, induction
of a positive definite inner product, compatibility with the standard S-matrix
picture and recovery of standard structures in Minkowski spacetime under a
limit of vanishing curvature. While there is no complex structure that
satisfies all demands, we emphasize two interesting candidates that satisfy
most: In one case we have to give up part of the isometry invariance, in the
other case the induced inner product is indefinite. | Janus field theories from multiple M2 branes: Based on the recent proposal of N=8 superconformal gauge theories of the
multiple M2 branes, we derive (2+1)-dimensional supersymmetric Janus field
theories with a space-time dependent coupling constant. From the original
Bagger-Lambert model, we get a supersymmetric field theory with a similar
action to the N D2 branes, but the coupling varies with the space-time as a
function of the light-cone coordinate, g(t+x). Half of the supersymmetries can
be preserved. We further investigate the M2 brane action deformed by mass and
Myers-like terms. In this case, the final YM action is deformed by mass and
Myers terms and the coupling behaves as exp(\mu x) where \mu is a constant mass
parameter. Weak coupling gauge theory is continuously changed to strong
coupling in the large x region. |
Magnetic monopole loop for the Yang-Mills instanton: We investigate 't Hooft-Mandelstam monopoles in QCD in the presence of a
single classical instanton configuration. The solution to the Maximal Abelian
projection is found to be a circular monopole trajectory with radius $R$
centered on the instanton. At zero loop radius, there is a marginally stable
(or flat) direction for loop formation to $O(R^4 logR)$. We argue that loops
will form, in the semi-classical limit, due to small perturbations such as the
dipole interaction between instanton anti-instanton pairs. As the instanton gas
becomes a liquid, the percolation of the monopole loops may therefore provide a
semi-classical precursor to the confinement mechanism. | Physical renormalization schemes and asymptotic safety in quantum
gravity: The methods of the renormalization group and the $\varepsilon$-expansion are
applied to quantum gravity revealing the existence of an asymptotically safe
fixed point in spacetime dimensions higher than two. To facilitate this,
physical renormalization schemes are exploited where the renormalization group
flow equations take a form which is independent of the parameterisation of the
physical degrees of freedom (i.e. the gauge fixing condition and the choice of
field variables). Instead the flow equation depends on the anomalous dimensions
of reference observables. In the presence of spacetime boundaries we find that
the required balance between the Einstein-Hilbert action and
Gibbons-Hawking-York boundary term is preserved by the beta functions.
Exploiting the $\varepsilon$-expansion near two dimensions we consider Einstein
gravity coupled to matter. Scheme independence is generically obscured by the
loop-expansion due to breaking of two-dimensional Weyl invariance. In schemes
which preserve two-dimensional Weyl invariance we avoid the loop expansion and
find a unique ultra-violet (UV) fixed point. At this fixed point the anomalous
dimensions are large and one must resum all loop orders to obtain the critical
exponents. Performing the resummation a set of universal scaling dimensions are
found. These scaling dimensions show that only a finite number of matter
interactions are relevant. This is a strong indication that quantum gravity is
renormalizable. |
Existence of Majorana fermions for M-branes wrapped in space and time: We show that it is possible to define Majorana (s)pinor fields on M-branes
which have been identified under the action of the antipodal map on the adS
factor of the throat geometry, or which have been wrapped on two-cycles of
arbitrary genus. This is an important consistency check, since it means that
one may still take the generators of supertranslations in superspace to
transform as Majorana fermions under the adjoint action of $Spin(10,1)$, even
though the antipodally identified M2-brane is {\it not} space-orientable. We
point out that similar conclusions hold for any p-branes which have the generic
(adS)$~{\times}~$(Sphere) throat geometry. | Instantons and Holomorphic Couplings in Intersecting D-brane Models: We clarify certain aspects and discuss extensions of the recently introduced
string D-instanton calculus (hep-th/0609191). The one-loop determinants are
related to one-loop open string threshold corrections in intersecting D6-brane
models. Utilising a non-renormalisation theorem for the holomorphic Wilsonian
gauge kinetic functions, we derive a number of constraints for the moduli
dependence of the matter field Kaehler potentials of intersecting D6-brane
models on the torus. Moreover, we compute string one-loop corrections to the
Fayet-Iliopoulos terms on the D6-branes finding that they are proportional to
the gauge threshold corrections. Employing these results, we discuss the issue
of holomorphy for E2-instanton corrections to the superpotential. Eventually,
we discuss E2-instanton corrections to the gauge kinetic functions and the
FI-terms. |
Quantum Optimal Control Theory: The possibility of control of phenomena at microscopic level compatible with
quantum mechanics and quantum field theory is outlined. The theory could be
used in nanotechnology. | Compact, Singular G2-Holonomy Manifolds and M/Heterotic/F-Theory Duality: We study the duality between M-theory on compact holonomy G2-manifolds and
the heterotic string on Calabi-Yau three-folds. The duality is studied for
K3-fibered G2-manifolds, called twisted connected sums, which lend themselves
to an application of fiber-wise M-theory/Heterotic Duality. For a large class
of such G2-manifolds we are able to identify the dual heterotic as well as
F-theory realizations. First we establish this chain of dualities for smooth
G2-manifolds. This has a natural generalization to situations with non-abelian
gauge groups, which correspond to singular G2-manifolds, where each of the
K3-fibers degenerates. We argue for their existence through the chain of
dualities, supported by non-trivial checks of the spectra. The corresponding 4d
gauge groups can be both Higgsable and non-Higgsable, and we provide several
explicit examples of the general construction. |
The sine-Gordon model in the presence of defects: The sine-Gordon model in the presence of dynamical integrable defects is
investigated. This is an application of the algebraic formulation introduced
for integrable defects in earlier works. The quantities in involution as well
as the associated Lax pairs are explicitly extracted. Integrability i also
shown using certain sewing constraints, which emerge as suitable continuity
conditions. | Supersymmetry, Supercurrent and Scale Invariance: Contents: Generalities, Chiral supermultiplets, Super Yang-Mills theory,
Superspace Feynman graphs, Renormalization, Supercurrent, Finite theories. |
Bimodule structure in the periodic gl(1|1) spin chain: This paper is second in a series devoted to the study of periodic super-spin
chains. In our first paper at 2011, we have studied the symmetry algebra of the
periodic gl(1|1) spin chain. In technical terms, this spin chain is built out
of the alternating product of the gl(1|1) fundamental representation and its
dual. The local energy densities - the nearest neighbor Heisenberg-like
couplings - provide a representation of the Jones Temperley Lieb (JTL) algebra.
The symmetry algebra is then the centralizer of JTL, and turns out to be
smaller than for the open chain, since it is now only a subalgebra of U_q sl(2)
at q=i, dubbed U_q^{odd} sl(2). A crucial step in our associative algebraic
approach to bulk logarithmic conformal field theory (LCFT) is then the analysis
of the spin chain as a bimodule over U_q^{odd} sl(2) and JTL. While our
ultimate goal is to use this bimodule to deduce properties of the LCFT in the
continuum limit, its derivation is sufficiently involved to be the sole subject
of this paper. We describe representation theory of the centralizer and then
use it to find a decomposition of the periodic gl(1|1) spin chain over JTL for
any even number N of tensorands and ultimately a corresponding bimodule
structure. Applications of our results to the analysis of the bulk LCFT will
then be discussed in the third part of this series. | Type IIB at eight derivatives: insights from Superstrings, Superfields
and Superparticles: We study the non-linear structure of Type IIB eight-derivative couplings
involving the metric and the complexified three-form $G_3$. We show that, at
the level of five-point string amplitudes, the kinematics in the maximally
R-symmetry-violating sector is fully matched by standard superspace integrals
and by superparticle amplitudes in M-theory on a two-torus. The latter approach
is used to determine the complete effective action in this sector and to verify
its invariance under SL$(2,\mathbb{Z})$ duality. We further comment on the
general structure of the higher-point kinematics. Compactifications to lower
dimensions provide both tests for our results and the arena for their
applications. We verify that K3 reductions are fully consistent with the
constraints of six-dimensional supersymmetry, and derive the four-dimensional
flux scalar potential and axion kinetic terms at order $(\alpha^{\prime})^{3}$
in Calabi-Yau threefold reductions. |
Conformal Anomaly of String Theory in the Harmonic Gauge: Considering the conformal anomaly in an effective action, the critical
dimension of string theory can be decided in the harmonic gauge, in which it
had been reported before to be indefinite. In this gauge, there is no anomaly
for the ghost number symmetry. This can be naturally understood in terms of
Faddeev-Popov conjugation in the theory. | RG flow of entanglement entropy to thermal entropy: Utilizing the holographic technique, we investigate how the entanglement
entropy evolves along the RG flow. After introducing a new generalized
temperature which satisfies the thermodynamics-like law even in the IR regime,
we find that the renormalized entropy and the generalized temperature in the IR
limit approach the thermal entropy and thermodynamic temperature of a real
thermal system. This result implies that the microscopic quantum entanglement
entropy in the IR region leads to the thermodynamic relation up to small
quantum corrections caused by the quantum entanglement near the entangling
surface. Intriguingly, this IR feature of the entanglement entropy universally
happens regardless of the detail of the dual field theory and the shape of the
entangling surface. We check this IR universality with a most general geometry
called the hyperscaling violation geometry which is dual to a relativistic
non-conformal field theory. |
Positivity Bounds for Scalar Theories: Assuming the existence of a local, analytic, unitary UV completion in a
Poincar\'{e} invariant scalar field theory with a mass gap, we derive an
infinite number of positivity requirements using the known properties of the
amplitude at and away from the forward scattering limit. These take the form of
bounds on combinations of the pole subtracted scattering amplitude and its
derivatives. In turn, these positivity requirements act as constraints on the
operator coefficients in the low energy effective theory. For certain theories
these constraints can be used to place an upper bound on the mass of the next
lightest state that must lie beyond the low energy effective theory if such a
UV completion is to ever exist. | Permutation Branes: N-fold tensor products of a rational CFT carry an action of the permutation
group S_N. These automorphisms can be used as gluing conditions in the study of
boundary conditions for tensor product theories. We present an ansatz for such
permutation boundary states and check that it satisfies the cluster condition
and Cardy's constraints. For a particularly simple case, we also investigate
associativity of the boundary OPE, and find an intriguing connection with the
bulk OPE. In the second part of the paper, the constructions are slightly
extended for application to Gepner models. We give permutation branes for the
quintic, together with some formulae for their intersections. |
On the asymptotic states and the quantum S matrix of the $η$-deformed
$AdS_5\times S^5$ superstring: We investigate the worldsheet S matrix of string theory in $\eta$-deformed
$AdS_5\times S^5$. By computing the six-point tree-level S matrix we explicitly
show that there is no particle production at this level, as required by the
classical integrability of the theory. At one and two loops we show that
integrability requires that the classical two-particle states be redefined in a
non-local and $\eta$-dependent way. This is a significant departure from the
undeformed theory which is probably related to the quantum group symmetry of
the worldsheet theory. We use generalized unitarity to carry out the loop
calculations and identify a set of integrals that allow us to give a two-loop
Feynman integral representation of the logarithmic terms of the two-loop S
matrix. We finally also discuss aspects of the calculation of the two-loop
rational terms. | Non-commutative flux representation for loop quantum gravity: The Hilbert space of loop quantum gravity is usually described in terms of
cylindrical functionals of the gauge connection, the electric fluxes acting as
non-commuting derivation operators. It has long been believed that this
non-commutativity prevents a dual flux (or triad) representation of loop
quantum gravity to exist. We show here, instead, that such a representation can
be explicitly defined, by means of a non-commutative Fourier transform defined
on the loop gravity state space. In this dual representation, flux operators
act by *-multiplication and holonomy operators act by translation. We describe
the gauge invariant dual states and discuss their geometrical meaning. Finally,
we apply the construction to the simpler case of a U(1) gauge group and compare
the resulting flux representation with the triad representation used in loop
quantum cosmology. |
End of the World Branes from Dimensional Reduction: We consider dimensional reduction of cigar geometries which are obtained by a
Wick rotation of black hole solutions. Originally the cigar geometry is smooth
around the tip, but after the dimensional reduction along the Euclidean time
direction, there appears an end-of-the-world brane (ETW brane). We derive the
tension of the brane by two methods: bulk equations of motion and boundary
equations of motion. In particular, for AdS7-soliton cross S4 and AdS4-soliton
cross S7 backgrounds in M-theory, we find that the tension of the emerging ETW
branes behaves as exp(-3Phi) in the string frame. This indicates the existence
of such ETW branes in the strongly coupled regime of type 0A string theory. | 3-Cocycles and the Operator Product Expansion: Anomalous contributions to the Jacobi identity of chromo-electric fields and
non-Abelian vector currents are calculated using a non-perturbative approach
that combines operator product expansion and a generalization of
Bjorken-Johnson-Low limit. The failure of the Jacobi identity and the
associated 3-cocycles are discussed. |
Infrared Effects and the Soft Photon Theorem in Massive QED: Stueckelberg QED with massive photon is known to be renormalizable. But the
limit of the mass going to zero is interesting because it brings the resolution
to infrared questions through the role of Stueckelberg field at null infinity
in addition to providing new asymptotic symmetries. Such symmetries facilitate
the soft photon theorems also. | Spinning particles and higher spin field equations: Relativistic particles with higher spin can be described in first
quantization using actions with local supersymmetry on the worldline. First, we
present a brief review of these actions and their use in first quantization. In
a Dirac quantization scheme the field equations emerge as Dirac constraints on
the Hilbert space, and we outline how they lead to the description of higher
spin fields in terms of the more standard Fronsdal-Labastida equations. Then,
we describe how these actions can be extended so that the propagating particle
is allowed to take different values of the spin, i.e. carry a reducible
representation of the Poincar\'e group. This way one may identify a four
dimensional model that carries the same degrees of freedom of the minimal
Vasiliev's interacting higher spin field theory. Extensions to massive
particles and to propagation on (A)dS spaces are also briefly commented upon. |
Gauge Theory and Integrability, I: Several years ago, it was proposed that the usual solutions of the
Yang-Baxter equation associated to Lie groups can be deduced in a systematic
way from four-dimensional gauge theory. In the present paper, we extend this
picture, fill in many details, and present the arguments in a concrete and
down-to-earth way. Many interesting effects, including the leading nontrivial
contributions to the $R$-matrix, the operator product expansion of line
operators, the framing anomaly, and the quantum deformation that leads from
$\mathfrak{g}[[z]]$ to the Yangian, are computed explicitly via Feynman
diagrams. We explain how rational, trigonometric, and elliptic solutions of the
Yang-Baxter equation arise in this framework, along with a generalization that
is known as the dynamical Yang-Baxter equation. | Perturbation Theory for the Logarithm of a Positive Operator: In various contexts in mathematical physics one needs to compute the
logarithm of a positive unbounded operator. Examples include the von Neumann
entropy of a density matrix and the flow of operators with the modular
Hamiltonian in the Tomita-Takesaki theory. Often, one encounters the situation
where the operator under consideration, that we denote by $\Delta$, can be
related by a perturbative series to another operator $\Delta_0$, whose
logarithm is known. We set up a perturbation theory for the logarithm $\log
\Delta$. It turns out that the terms in the series possess remarkable algebraic
structure, which enable us to write them in the form of nested commutators plus
some "contact terms." |
Complexified path integrals, exact saddles and supersymmetry: In the context of two illustrative examples from supersymmetric quantum
mechanics we show that the semi-classical analysis of the path integral
requires complexification of the configuration space and action, and the
inclusion of complex saddle points, even when the parameters in the action are
real. We find new exact complex saddles, and show that without their
contribution the semi-classical expansion is in conflict with basic properties
such as positive-semidefiniteness of the spectrum, and constraints of
supersymmetry. Generic saddles are not only complex, but also possibly
multi-valued, and even singular. This is in contrast to instanton solutions,
which are real, smooth, and single-valued. The multi-valuedness of the action
can be interpreted as a hidden topological angle, quantized in units of $\pi$
in supersymmetric theories. The general ideas also apply to non-supersymmetric
theories. | M(atrix) Theory on the Negative Light-Front: M(atrix) theory defines light-front description of M-theory boosted along
positive direction of eleventh, M-coordinate. Rank of M(atrix) gauge group is
directly related to M-momentum $P_{11} = N / R_{11}$ or, equivalently, to total
number of D0-partons. Alternatively, M-theory may be boosted along opposite
direction of M-coordinate, for which the theory consists only of anti-D0
partons. In M(atrix) theory description, we interpret this as analytic
continuation of dimension of the gauge group: $U(-N) \sim U(N)$, $SO(-2N) \sim
USp(2N)$ and $USp(-2N) \sim SO(2N)$. We check these reciprocity relations
explicitly for uncompactified, heterotic, and CHL M(atrix) theories as well as
effective M(atrix) gauge theories of $T_5/Z_2$ and $T_9/Z_2$ compactifications.
In all cases, we show that absence of parity, gauge and supersymmetry anomalies
require introduction of a twisted sector with negative numbers of matter
multiplets. They are interpreted as massless open string excitations connected
to anti-D-brane background. |
AdS$_5$ vacua from type IIB supergravity on $T^{1,1}$: We study maximally supersymmetric Anti-de Sitter backgrounds in consistent
N=2 truncations of type IIB supergravity compactified on the Sasaki-Einstein
manifold $T^{1,1}$. In particular, we focus on truncations that contain fields
coming from the nontrivial second and third cohomology forms on $T^{1,1}$.
These give rise to N=2 supergravity coupled to two vector- and two
hypermultiplets (Betti-vector truncation) or one vector- and three
hypermultiplets (Betti-hyper truncation), respectively. We find that both
truncations admit AdS$_5$ backgrounds with the gauge group always being broken
but containing at least an $U(1)_R$ factor. Moreover, in both cases we show
that the moduli space of AdS vacua is nontrivial and of maximal dimension.
Finally, we explicitly compute the metrics on these moduli spaces. | Supersymmetric Field Theories on Three-Manifolds: We construct supersymmetric field theories on Riemannian three-manifolds M,
focusing on N=2 theories with a U(1)_R symmetry. Our approach is based on the
rigid limit of new minimal supergravity in three dimensions, which couples to
the flat-space supermultiplet containing the R-current and the energy-momentum
tensor. The field theory on M possesses a single supercharge, if and only if M
admits an almost contact metric structure that satisfies a certain
integrability condition. This may lead to global restrictions on M, even though
we can always construct one supercharge on any given patch. We also analyze the
conditions for the presence of additional supercharges. In particular, two
supercharges of opposite R-charge exist on every Seifert manifold. We present
general supersymmetric Lagrangians on M and discuss their flat-space limit,
which can be analyzed using the R-current supermultiplet. As an application, we
show how the flat-space two-point function of the energy-momentum tensor in N=2
superconformal theories can be calculated using localization on a squashed
sphere. |
Non-Abelian Einstein-Born-Infeld Black Holes: We construct regular and black hole solutions in SU(2) Einstein-Born-Infeld
theory. These solutions have many features in common with the corresponding
SU(2) Einstein-Yang-Mills solutions. In particular, sequences of neutral
non-abelian solutions tend to magnetically charged limiting solutions, related
to embedded abelian solutions. Thermodynamic properties of the black hole
solutions are addressed. | Phases in noncommutative quantum mechanics on (pseudo)sphere: We compare the non-commutative quantum mechanics (NCQM) on sphere and the
discrete part of the spectrum of NCQM on pseudosphere (Lobachevsky plane, or
$AdS_2$) in the presence of a constant magnetic field $B$ with planar NCQM. We
show, that (pseudo)spherical NCQM has a ``critical point'', where the system
becomes effectively one-dimensional, and two different ``phases'', which the
phases of the planar system originate from, specified by the sign of the
parameter $\kappa=1-B\theta$. The ``critical point'' of (pseudo)spherical NCQM
corresponds to the $\kappa\to\infty $ point of conventional planar NCQM, and to
the ``critical point'' $\kappa=0$ of the so-called ``exotic'' planar NCQM, with
a symplectic coupling of the (commutative) magnetic field. |
Geometry and Topology of Anti-BRST Symmetry in Quantized Yang-Mills
Gauge Theories: The entire geometric formulations of the BRST and the anti-BRST structures
are worked out in presence of the Nakanishi-Lautrup field. It is shown that in
the general form of gauge fixing mechanisms within the Faddeev-Popov
quantization approach, the antiBRST invariance reflects thoroughly the
classical symmetry of the Yang-Mills theories with respect to gauge fixing
methods. The Nakanishi-Lautrup field is also defined and worked out as a
geometric object. This formulation helps us to introduce two absolutely new
topological invariants of quantized Yang-Mills theories, so called the
Nakanishi-Lautrup invariants. The cohomological structure of the anti-BRST
symmetry is also studied and the anti-BRST topological index is derived
accordingly. | Ryu-Takayanagi Area as an Entanglement Edge Term: By comparing entanglement in emergent gauge theories to the bulk in AdS/CFT,
I suggest that the Ryu-Takayanagi area term is an entanglement edge term
related to a natural measure on the gauge group. The main technical result in
this paper is an argument why the "extended Hilbert space" definition of
entanglement entropy in a lattice gauge theory is applicable to an emergent
gauge theory. |
WKB Method and Quantum Periods beyond Genus One: We extend topological string methods in order to perform WKB approximations
for quantum mechanical problems with higher order potentials efficiently. This
requires techniques for the evaluation of the relevant quantum periods for
Riemann surfaces beyond genus one. The basis of these quantum periods is fixed
using the leading behaviour of the classical periods. The full expansion of the
quantum periods is obtained using a system of Picard-Fuchs like operators for a
sequence of integrals of meromorphic forms of the second kind. Discrete
automorphisms of simple higher order potentials allow to view the corresponding
higher genus curves as covering of a genus one curve. In this case the quantum
periods can be alternatively obtained using the holomorphic anomaly solved in
the holomorphic limit within the ring of quasi modular forms of a congruent
subgroup of SL$(2,\mathbb{Z})$ as we check for a symmetric sextic potential. | Gravitational fields on a noncommutative space: Noncommutative three-dimensional gravity can be described in terms of a
noncommutative Chern-Simons theory. We extend this structure and also propose
an action for gravitational fields on an even dimensional noncommutative space.
The action is worked out in some detail for fields on a noncommutative ${\bf
CP}^2$ and on $S^4$. |
Taming Nonrenormalizability: Nonrenormalizable scalar fields, such as \varphi^4_n, n\ge5, require
infinitely many distinct counter terms when perturbed about the free theory,
and lead to free theories when defined as the continuum limit of a lattice
regularized theory restricted only to arbitrary mass and coupling constant
renormalization. Based on the proposal that functional integrals for
interacting nonrenormalizable models do not reduce to the expression for the
free field functional integral as the coupling constant vanishes -- a proposal
supported by the fact that even the set of classical solutions for such models
does not reduce to the set of free field solutions as the coupling constant
vanishes -- it has been conjectured that for nonrenormalizable models the
interaction term acts partially as a hard core eliminating certain fields
otherwise allowed by the free theory. As a consequence, interacting models are
continuously connected to a pseudofree theory that takes into account the hard
core as the coupling constant vanishes, and this general view is supported not
only by simple quantum mechanical examples as well as soluble but
nonrelativistic nonrenormalizable models. The present article proposes a
pseudofree model for relativistic nonrenormalizable models about which it is
argued that a perturbation expansion of the interaction is term-by-term
divergence free. | Late-time Evolution of a Charged Massless Scalar Field in the Spacetime
of a Dilaton Black Hole: We investigate the power-law tails in the evolution of a charged massless
scalar field around a fixed background of a dilaton black hole. Using both
analytical and numerical methods we find the inverse power-law relaxation of
charged fields at future timelike infinity, future null infinity, and along the
outer horizon of the considered black hole. We invisage that a charged hair
decays slower than neutral ones. The oscillatory inverse power law along the
outer horizon of the dilaton black hole is of a great importance for a mass
inflation scenario along the Cauchy horizon of a dynamically formed dilaton
black hole. |
General Metrics of G_2 Holonomy and Contraction Limits: We obtain first-order equations for G_2 holonomy of a wide class of metrics
with S^3\times S^3 principal orbits and SU(2)\times SU(2) isometry, using a
method recently introduced by Hitchin. The new construction extends previous
results, and encompasses all previously-obtained first-order systems for such
metrics. We also study various group contractions of the principal orbits,
focusing on cases where one of the S^3 factors is subjected to an Abelian,
Heisenberg or Euclidean-group contraction. In the Abelian contraction, we
recover some recently-constructed G_2 metrics with S^3\times T^3 principal
orbits. We obtain explicit solutions of these contracted equations in cases
where there is an additional U(1) isometry. We also demonstrate that the only
solutions of the full system with S^3\times T^3 principal orbits that are
complete and non-singular are either flat R^4 times T^3, or else the direct
product of Eguchi-Hanson and T^3, which is asymptotic to R^4/Z_2\times T^3.
These examples are in accord with a general discussion of isometric fibrations
by tori which, as we show, in general split off as direct products. We also
give some (incomplete) examples of fibrations of G_2 manifolds by associative
3-tori with either T^4 or K3 as base. | Crossing Symmetry for Long Multiplets in 4D $\mathcal{N}=1$ SCFTs: In this work we construct the crossing symmetry equations for mixed
correlators of two long and two BPS operators in 4D $\mathcal{N}=1$ SCFTs. The
analysis presented here illustrates how our general group theoretic approach to
long superblocks and tensor structures of superconformal algebras can be
applied to give explicit ready-to-use expressions. In the case at hand, we
obtain a system of four crossing symmetry equations for the relevant OPE
coefficients. One of these four equations coincides with the equation found and
analysed by Li, Meltzer and Stergiou by restricting to the superprimary
component of the long multiplets. The other three equations are new and they
provide powerful additional constraints on the same OPE data. |
On Semi-Classical States of Quantum Gravity and Noncommutative Geometry: We construct normalizable, semi-classical states for the previously proposed
model of quantum gravity which is formulated as a spectral triple over holonomy
loops. The semi-classical limit of the spectral triple gives the Dirac
Hamiltonian in 3+1 dimensions. Also, time-independent lapse and shift fields
emerge from the semi-classical states. Our analysis shows that the model might
contain fermionic matter degrees of freedom.
The semi-classical analysis presented in this paper does away with most of
the ambiguities found in the initial semi-finite spectral triple construction.
The cubic lattices play the role of a coordinate system and a divergent
sequence of free parameters found in the Dirac type operator is identified as a
certain inverse infinitesimal volume element. | M-Theory Superalgebra From Multiple Membranes: We investigate space-time supersymmetry of the model of multiple M2-branes
proposed by Bagger-Lambert and Gustavsson. When there is a central element in
Lie 3-algebra, the model possesses an extra symmetry shifting the fermions in
the central element. Together with the original worldvolume supersymmetry
transformation, we construct major part of the eleven dimensional space-time
super-Poincar\'{e} algebra with central extensions. Implications to transverse
five-branes in the matrix model for M-theory are also discussed. |
Non-Relativistic Supersymmetry on Curved Three-Manifolds: We construct explicit examples of non-relativistic supersymmetric field
theories on curved Newton-Cartan three-manifolds. These results are obtained by
performing a null reduction of four-dimensional supersymmetric field theories
on Lorentzian manifolds and the Killing spinor equations that their
supersymmetry parameters obey. This gives rise to a set of algebraic and
differential Killing spinor equations that are obeyed by the supersymmetry
parameters of the resulting three-dimensional non-relativistic field theories.
We derive necessary and sufficient conditions that determine whether a
Newton-Cartan background admits non-trivial solutions of these Killing spinor
equations. Two classes of examples of Newton-Cartan backgrounds that obey these
conditions are discussed. The first class is characterised by an integrable
foliation, corresponding to so-called twistless torsional geometries, and
includes manifolds whose spatial slices are isomorphic to the Poincar\'e disc.
The second class of examples has a non-integrable foliation structure and
corresponds to contact manifolds. | Calculations of Delbrück scattering to all orders in $αZ$: We present a theoretical method to calculate Delbr\"uck scattering
amplitudes. Our formalism is based on the exact analytical Dirac-Coulomb
Green's function and, therefore, accounts for the interaction of the virtual
electron-positron pair with the nucleus to all orders, including the Coulomb
corrections. The numerical convergence of our calculations is accelerated by
solving the radial integrals that are involved analytically in the asymptotic
region. Numerical results for the collision of photons with energies 102.2 keV
and 255.5 keV with bare neon and lead nuclei are compared with the predictions
of the lowest-order Born approximation. We find that our method can produce
accurate results within a reasonable computation time and that the Coulomb
corrections enhance the absolute value of the Delbr\"uck amplitude by a few
percent for the studied photon energies. |
Complete nonlinear action for supersymmetric multiple D$0$-brane system: We present a complete nonlinear action for the dynamical system of nearly
coincident multiple D$0$-branes (mD$0$) which possesses, besides manifest
spacetime (target superspace) supersymmetry, also the worldline supersymmetry,
a counterpart of the local fermionic $\kappa$-symmetry of single D$0$-brane
(Dirichlet superparticle). The action contains an arbitrary non-vanishing
function ${\cal M}({\cal H})$ of the relative motion Hamiltonian ${\cal H}$.
The $D=10$ mD$0$ model with particular form of ${\cal M}({\cal H})$ can be
obtained by dimensional reduction from the action of eleven-dimensional
($D=11$) multiple M-wave (mM$0$) system. | Generalized N=2 Supersymmetric Toda Field Theories: In this paper we introduce a class of generalized supersymmetric Toda field
theories. The theories are labeled by a continuous parameter and have $N=2$
supersymmetry. They include previously known $N=2$ Toda theories as special
cases. Using the WZNW -->Toda reduction approach we obtain a closed expression
for the bracket of the associated ${\cal W}$ algebras. We also derive an
expression for the generators of the ${\cal W}$ algebra in a free superfield
realization. |
Cosmic Inflation: The Most Powerful Microscope in the Universe: How well can we constrain the initial quantum state of metric perturbations
sourced during inflation? We exhibit an interesting new class of quantum states
that entangle the scalar metric perturbations {\zeta} with other fields such as
scalars as well as the tensor metric perturbations hij. These states are
theoretically consistent, for inflation that lasts close to its minimum number
of e-folds. They give distinguishable signatures in the power spectrum and may
be able to explain some long-standing anomalies in the CMB power spectrum. We
advocate using a generalized effective theory of quantum states (of which our
work is an example) that, using inflation as a powerful microscope, could
provide deep insights into the quantum state of matter on the smallest scales. | A loop of SU(2) gauge fields stable under the Yang-Mills flow: The gradient flow of the Yang-Mills action acts pointwise on closed loops of
gauge fields. We construct a topologically nontrivial loop of SU(2) gauge
fields on S4 that is locally stable under the flow. The stable loop is written
explicitly as a path between two gauge fields equivalent under a topologically
nontrivial SU(2) gauge transformation. Local stability is demonstrated by
calculating the flow equations to leading order in perturbations of the loop.
The stable loop might play a role in physics as a classical winding mode of the
lambda model, a 2-d quantum field theory that was proposed as a mechanism for
generating spacetime quantum field theory. We also present evidence for
2-manifolds of SU(2) and SU(3) gauge fields that are stable under the
Yang-Mills flow. These might provide 2-d instanton corrections in the lambda
model. For Isidore M. Singer in celebration of his eighty-fifth birthday. |
Topologically protected qubits as minimal Josephson junction arrays with
non trivial boundary conditions: a proposal: Recently a one-dimensional closed ladder of Josephson junctions has been
studied (G. Cristofano et al., Phys. Lett. A 372 (2008) 2464) within a twisted
conformal field theory (CFT) approach (G. Cristofano et al., Mod. Phys. Lett. A
15 (2000) 1679; Nucl. Phys. B 641 (2002) 547) and shown to develop the
phenomenon of flux fractionalization (G. Cristofano et al., Eur. Phys. J. B 49
(2006) 83). That led us to predict the emergence of a topological order in such
a system (G. Cristofano et al., JSTAT (2005) P03006). In this letter we analyze
the ground states and the topological properties of fully frustrated Josephson
junction arrays (JJA) arranged in a Corbino disk geometry for a variety of
boundary conditions. In particular minimal configurations of fully frustrated
JJA are considered and shown to exhibit the properties needed in order to build
up a solid state qubit, protected from decoherence. The stability and
transformation properties of the ground states of the JJA under adiabatic
magnetic flux changes are analyzed in detail in order to provide a tool for the
manipulation of the proposed qubit. | Standard Model from A Supergravity Model with a Naturally Small
Cosmological Constant: Guided by the naturalness criterion for an exponentially small cosmological
constant, we present a string theory motivated 4-dimensional $\mathcal{N}=1$
non-linear supergravity model (or its linear version with a nilpotent
superfield) with spontaneous supersymmetry breaking. The model encompasses the
minimal supersymmetric standard model, the racetrack K\"ahler uplift, and the
KKLT anti-$\rm D3$-branes, and use the nilpotent superfield to project out the
undesirable interaction terms as well as the unwanted degrees of freedom to end
up with the standard model (not the supersymmetric version) of strong and
electroweak interactions. |
Multi-instantons in minimal string theory and in matrix integrals: We compute the normalization of the general multi-instanton contribution to
the partition function of $(p',p)$ minimal string theory and also to the dual
two-matrix integral. We find perfect agreement between the two results. | Bounds in 4D Conformal Field Theories with Global Symmetry: We explore the constraining power of OPE associativity in 4D Conformal Field
Theory with a continuous global symmetry group. We give a general analysis of
crossing symmetry constraints in the 4-point function <Phi Phi Phi* Phi*>,
where Phi is a primary scalar operator in a given representation R. These
constraints take the form of 'vectorial sum rules' for conformal blocks of
operators whose representations appear in R x R and R x Rbar. The coefficients
in these sum rules are related to the Fierz transformation matrices for the R x
R x Rbar x Rbar invariant tensors. We show that the number of equations is
always equal to the number of symmetry channels to be constrained. We also
analyze in detail two cases - the fundamental of SO(N) and the fundamental of
SU(N). We derive the vectorial sum rules explicitly, and use them to study the
dimension of the lowest singlet scalar in the Phi x Phi* OPE. We prove the
existence of an upper bound on the dimension of this scalar. The bound depends
on the conformal dimension of Phi and approaches 2 in the limit dim(Phi)-->1.
For several small groups, we compute the behavior of the bound at dim(Phi)>1.
We discuss implications of our bound for the Conformal Technicolor scenario of
electroweak symmetry breaking. |
Can the clustered dark matter and the smooth dark energy arise from the
same scalar field ?: Cosmological observations suggest the existence of two different kinds of
energy densities dominating at small ($ \lesssim 500$ Mpc) and large ($\gtrsim
1000 $ Mpc) scales. The dark matter component, which dominates at small scales,
contributes $\Omega_m \approx 0.35$ and has an equation of state $p=0$ while
the dark energy component, which dominates at large scales, contributes
$\Omega_V \approx 0.65$ and has an equation of state $p\simeq -\rho$. It is
usual to postulate wimps for the first component and some form of scalar field
or cosmological constant for the second component. We explore the possibility
of a scalar field with a Lagrangian $L =- V(\phi) \sqrt{1 - \del^i \phi \del_i
\phi}$ acting as {\it both} clustered dark matter and smoother dark energy and
having a scale dependent equation of state. This model predicts a relation
between the ratio $ r = \rho_V/\rho_{\rm DM}$ of the energy densities of the
two dark components and expansion rate $n$ of the universe (with $a(t) \propto
t^n$) in the form $n = (2/3) (1+r) $. For $r \approx 2$, we get $n \approx 2$
which is consistent with observations. | SL(2,R) matrix model and supersymmetric Yang-Mills integrals: The density of states of Yang-Mills integrals in the supersymmetric case is
characterized by power-law tails whose decay is independent of N, the rank of
the gauge group. It is believed that this has no counterpart in matrix models,
but we construct a matrix model that exactly exhibits this property. In
addition, we show that the eigenfunctions employed to construct the matrix
model are invariant under the collinear subgroup of conformal transformations,
SL(2,R). We also show that the matrix model itself is invariant under a
fractional linear transformation. The wave functions of the model appear in the
trigonometric Rosen-Morse potential and in free relativistic motion on AdS
space. |
Dynamical Behavior of the BTZ Black Hole: We study the dynamical behavior of the BTZ (Banados-Teitelboim-Zanelli) black
hole with the low-energy string effective action. The perturbation analysis
around the BTZ black hole reveals a mixing between the dilaton and other
fields. Introducing the new gauge (dilaton gauge), we disentangle this mixing
completely and obtain one decoupled dilaton equation. We obtain the decay rate
$\Gamma$ of BTZ black hole. | On holographic thermalization and gravitational collapse of tachyonic
scalar fields: In this paper we study the thermalization of a spatially homogeneous system
in a strongly coupled CFT. The non-equilibrium initial state is created by
switching on a relevant perturbation in the CFT vacuum during Delta t >= t >=
-Delta t. Via AdS/CFT, the thermalization process corresponds to the
gravitational collapse of a tachyonic scalar field (m^2 = -3) in the Poincare
patch of AdS_5. In the limit Delta t < 0.02/T, the thermalization time t_T is
found to be quantitatively the same as that of a non-equilibrium state created
by a marginal perturbation discussed in Ref. [5]. In the case Delta t >= 1/T,
we also obtain double-collapse solutions but with a non-equilibrium
intermediate state at t = 0. In all the cases our results show that the system
thermalizes in a typical time t_T ~ O(1)/T. Besides, a conserved energy-moment
current in the bulk is found, which helps understand the qualitative difference
of the collapse process in the Poincare patch from that in global AdS[9, 10]. |
Entanglement entropy of linearized gravitons in a sphere: We compute the entanglement entropy of a massless spin $2$ field in a sphere
in flat Minkowski space. We describe the theory with a linearized metric
perturbation field $h_{\mu\nu}$ and decompose it in tensor spherical harmonics.
We fix the gauge such that a) the two dynamical modes for each angular momentum
decouple and have the dynamics of scalar spherical modes, and b) the
gauge-fixed field degrees of freedom inside the sphere represent gauge
invariant operators of the theory localized in the same region. In this way the
entanglement entropy turns out to be equivalent to the one of a pair of free
massless scalars where the contributions of the $l=0$ and $l=1$ modes have been
subtracted. The result for the coefficient of the universal logarithmic term is
$-61/45$ and coincides with the one computed using the mutual information. | Non-Relativistic Gravitation: From Newton to Einstein and Back: We present an improvement to the Classical Effective Theory approach to the
non-relativistic or Post-Newtonian approximation of General Relativity. The
"potential metric field" is decomposed through a temporal Kaluza-Klein ansatz
into three NRG-fields: a scalar identified with the Newtonian potential, a
3-vector corresponding to the gravito-magnetic vector potential and a 3-tensor.
The derivation of the Einstein-Infeld-Hoffmann Lagrangian simplifies such that
each term corresponds to a single Feynman diagram providing a clear physical
interpretation. Spin interactions are dominated by the exchange of the
gravito-magnetic field. Leading correction diagrams corresponding to the 3PN
correction to the spin-spin interaction and the 2.5PN correction to the
spin-orbit interaction are presented. |
Manifest causality in quantum field theory with sources and detectors: We introduce a way to compute scattering amplitudes in quantum field theory
including the effects of particle production and detection. Our amplitudes are
manifestly causal, by which we mean that the source and detector are always
linked by a connected chain of retarded propagators. We show how these
amplitudes can be derived from a path integral, using the Schwinger-Keldysh
"in-in" formalism. Focussing on phi-cubed theory, we confirm that our approach
agrees with the standard S-matrix approach in the case of positive energy
plane-wave scattering. | Liouville-like solutions in dilaton gravity with Gauss-Bonnet
modifications: We investigate nonperturbative dilatonic solutions of the wide class of the
modified gravity models including the Gauss-Bonnet terms with a general $F(G)$
Lagrangian. We show that presence of the Liouville-like solutions is a
characteristic feature of these models. |
The World in a Grain of Sand: Condensing the String Vacuum Degeneracy: We propose a novel approach toward the vacuum degeneracy problem of the
string landscape, by finding an efficient measure of similarity amongst
compactification scenarios. Using a class of some one million Calabi-Yau
manifolds as concrete examples, the paradigm of few-shot machine-learning and
Siamese Neural Networks represents them as points in R(3) where the similarity
score between two manifolds is the Euclidean distance between their R(3)
representatives. Using these methods, we can compress the search space for
exceedingly rare manifolds to within one percent of the original data by
training on only a few hundred data points. We also demonstrate how these
methods may be applied to characterize `typicality' for vacuum representatives. | Holography Principle and Topology Change in String Theory: D-instantons of Type IIB string theory are Ramond-Ramond counterpart of
Giddings-Strominger wormholes connecting two asymptotic regions of spacetime.
Such wormholes, according to Coleman, might lead to spacetime topology change,
third-quantized baby universes and probabilistic determination of fundamental
coupling parameters. Utilizing correspondence between AdS5 x M5 Type IIB
supergravity and d=4 super Yang-Mills theory, we point out that topology change
and sum over topologies not only take place in string theory but also are
required for consistency with holography. Nevertheless, the effects of
D-instanton wormholes remain completely deterministic, in sharp contrast to
Coleman's scenario. |
Spontaneous CP violation and symplectic modular symmetry in Calabi-Yau
compactifications: We explore the geometrical origin of CP and the spontaneous CP violation in
Calabi-Yau compactifications. We find that the CP symmetry is identified with
an outer automorphism of the symplectic modular group in the large complex
structure regime of Calabi-Yau threefolds, thereby enlarging the symplectic
modular group to their semidirect product group. The spontaneous CP violation
is realized by the introduction of fluxes, whose effective action is invariant
under CP as well as the discrete $\mathbb{Z}_2$ symmetry or $\mathbb{Z}_4$
R-symmetry. We explicitly demonstrate the spontaneous CP violation on a
specific Calabi-Yau threefold. | Noncritical Einstein-Weyl Gravity and the AdS/CFT Correspondence: We explore four-dimensional Einstein-Weyl gravity and supergravity on anti-de
Sitter spacetime. For a specific range of the coupling with appropriate
boundary conditions, we show the effective equivalence of the theory with
Einstein gravity and AdS supergravity at the quadratic Lagrangian level.
Furthermore we show that these equivalences can be promoted to the full
nonlinear level. We also show that the similar behavior holds for the
generalized Gibbons-Hawking terms. From this we find that the correlation
functions in the dual conformal field theory of Einstein-Weyl gravity and
supergravity can be readily read off from corresponding ones from Einstein
gravity and AdS supergravity. We also give comments on some issues in critical
gravity and supergravity as well as conformal gravity and supergravity. |
Quasinormal modes of large AdS black holes: We develop a perturbative approach to the solution of the scalar wave
equation for a large AdS black hole. In three dimensions, our method coincides
with the known exact solution. We discuss the five-dimensional case in detail
and apply our procedure to the Heun equation. We calculate the quasi-normal
modes analytically and obtain good agreement with numerical results for the
low-lying frequencies. | Unitarity bounds and RG flows in time dependent quantum field theory: We generalize unitarity bounds on operator dimensions in conformal field
theory to field theories with spacetime dependent couplings. Below the energy
scale of spacetime variation of the couplings, their evolution can strongly
affect the physics, effectively shifting the infrared operator scaling and
unitarity bounds determined from correlation functions in the theory. We
analyze this explicitly for large-$N$ double-trace flows, and connect these to
UV complete field theories. One motivating class of examples comes from our
previous work on FRW holography, where this effect explains the range of
flavors allowed in the dual, time dependent, field theory. |
New non-supersymmetric flux vacua from generalised calibrations: We construct a new class of non-supersymmetric ten-dimensional type II flux
vacua, by studying first order differential equations which are deformations of
the $\mathcal{N}=1$ supersymmetry conditions. We do so within the context of
Generalised Complex Geometry, where there is a natural interpretation of the
$\mathcal{N}=1$ supersymmetry conditions in terms of calibration conditions for
probe D-branes, called D-string, domain-wall or space-filling branes, depending
on them wrapping two, three or four non-compact dimensions. We focus on the
class of non-supersymmetric vacua violating the D-string calibration condition,
and write down their general equations of motion in the language of pure
spinors. We solve them for a subclass of vacua, where the deformation of the
calibration condition is dictated by the foliated geometry of the internal
space. We also construct backgrounds violating both the domain-wall and
D-string calibration conditions, generalising the one-parameter DWSB class of
backgrounds introduced in L\"ust et al. We present several explicit solutions
with SU$(2)$ and SU$(3)$ structures, and we investigate briefly their
associated low energy effective theories. | The Quantum Yang Baxter conditions: The fundamental relations behind the
Nambu-Goldstone theorem: We demonstrate that when there is spontaneous symmetry breaking in any
system, relativistic or non-relativistic, the dynamic of the Nambu-Goldstone
bosons is governed by the Quantum Yang-Baxter equations. These equations
describe the triangular dynamical relations between pairs of Nambu-Goldstone
bosons and the degenerate vacuum. We then formulate a theorem and a corollary
showing that these relations guarantee the appropriate dispersion relation and
the appropriate counting for the Nambu-Goldstone bosons. |
Thermodynamics of accelerated fermion gas and instability at Unruh
temperature: We demonstrate that the energy density of an accelerated fermion gas
evaluated within quantum statistical approach in Minkowski space is related to
a quantum correction to the vacuum expectation value of the energy-momentum
tensor in a space with non-trivial metric and conical singularity. The key
element of the derivation is the existence of a novel class of polynomial
Sommerfeld integrals. The emerging duality of quantum statistical and
geometrical approaches is explicitly checked at temperatures $T$ above or equal
to the Unruh temperature $T_U$. Treating the acceleration as an imaginary part
of the chemical potential allows for an analytical continuation to temperatures
$T<T_U$ . There is a discontinuity at $T=T_U$ manifested in the second
derivative of the energy density with respect to the temperature. Moreover,
energy density becomes negative at $T<T_U$, apparently indicating some
instability. Obtained results might have phenomenological implications for the
physics of heavy-ion collisions. | Self-accelerating Massive Gravity: Covariant Perturbation Theory: We undertake a complete and covariant treatment for the quadratic Lagrangian
of all of the degrees of freedom of massive gravity with a fixed flat fiducial
metric for arbitrary massive gravity parameters around any isotropic
self-accelerating background solution. Generically, 3 out of 4 Stuckelberg
degrees of freedom propagate in addition to the usual 2 tensor degrees of
freedom of general relativity. The complete kinetic structure typically is only
revealed at an order in the graviton mass that is equivalently to retaining
curvature terms in a locally flat expansion. These results resolve several
apparent discrepancies in the literature where zero degrees of freedom
propagate in either special cases or approximate treatments as well as
decoupling limit analyses which attempt to count longitudinal degrees of
freedom. |
Geometrothermodynamics of Myers-Perry black holes: We consider the thermodynamics and Geometrothermodynamics of the Myers-Perry
black holes in five dimensions for three different cases, depending on the
values of the angular momenta. We follow Davies approach to study the
thermodynamics of black holes and find a non-trivial thermodynamic structure in
all cases, which is fully reproduced by the analysis performed with the
techniques of Geometrothermodynamics. Moreover, we observe that in the cases
when only one angular momentum is present or the two angular momenta are fixed
to be equal, i.e. when the thermodynamic system is two dimensional, there is a
complete agreement between the divergences of the generalized susceptibilities
and the singularities of the equilibrium manifold, whereas when the two angular
momenta are fully independent, that is, when the thermodynamic system is three
dimensional, additional singularities in the curvature appear. However, we
prove that such singularities are due to the changing from a stable phase to an
unstable one. | (2,0) Chern-Simons Supergravity Plus Matter Near the Boundary of AdS_3: We examine the boundary behaviour of the gauged N=(2,0) supergravity in D=3
coupled to an arbitrary number of scalar supermultiplets which parametrize a
Kahler manifold. In addition to the gravitational coupling constant, the model
depends on two parameters, namely the cosmological constant and the size of the
Kahler manifold. It is shown that regular and irregular boundary conditions can
be imposed on the matter fields depending on the size of the sigma model
manifold. It is also shown that the super AdS transformations in the bulk
produce the transformations of the N=(2,0) conformal supergravity and scalar
multiplets on the boundary, containing fields with nonvanishing Weyl weights
determined by the ratio of the sigma model and the gravitational coupling
constants. Various types of (2,0) superconformal multiplets are found on the
boundary and in one case the superconformal symmetry is shown to be realized in
an unconventional way. |
Novel construction and the monodromy relation for three-point functions
at weak coupling: In this article, we shall develop and formulate two novel viewpoints and
properties concerning the three-point functions at weak coupling in the SU(2)
sector of the N = 4 super Yang-Mills theory. One is a double spin-chain
formulation of the spin-chain and the associated new interpretation of the
operation of Wick contraction. It will be regarded as a skew symmetric pairing
which acts as a projection onto a singlet in the entire SO(4) sector, instead
of an inner product in the spin-chain Hilbert space. This formalism allows us
to study a class of three-point functions of operators built upon more general
spin-chain vacua than the special configuration discussed so far in the
literature. Furthermore, this new viewpoint has the signicant advantage over
the conventional method: In the usual "tailoring" operation, the Wick
contraction produces inner products between off-shell Bethe states, which
cannot be in general converted into simple expressions. In contrast, our
procedure directly produces the so-called partial domain wall partition
functions, which can be expressed as determinants. Using this property, we
derive simple determinantal representation for a broader class of three-point
functions. The second new property uncovered in this work is the non-trivial
identity satisfied by the three-point functions with monodromy operators
inserted. Generically this relation connects three-point functions of different
operators and can be regarded as a kind of Schwinger-Dyson equation. In
particular, this identity reduces in the semiclassical limit to the triviality
of the product of local monodromies around the vertex operators, which played a
crucial role in providing all important global information on the three-point
function in the strong coupling regime. This structure may provide a key to the
understanding of the notion of "integrability" beyond the spectral level. | Gravity is not an entropic force: We argue that experiments with ultra-cold neutrons in the gravitational field
of Earth disprove recent speculations on the entropic origin of gravitation. |
Towards Massless Sector of Tensionless Strings on $AdS_5$: {A} Higher Spin Gravity in five dimensions is constructed. It was shown
recently that constructing formally consistent classical equations of motion of
higher spin gravities is equivalent to finding a certain deformation of a given
higher spin algebra. A strong homotopy algebra encoding the interaction
vertices then follows. We propose two different and novel realizations of the
deformed higher spin algebra in the case of five dimensions: one in terms of
the universal enveloping algebra of $su(2,2)$ and the other by means of
oscillator variables. Both the new realizations admit supersymmetric extensions
and the $\mathcal{N}=8$ case underlies the massless sector of tensionless
strings. | Demonstration of how the zeta function method for effective potential
removes the divergences: The calculation of the minimum of the effective potential using the zeta
function method is extremely advantagous, because the zeta function is regular
at $s=0$ and we gain immediately a finite result for the effective potential
without the necessity of subtratction of any pole or the addition of infinite
counter-terms. The purpose of this paper is to explicitly point out how the
cancellation of the divergences occurs and that the zeta function method
implicitly uses the same procedure used by Bollini-Giambiagi and
Salam-Strathdee in order to gain finite part of functions with a simple pole. |
Green functions and dimensional reduction of quantum fields on product
manifolds: We discuss Euclidean Green functions on product manifolds P=NxM. We show that
if M is compact then the Euclidean field on P can be approximated by its zero
mode which is a Euclidean field on N. We estimate the remainder of this
approximation. We show that for large distances on N the remainder is small. If
P=R^{D-1}xS^{beta}, where S^{beta} is a circle of radius beta, then the result
reduces to the well-known approximation of the D dimensional finite temperature
quantum field theory to D-1 dimensional one in the high temperature limit.
Analytic continuation of Euclidean fields is discussed briefly. | Kerr-Schild perturbations of coset CFTs as scale invariant integrable
$σ$-models: Kerr-Schild perturbations in General Relativity provide a fruitful way of
constructing new exact solutions starting from known ones, elucidating also the
structure of the spacetimes. We initiate such a study in the context of string
theory and supergravity. Specifically, we explicitly construct Kerr-Schild
perturbations of coset CFTs based on low dimensionality orthogonal groups. We
show that these give rise to scale, but not Weyl, invariant integrable
$\sigma$-models. We explicitly demonstrate that these models can also be
derived from a particular limiting procedure of $\lambda$-deformed coset CFTs
based on non-compact groups. The target space of the simplest $\sigma$-model
describes a two-dimensional scale invariant black hole for which we also
provide two different embeddings to type-II supergravity. |
On gravity localization in scalar braneworlds with a super-exponential
warp factor: We show that within tachyonic braneworld models,"super-exponential" warp
factors of the form $e^{-2f} \sim e^{-2c_1e^{c_2 |\sigma|}}$ are problematic
when dealing with both the finiteness of the effective four-dimensional (4d)
Planck mass and the localization of 4d gravity, which can be stated by the
requirement that $\int e^{-2f(\sigma)}d\sigma < \infty$, because this condition
necessarily implies that c_1 and c_2 should be positive. As a consequence of
this fact the tachyonic field $T$ turns out to be complex in contradiction with
the real nature of the starting action for the tachyonic braneworld. Conversely
if one requires to have a real tachyon field, 4d gravity will not be localized
and the effective gravitational coupling will be infinite. We present several
typical examples where this problem occurs: we have analysed this situation for
thin as well as thick tachyonic braneworlds with 4d Poincare symmetry, for the
case when a bulk cosmological constant is present, and even for a brane with an
induced spatially flat 4d cosmological background, and shown that in all cases
the tachyon field T comes out to be inconsistently complex when imposing
localization of 4d gravity. On the other hand, when dealing with a further
reduction of the hierarchy problem one should carefully consider the sign of
the constants c_1 and c_2 to avoid inconsistencies in the tachyonic braneworld
model. We also present a similar discusion involving a canonical scalar field
in the bulk where none of these problems arise and hence, the mass hierarchy
and 4d gravity localization problems can be successfully addressed at once.
Finally, the stability analysis of this scalar tensor braneworld model with a
super-exponential warp factor is performed. | Witten Index and Wall Crossing: We compute the Witten index of one-dimensional gauged linear sigma models
with at least ${\mathcal N}=2$ supersymmetry. In the phase where the gauge
group is broken to a finite group, the index is expressed as a certain residue
integral. It is subject to a change as the Fayet-Iliopoulos parameter is varied
through the phase boundaries. The wall crossing formula is expressed as an
integral at infinity of the Coulomb branch. The result is applied to many
examples, including quiver quantum mechanics that is relevant for BPS states in
$d=4$ ${\mathcal N}=2$ theories. |
Black Hole Information Revisited: We argue that four-dimensional black hole evaporation inevitably produces an
infinite number of soft particles in addition to the thermally distributed
`hard' Hawking quanta, and moreover that the soft and hard particles are highly
correlated. This raises the possibility that quantum purity is restored by
correlations between the hard and soft radiation, while inclusive measurements
which omit the soft radiation observe the thermal Hawking spectrum. In theories
whose only stable particle is the graviton, conservation laws are used to argue
that such correlations are in principle sufficient for the soft gravitons to
purify the hard thermal ones. | Scattering between wobbling kinks: In this paper the scattering between a wobbling kink and a wobbling antikink
in the standard $\phi^4$ model is numerically investigated. The dependence of
the final velocities, wobbling amplitudes and frequencies of the scattered
kinks on the collision velocity and on the initial wobbling amplitude is
discussed. The fractal structure becomes more intricate due to the emergence of
new resonance windows and the splitting of those arising in the non-excited
kink scattering. Outside this phase the final wobbling amplitude exhibits a
linear dependence of the collision velocity whereas the final frequency is a
decreasing function. By contrast these magnitudes are almost independent of the
initial wobbling amplitude. |
Stability and duality in N=2 supergravity: The BPS-spectrum is known to change when moduli cross a wall of marginal
stability. This paper tests the compatibility of wall-crossing with S-duality
and electric-magnetic duality for N=2 supergravity. To this end, the
BPS-spectrum of D4-D2-D0 branes is analyzed in the large volume limit of
Calabi-Yau moduli space. Partition functions are presented, which capture the
stability of BPS-states corresponding to two constituents with primitive
charges and supported on very ample divisors in a compact Calabi-Yau. These
functions are `mock modular invariant' and therefore confirm S-duality.
Furthermore, wall-crossing preserves electric-magnetic duality, but is shown to
break the `spectral flow' symmetry of the N=(4,0) CFT, which captures the
degrees of freedom of a single constituent. | New brane solutions in higher order gravity: We consider the higher order gravity with dilaton and with the leading string
theory corrections taken into account. The domain wall type solutions are
investigated for arbitrary number of space-time dimensions. The explicit
formulae for the fixed points and asymptotic behavior of generic solutions are
given. We analyze and classify solutions with finite effective gravitational
constant. There is a class of such solutions which have no singularities. We
discuss in detail the relation between fine tuning and self tuning and clarify
in which sense our solutions are fine-tuning free. The stability of such
solutions is also discussed. |
Expanding Einstein-Yang-Mills by Yang-Mills in CHY frame: Using the Cachazo-He-Yuan (CHY) formalism, we prove a recursive expansion of
tree level single trace Einstein-Yang-Mills (EYM) amplitudes with arbitrary
number of gluons and gravitons, which is valid for general spacetime dimensions
and any helicity configurations. The recursion is written in terms of
fewer-graviton EYM amplitudes and pure Yang-Mills (YM) amplitudes, which can be
further carried out until we reach an expansion in terms of pure YM amplitudes
in Kleiss-Kuijf (KK) basis. Our expansion then generates naturally a spanning
tree structure rooted on gluons whose vertices are gravitons. We further
propose a set of graph theoretical rules based on spanning trees that evaluate
directly the pure YM expansion coefficients. | Families of Singular and Subsingular Vectors of the Topological N=2
Superconformal Algebra: We analyze several issues concerning the singular vectors of the Topological
N=2 Superconformal algebra. First we investigate which types of singular
vectors exist, regarding the relative U(1) charge and the BRST-invariance
properties, finding four different types in chiral Verma modules and
twenty-nine different types in complete Verma modules. Then we study the family
structure of the singular vectors, every member of a family being mapped to any
other member by a chain of simple transformations involving the spectral flows.
The families of singular vectors in chiral Verma modules follow a unique
pattern (four vectors) and contain subsingular vectors. We write down these
families until level 3, identifying the subsingular vectors. The families of
singular vectors in complete Verma modules follow infinitely many different
patterns, grouped roughly in five main kinds. We present a particularly
interesting thirty-eight-member family at levels 3, 4, 5, and 6, as well as the
complete set of singular vectors at level 1 (twenty-eight different types).
Finally we analyze the D\"orrzapf conditions leading to two linearly
independent singular vectors of the same type, at the same level in the same
Verma module, and we write down four examples of those pairs of singular
vectors, which belong to the same thirty-eight-member family. |
Pure spinor superfields -- an overview: Maximally supersymmetric theories do not allow off-shell superspace
formulations with traditional superfields containing a finite set of auxiliary
fields. It has become clear that off-shell supersymmetric action formulations
of such models can be achieved by the introduction of pure spinors. In this
talk, an overview of this formalism is given, with emphasis on D=10
super-Yang-Mills theory and D=11 supergravity. This a somewhat expanded version
of a talk presented at the workshop "Breaking of supersymmetry and ultraviolet
divergences in extended supergravity" (BUDS), Laboratori Nazionali di Frascati,
March 25-28, 2013. | Novel Type I Compactifications: We argue that there are two distinct classes of type I compactification to
four dimensions on any space. These two classes are distinguished in a
mysterious way by the presence (or absence) of a discrete 6-form potential. In
simple examples, duality suggests that the new class of compactifications have
reduced numbers of moduli. We also point out analogous discrete choices in M, F
and type II compactifications, including some with $G_2$ holonomy. These
choices often result in spaces with frozen singularities. |
Inhomogeneous states in two dimensional linear sigma model at large N: In this note we consider inhomogeneous solutions of two-dimensional linear
sigma model in the large $N$ limit. These solutions are similar to the ones
found recently in two-dimensional $CP^N$ sigma model. The solution exists only
for some range of coupling constant. We calculate energy of the solutions as
function of parameters of the model and show that at some value of the coupling
constant it changes sign signaling a possible phase transition. The case of the
nonlinear model at finite temperature is also discussed. The free energy of the
inhomogeneous solution is shown to change sign at some critical temperature. | Strings with Non-Relativistic Conformal Symmetry and Limits of the
AdS/CFT Correspondence: We find a Polyakov-type action for strings moving in a torsional
Newton-Cartan geometry. This is obtained by starting with the relativistic
Polyakov action and fixing the momentum of the string along a non-compact null
isometry. For a flat target space, we show that the world-sheet theory becomes
the Gomis-Ooguri action. From a target space perspective these strings are
non-relativistic but their world-sheet theories are still relativistic. We show
that one can take a scaling limit in which also the world-sheet theory becomes
non-relativistic with an infinite-dimensional symmetry algebra given by the
Galilean conformal algebra. This scaling limit can be taken in the context of
the AdS/CFT correspondence and we show that it is realized by the `Spin Matrix
Theory' limits of strings on AdS$_5$ $\times$ $S^5$. Spin Matrix theory arises
as non-relativistic limits of the AdS/CFT correspondence close to BPS bounds.
The duality between non-relativistic strings and Spin Matrix theory provides a
holographic duality of its own and points towards a framework for more
tractable holographic dualities whereby non-relativistic strings are dual to
near BPS limits of the dual field theory. |
Seiberg Witten Map and the Axial Anomaly in Noncommutative Field Theory: Using the point-splitting regularisation, we calculate the axial anomaly in
an arbitrary even dimensional Non-Commutative (NC) field theory. Our result is
(star) gauge invariant in its {\it unintegrated} form, to the leading order in
the NC parameter.
Exploiting the Seiberg Witten map, this result gets transformed to the
familiar Adler-Bell-Jackiw anomaly in ordinary space-time. Furthermore, using
this map, we derive an expression for the unintegrated axial anomaly for
constant fields in NC space-time, that is valid to all finite orders of the NC
parameter. | Intersecting Branes, Domain Walls and Superpotentials in 3d Gauge
Theories: We revisit the Hanany-Witten brane construction of 3d gauge theories with N=2
supersymmetry. Instantons are known to generate a superpotential on the Coulomb
branch of the theory. We show that this superpotential can be viewed as arising
from the classical scattering of domain wall solitons. The domain walls live on
the worldvolume of the fivebranes and their existence relies on the recent
observation that the charged hypermultiplet at the intersection of
perpendicular D-branes has non-canonical kinetic terms. We further show how Dp
branes may be absorbed at the intersection of perpendicular D(p+4)-branes where
they appear as BPS sigma-model lumps. |
Supersymmetry and Fredholm modules over quantized spaces: The purpose of this paper is to apply the framework of non- commutative
differential geometry to quantum deformations of a class of Kahler manifolds.
For the examples of the Cartan domains of type I and flat space, we construct
Fredholm modules over the quantized manifolds using the supercharges which
arise in the quantization of supersymmetric generalizations of the manifolds.
We compute the explicit formula for the Chern character on generators of the
Toeplitz C^* -algebra. | Tensor models and 3-ary algebras: Tensor models are the generalization of matrix models, and are studied as
models of quantum gravity in general dimensions. In this paper, I discuss the
algebraic structure in the fuzzy space interpretation of the tensor models
which have a tensor with three indices as its only dynamical variable. The
algebraic structure is studied mainly from the perspective of 3-ary algebras.
It is shown that the tensor models have algebraic expressions, and that their
symmetries are represented by 3-ary algebras. It is also shown that the 3-ary
algebras of coordinates, which appear in the nonassociative fuzzy flat
spacetimes corresponding to a certain class of configurations with Gaussian
functions in the tensor models, form Lie triple systems, and the associated Lie
algebras are shown to agree with those of the Snyder's noncommutative
spacetimes. The Poincare transformations on the fuzzy flat spacetimes are shown
to be generated by 3-ary algebras. |
Dynamical Domain Wall Defects in 2+1 Dimensions: We study some dynamical properties of a Dirac field in 2+1 dimensions with
spacetime dependent domain wall defects. We show that the Callan and Harvey
mechanism applies even to the case of defects of arbitrary shape, and in a
general state of motion. The resulting chiral zero modes are localized on the
worldsheet of the defect, an embedded curved two dimensional manifold. The
dynamics of these zero modes is governed by the corresponding induced metric
and spin connection. Using known results about determinants and anomalies for
fermions on surfaces embedded in higher dimensional spacetimes, we show that
the chiral anomaly for this two dimensional theory is responsible for the
generation of a current along the defect. We derive the general expression for
such a current in terms of the geometry of the defect, and show that it may be
interpreted as due to an "inertial" electric field, which can be expressed
entirely in terms of the spacetime curvature of the defects. We discuss the
application of this framework to fermionic systems with defects in condensed
matter. | A modified Schwinger's formula for the Casimir effect: After briefly reviewing how the (proper-time) Schwinger's formula works for
computing the Casimir energy in the case of "scalar electrodynamics" where the
boundary conditions are dictated by two perfectly conducting parallel plates
with separation "a" in the Z-axis, we propose a slightly modification in the
previous approach based on an analytical continuation method. As we will see,
for the case at hand our formula does not need the use of Poisson summation to
get a (renormalized) finite result. |
Manifestly N=3 supersymmetric Euler-Heisenberg action in light-cone
superspace: We find a manifestly N=3 supersymmetric generalization of the
four-dimensional Euler-Heisenberg (four-derivative, or F^4) part of the
Born-Infeld action in light-cone gauge, by using N=3 light-cone superspace. | Partial breaking of global supersymmetry and super particle actions: We argue the conjecture that the on-shell component super particle actions
have a universal form, in which the physical fermions enter the action through
the ein-bein and the space-time derivatives of the matter fields, only. We
explicitly constructed the actions for the super particles in $D=3$ realizing
the $N=4\cdot 2^{k} \rightarrow N=2\cdot 2^k$ pattern of supersymmetry
breaking, and in $D=5$ with the $N=16$ supersymmetry broken down to the $N=8$
one. All constructed actions have indeed a universal form, confirming our
conjecture. Our construction is strictly based on the assumption that in the
system we have one half breaking of the global supersymmetry, and on the very
special choice of the superspace coordinates and component fields. |
Critical thermodynamics of the two-dimensional systems in five-loop
renormalization-group approximation: The RG functions of the 2D $n$-vector $\phi^4$ model are calculated in the
five-loop approximation. Perturbative series for the $\beta$ function and
critical exponents are resummed by the Pade-Borel and Pade-Borel-Leroy
techniques, resummation procedures are optimized and an accuracy of the
numerical results is estimated. In the Ising case $n = 1$ as well as in the
others ($n = 0$, $n = -1$, $n = 2, 3,...32$) an account for the five-loop term
is found to shift the Wilson fixed point location only briefly, leaving it
outside the segment formed by the results of the corresponding lattice
calculations; even error bars of the RG and lattice estimates do not overlap in
the most cases studied. This is argued to reflect the influence of the singular
(non-analytical) contribution to the $\beta$ function that can not be found
perturbatively. The evaluation of the critical exponents for $n = 1$, $n = 0$
and $n = -1$ in the five-loop approximation and comparison of the numbers
obtained with their known exact counterparts confirm the conclusion that
non-analytical contributions are visible in two dimensions. | Bare vs. Effective Fixed Point Action in Asymptotic Safety: The
Reconstruction Problem: We propose a method for the (re)-construction of a regularized functional
integral, well defined in the ultraviolet limit, from a solution of the
functional renormalization group equation of the effective average action. The
functional integral is required to reproduce this solution. The method is of
particular interest for asymptotically safe theories. The bare action for the
Einstein-Hilbert truncation of Quantum Einstein Gravity (QEG) is computed and
its flow is analyzed. As a second example conformally reduced gravity is
explored. Various conceptual issues related to the reconstruction problem are
discussed. |
Supersymmetry, Vacuum Statistics, and the Fundamental Theorem of Algebra: I give an interpretation of the fundamental theorem of algebra based on
supersymmetry and the Witten index. The argument gives a physical explanation
of why a real polynomial of degree $n$ need not have $n$ real zeroes, while a
complex polynomial of degree $n$ must have $n$ complex zeroes. This paper also
addresses in a general and model-independent way the statistics of the
perturbative ground states (the states which correspond to classical vacua) in
supersymmetric theories with complex and with real superfields. | Minimal Length and the Quantum Bouncer: A Nonperturbative Study: We present the energy eigenvalues of a quantum bouncer in the framework of
the Generalized (Gravitational) Uncertainty Principle (GUP) via quantum
mechanical and semiclassical schemes. In this paper, we use two equivalent
nonperturbative representations of a deformed commutation relation in the form
[X,P]=i\hbar(1+\beta P^2) where \beta is the GUP parameter. The new
representation is formally self-adjoint and preserves the ordinary nature of
the position operator. We show that both representations result in the same
modified semiclassical energy spectrum and agrees well with the quantum
mechanical description. |
Perturbing Around A Warped Product Of AdS_4 and Seven-Ellipsoid: We compute the spin-2 Kaluza-Klein modes around a warped product of AdS_4 and
a seven-ellipsoid. This background with global G_2 symmetry is related to a
U(N) x U(N) N=1 superconformal Chern-Simons matter theory with sixth order
superpotential. The mass-squared in AdS_4 is quadratic in G_2 quantum number
and KK excitation number. We determine the dimensions of spin-2 operators using
the AdS/CFT correspondence. The connection to N=2 theory preserving SU(3) x
U(1)_R is also discussed. | On features of the radiation from an electron moving along a helix
inside a cylindrical hole in a homogeneous dielectric: The radiation from a charge moving along a helical trajectory inside a
cylindrical hole in homogeneous dielectric medium is investigated. Prompted by
availability of materials with large dielectric permittivity $\epsilon $ and
small absorption, we discuss the features of this type of radiation for media
with $\epsilon \gg 1$. It is shown that there are high peaks in the angular
distribution of radiation intensity at well-defined harmonics. The conditions
are specified for the cavity-to-helix radii ratio, $\rho_{1}/\rho_{0}$, under
which the angle-integrated radiation intensity on some harmonics exceeds that
in the empty space. Though the amplification of radiation intensity increases
with increasing $\epsilon $, the corresponding "resonant" values of $\rho
_{1}/\rho_{0}$ ratio are practically independent of the dielectric permittivity
of surrounding medium. It is shown that an analogous amplification of radiation
takes place essentially for the same values of $\rho_{1}/\rho_{0}$ also for the
radiation in a cylindrical waveguide with conducting walls. An explanation of
this phenomenon is given. |
A geodesic Witten diagram description of holographic entanglement
entropy and its quantum corrections: We use the formalism of geodesic Witten diagrams to study the holographic
realization of the conformal block expansion for entanglement entropy of two
disjoint intervals. The agreement between the Ryu-Takayanagi formula and the
identity block contribution has a dual realization as the product of bulk to
boundary propagators. Quantum bulk corrections instead arise from stripped
higher order diagrams and back-reaction effects; these are also mapped to the
structure for $G_N^0$ terms found in \cite{Faulkner:2013ana}, with the former
identified as the bulk entanglement entropy across the Ryu-Takayanagi surfaces.
An independent derivation of this last statement is provided by implementing a
twist-line formalism in the bulk, and additional checks from the computation of
mutual information and single interval entanglement entropy. Finally an
interesting correspondence is found between the recently proposed holographic
entanglement of purification, and an approximated form for certain $1/c$ Renyi
entropies corrections. | Timelike U-dualities in Generalised Geometry: We study timelike U-dualities acting in three and four directions of
11-dimensional supergravity, which form the groups $SL(2)\times SL(3)$ and
SL(5). Using generalised geometry, we find that timelike U-dualities, despite
previous conjectures, do not change the signature of the spacetime.
Furthermore, we prove that the spacetime signature must be $(-,+,...,+)$ when
the U-duality modular group is either $\frac{SL(2)\times SL(3)}{SO(1,1)\times
SO(2,1)}$ or $\frac{SL(5)}{SO(3,2)}$. We find that for some dual solutions it
is necessary to include a trivector field which is related to the existence of
non-geometric fluxes in lower dimensions. In the second part of the paper, we
explicitly study the action of the dualities on supergravity solutions
corresponding to M2-branes. For a finite range of the transformation, the
action of $SL(2)\otimes SL(3)$ on the worldvolume of uncharged M2-branes
charges them while it changes the charge of extreme M2-branes. It thus acts as
a Harrison transformation. At the limits of the range, we obtain the
"subtracted geometries" which correspond to an infinite Harrison boost. Outside
this range the trivector field becomes non-zero and we obtain a dual solution
that cannot be uniquely written in terms of a metric, 3-form and trivector.
Instead it corresponds to a family of solutions linked by a local SO(1,1)
rotation. The SL(5) duality is used to act on a smeared extreme M2-brane giving
a brane-like solution carrying momentum in the transverse direction that the
brane was delocalised along. |
Definition of the Dirac Sea in the Presence of External Fields: It is shown that the Dirac sea can be uniquely defined for the Dirac equation
with general interaction, if we impose a causality condition on the Dirac sea.
We derive an explicit formula for the Dirac sea in terms of a power series in
the bosonic potentials.
The construction is extended to systems of Dirac seas. If the system contains
chiral fermions, the causality condition yields a restriction for the bosonic
potentials. | Discrete Kaluza-Klein from scalar fluctuations in noncommutative
geometry: We compute the metric associated to noncommutative spaces described by a
tensor product of spectral triples. Well known results of the two-sheets model
(distance on a sheet, distance between the sheets) are extended to any product
of two spectral triples. The distance between different points on different
fibres is investigated. When one of the triple describes a manifold, one find a
Pythagorean theorem as soon as the direct sum of the internal states (viewed as
projections) commutes with the internal Dirac operator. Scalar fluctuations
yield a discrete Kaluza-Klein model in which the extra metric component is
given by the internal part of the geometry. In the standard model, this extra
component comes from the Higgs field. |
Supersymmetric codimension-two branes and U(1)_R mediation in 6D gauged
supergravity: We construct a consistent supersymmetric action for brane chiral and vector
multiplets in a six-dimensional chiral gauged supergravity. A nonzero brane
tension can be accommodated by allowing for a brane-localized Fayet-Iliopoulos
term proportional to the brane tension. When the brane chiral multiplet is
charged under the bulk U(1)_R, we obtain a nontrivial coupling to the extra
component of the U(1)_R gauge field strength as well as a singular scalar
self-interaction term. Dimensionally reducing to 4D on a football
supersymmetric solution, we discuss the implication of such interactions for
obtaining the U(1)_R D-term in the 4D effective supergravity. By assuming the
bulk gaugino condensates and nonzero brane F- and/or D-term for the uplifting
potential, we have all the moduli stabilized with a vanishing cosmological
constant. The brane scalar with nonzero R charge then gets a soft mass of order
the gravitino mass. The overall sign of the soft mass squared depends on the
sign of the R charge as well as whether the brane F- or D-term dominates. | Semiclassical Strings on Curved Branes: We study semiclassical strings in the near horizon geometry of certain curved
branes. We investigate the rigidly rotating strings in the near horizon
geometry of NS5-branes wrapped on AdS3 x S3 and in the presence of background
NS-NS flux. We study several string solutions corresponding to giant magnon,
single spike and more general folded strings for the fundamental string in this
background. We comment that in the S-dual background the situation changes
drastically. |
Entanglement, Observers and Cosmology: a view from von Neumann Algebras: Infinite entanglement fluctuations appear when a quantum field theory on a
causally complete domain of space-time is a type $III$ factor. In the weak
gravity limit $G_N=0$ this factor can be transformed into a crossed product
type $II$ factor with finite entanglement fluctuations by adding a physical
reference frame system (observer). The use of a physical reference frame to
define a regularization of divergent entanglement is formally identical to the
quantum information approach to superselection charges. In that case the added
reference frame allows quantum superpositions between different superselection
sectors. For the case of cosmological horizons we map the primordial
inflationary slow rolling phase into a type $II$ modification of the pure de
Sitter type $III$ factor and we use the so defined type $II$ finite
entanglement fluctuations to predict the primordial power spectrum of scalar
curvature fluctuations. For the Hagedorn high temperature phase of large $N$
Yang Mills, the type $II$ description of the Hagedorn phase accounts, in the
large $N$ limit, for the quantum fluctuations of the interval of the
corresponding matrix model eigenvalue distribution. | Probing the Vacuum Structure of Spacetime: We explore the question of how to probe the vacuum structure of space time by
a massive scalar field through interaction with background gravitons. Using the
$\Gamma$-regularization for the in-/out-state formalism, we find the effective
action of a scalar field in a conformally, asymptotically flat spacetime and a
four-dimensional de Sitter space, which is a gravitational analog of the
Heisenberg-Euler and Schwinger effective action for a charged scalar in a
constant electric field. The effective action is nonperturbative in that it
sums all one-loop diagrams with arbitrary number of external lines of
gravitons. The massive scalar field becomes unstable due to particle
production, the effective action has an imaginary part that determines the
decay rate of the vacuum, and the out-vacuum is unitarily inequivalent to the
in-vacuum. |
CFT$_D$ from TQFT$_{D+1}$ via Holographic Tensor Network, and Precision
Discretisation of CFT$_2$: We show that the path-integral of conformal field theories in $D$ dimensions
(CFT$_D$) can be constructed by solving for eigenstates of an RG operator
following from the Turaev-Viro formulation of a topological field theory in
$D+1$ dimensions (TQFT$_{D+1}$), explicitly realising the holographic sandwich
relation between a symmetric theory and a TQFT. Generically, exact eigenstates
corresponding to symmetric-TQFT$_D$ follow from Frobenius algebra in the
TQFT$_{D+1}$. For $D=2$, we constructed eigenstates that produce 2D rational
CFT path-integral exactly, which, curiously connects a continuous field
theoretic path-integral with the Turaev-Viro state sum. We also devise and
illustrate numerical methods for $D=2,3$ to search for CFT$_D$ as phase
transition points between symmetric TQFT$_D$. Finally since the RG operator is
in fact an exact analytic holographic tensor network, we compute
``bulk-boundary'' correlator and compare with the AdS/CFT dictionary at $D=2$.
Promisingly, they are numerically compatible given our accuracy, although
further works will be needed to explore the precise connection to the AdS/CFT
correspondence. | Hidden Symmetries of the Principal Chiral Model and a Nonstandard Loop
Algebra: We examine the precise structure of the loop algebra of `dressing' symmetries
of the Principal Chiral Model, and discuss a new infinite set of abelian
symmetries of the field equations which preserve a symplectic form on the space
of solutions. |
Computing topological invariants with one and two-matrix models: A generalization of the Kontsevich Airy-model allows one to compute the
intersection numbers of the moduli space of p-spin curves. These models are
deduced from averages of characteristic polynomials over Gaussian ensembles of
random matrices in an external matrix source. After use of a duality, and of an
appropriate tuning of the source, we obtain in a double scaling limit these
intersection numbers as polynomials in p. One can then take the limit p to -1
which yields a matrix model for orbifold Euler characteristics. The
generalization to a time-dependent matrix model, which is equivalent to a
two-matrix model, may be treated along the same lines ; it also yields a
logarithmic potential with additional vertices for general p. | Non-associative geometry and discrete structure of spacetime: A new mathematical theory, non-associative geometry, providing a unified
algebraic description of continuous and discrete spacetime, is introduced. |
Infrared and transcendental structure of two-loop supersymmetric QCD
amplitudes: Using a careful choice of infrared (IR) subtraction scheme, we demonstrate
the cancellation of all terms with transcendental weights 0,1,2 from the finite
part of the full-color two-loop four-gluon $\mathcal{N}=2$ supersymmetric QCD
amplitude, with $N_f$ massless supersymmetric quarks. This generalizes the
previously observed cancellation of weight-2 terms in the superconformal
theory, where $N_f=2N_c$ for gauge group SU$(N_c)$. The subtraction scheme
follows naturally both from general IR factorization principles and from an
integrand-level analysis of divergences in this amplitude. The divergences are
written in terms of scalar triangle integrals whose expressions are known to
all orders in the dimensional regulator $\epsilon=(4-D)/2$. We also present
integrated expressions for the full-color two-loop four-point amplitudes with
both matter and vectors on external legs in which lower-weight terms also
cancel using an appropriate IR scheme. This provides us with values for the
two-loop cusp, gluonic, and quark anomalous dimensions in $\mathcal{N}=2$
supersymmetric QCD, which are cross-checked between the three different
amplitudes. | Quantum Foam and de Sitter-like universe: We perform a foliation of a four dimensional Riemannian space-time with
respect to a discrete time which is an integer multiple of the Planck time. We
find that the quantum fluctuations of the metric have a discrete energy
spectrum. The metric field is expanded in stationary eigenstates, and this
leads to the description of a de Sitter-like universe. At the Planck scale the
model describes a Planckian Euclidean black hole. |
Nonabelian parafermions and their dimensions: We propose a generalization of the Zamolodchikov-Fateev parafermions which
are abelian, to nonabelian groups. The fusion rules are given by the tensor
product of representations of the group. Using Vafa equations we get the
allowed dimensions of the parafermions. We find for simple groups that the
dimensions are integers. For cover groups of simple groups, we find, for
$n.G.m$, that the dimensions are the same as $Z_n$ parafermions. Examples of
integral parafermionic systems are studied in detail. | Further Evidence for a Gravitational Fixed Point: A theory of gravity with a generic action functional and minimally coupled to
N matter fields has a nontrivial fixed point in the leading large N
approximation. At this fixed point, the cosmological constant and Newton's
constant are nonzero and UV relevant; the curvature squared terms are
asymptotically free with marginal behaviour; all higher order terms are
irrelevant and can be set to zero by a suitable choice of cutoff function. |
Calabi-Yau Moduli Space, Mirror Manifolds and Spacetime Topology Change
in String Theory: We analyze the moduli spaces of Calabi-Yau threefolds and their associated
conformally invariant nonlinear sigma-models and show that they are described
by an unexpectedly rich geometrical structure. Specifically, the Kahler sector
of the moduli space of such Calabi-Yau conformal theories admits a
decomposition into adjacent domains some of which correspond to the
(complexified) Kahler cones of topologically distinct manifolds. These domains
are separated by walls corresponding to singular Calabi-Yau spaces in which the
spacetime metric has degenerated in certain regions. We show that the union of
these domains is isomorphic to the complex structure moduli space of a single
topological Calabi-Yau space---the mirror. In this way we resolve a puzzle for
mirror symmetry raised by the apparent asymmetry between the Kahler and complex
structure moduli spaces of a Calabi-Yau manifold. Furthermore, using mirror
symmetry, we show that we can interpolate in a physically smooth manner between
any two theories represented by distinct points in the Kahler moduli space,
even if such points correspond to topologically distinct spaces. Spacetime
topology change in string theory, therefore, is realized by the most basic
operation of deformation by a truly marginal operator. Finally, this work also
yields some important insights on the nature of orbifolds in string theory. | The quantum non-linear Schrodinger model with point-like defect: We establish a family of point-like impurities which preserve the quantum
integrability of the non-linear Schrodinger model in 1+1 space-time dimensions.
We briefly describe the construction of the exact second quantized solution of
this model in terms of an appropriate reflection-transmission algebra. The
basic physical properties of the solution, including the space-time symmetry of
the bulk scattering matrix, are also discussed. |
Chiral vortical effect for vector fields: We consider photonic vortical effect, i.e. the difference of the flows of
left- and right-handed photons along the vector of angular velocity in rotating
photonic medium. Two alternative frameworks to evaluate the effect are
considered, both of which have already been tried in the literature. First, the
standard thermal fied theory and, alternatively, Hawking-radiation-type
derivation. In our earlier attempt to compare the two approaches, we found a
crucial factor of two difference. Here we revisit the problem, paying more
attention to details of infrared regularizations. We find out that introduction
of an infinitesimal mass of the vector field brings the two ways of evaluating
the chiral vortical effect into agreement with each other. Some implications,
both on the theoretical and phenomenological sides, are mentioned. | Quantum Mechanics on the Circle and W_{1+\INFTY}: The algebra W_{1+\infty} with central charge c=0 can be identified with the
algebra of quantum observables of a particle moving on a circle.
Mathematically, it is the universal enveloping algebra of the Euclidean algebra
in two dimensions. Similarly, the super W_\infty algebra is found to be the
universal enveloping algebra of the super-Euclidean algebra in two dimensions. |
PSS: A FORM Program to Evaluate Pure Spinor Superspace Expressions: A FORM program which is used to efficiently expand in components pure spinor
superfield expressions of kinematic factors is presented and comments on how it
works are made. It is highly customizable using the standard features of FORM
and can be used to help obtaining superstring effective actions from the
scattering amplitudes computed with the pure spinor formalism. | Topological M Theory from Pure Spinor Formalism: We construct multiloop superparticle amplitudes in 11d using the pure spinor
formalism. We explain how this construction reduces to the superparticle limit
of the multiloop pure spinor superstring amplitudes prescription. We then argue
that this construction points to some evidence for the existence of a
topological M theory based on a relation between the ghost number of the
full-fledged supersymmetric critical models and the dimension of the spacetime
for topological models. In particular, we show that the extensions at higher
orders of the previous results for the tree and one-loop level expansion for
the superparticle in 11 dimensions is related to a topological model in 7
dimensions. |
Abelian mirror symmetry of $\mathcal{N}=(2,2)$ boundary conditions: We evaluate half-indices of $\mathcal{N}=(2,2)$ half-BPS boundary conditions
in 3d $\mathcal{N}=4$ supersymmetric Abelian gauge theories. We confirm that
the Neumann boundary condition is dual to the generic Dirichlet boundary
condition for its mirror theory as the half-indices perfectly match with each
other. We find that a naive mirror symmetry between the exceptional Dirichlet
boundary conditions defining the Verma modules of the quantum Coulomb and Higgs
branch algebras does not always hold. The triangular matrix obtained from the
elliptic stable envelope describes the precise mirror transformation of a
collection of half-indices for the exceptional Dirichlet boundary conditions. | p-wave Holographic Superconductors and five-dimensional gauged
Supergravity: We explore five-dimensional ${\cal N}=4$ $SU(2)\times U(1)$ and ${\cal N}=8$
SO(6) gauged supergravities as frameworks for condensed matter applications.
These theories contain charged (dilatonic) black holes and 2-forms which have
non-trivial quantum numbers with respect to U(1) subgroups of SO(6). A question
of interest is whether they also contain black holes with two-form hair with
the required asymptotic to give rise to holographic superconductivity. We first
consider the ${\cal N}=4$ case, which contains a complex two-form potential
$A_{\mu\nu}$ which has U(1) charge $\pm 1$. We find that a slight
generalization, where the two-form potential has an arbitrary charge $q$, leads
to a five-dimensional model that exhibits second-order superconducting
transitions of p-wave type where the role of order parameter is played by
$A_{\mu\nu}$, provided $q \gtrsim 5.6$. We identify the operator that condenses
in the dual CFT, which is closely related to ${\cal N}=4$ Super Yang-Mills
theory with chemical potentials. Similar phase transitions between R-charged
black holes and black holes with 2-form hair are found in a generalized version
of the ${\cal N}=8$ gauged supergravity Lagrangian where the two-forms have
charge $q\gtrsim 1.8$. |
Stochastic tunneling in de Sitter spacetime: Tunneling processes in de Sitter spacetime are studied by using the
stochastic approach. We exploit the Martin-Siggia-Rose-Janssen-de Dominicis
(MSRJD) functional integral to obtain the tunneling rate. The applicability
conditions of this method are clarified using the Schwinger-Keldysh formalism.
In the case of a shallow potential barrier, we reproduce the Hawking-Moss (HM)
tunneling rate. Remarkably, in contrast to HM picture, the configuration
derived from the MSRJD functional integral satisfies physically natural
boundary conditions. We also discuss the case of a steep potential barrier and
find an interesting Coleman-de Luccia (CDL) bubble-like configuration. Our
results demonstrate how the bubble nucleation process could be described in the
stochastic approach. Our method turns out to be useful for investigating
various tunneling processes during inflation. | Holographic spectral functions and diffusion constants for fundamental
matter: The holographic dual of large-Nc super-Yang-Mills coupled to a small number
of flavours of fundamental matter, Nf << Nc, is described by Nf probe D7-branes
in the gravitational background of Nc black D3-branes. This system undergoes a
first order phase transition characterised by the `melting' of the mesons. We
study the high temperature phase in which the D7-branes extend through the
black hole horizon. In this phase, we compute the spectral function for vector,
scalar and pseudoscalar modes on the D7-brane probe. We also compute the
diffusion constant for the flavour currents. |
The Cohomological Supercharge: We discuss the supersymmetry operator in the cohomological formulation of
dimensionally reduced SYM. By establishing the cohomology, a large class of
invariants are classified. | Gauge theories in anti-selfdual variables: Some years ago the Nicolai map, viewed as a change of variables from the
gauge connection in a fixed gauge to the anti-selfdual part of the curvature,
has been extended by the first named author to pure YM from its original
definition in N=1 SUSY YM. We study here the perturbative 1PI effective action
in the anti-selfdual variables of any gauge theory, in particular pure YM, QCD
and N=1 SUSY YM. We prove that the one-loop 1PI effective action of a gauge
theory mapped to the anti-selfdual variables in any gauge is identical to the
one of the original theory. This is due to the conspiracy between the Jacobian
of the change to the anti-selfdual variables and an extra functional
determinant that arises from the non-linearity of the coupling of the
anti-selfdual curvature to an external source in the Legendre transform that
defines the 1PI effective action. Hence we establish the one-loop perturbative
equivalence of the mapped and original theories on the basis of the identity of
the one-loop 1PI effective actions. Besides, we argue that the identity of the
perturbative 1PI effective actions extends order by order in perturbation
theory. |
The Large N Harmonic Oscillator as a String Theory: We propose a duality between the large-N gauged harmonic oscillator and a
novel string theory in two dimensions. | The first heat: production of entanglement entropy in the early universe: Entanglement entropy (EE) of a spatial region quantifies correlations between
the region and its surroundings. For a free scalar in the adiabatic vacuum in
de Sitter space the EE is known to remain low, scaling as the surface area of
the region. Here, we study the evolution of entanglement after the universe
transitions from de Sitter to flat space. We concentrate on the case of a
massless minimally coupled scalar. We find numerically that, after the de
Sitter stage ends, the EE and the R\'enyi entropy rapidly grow and saturate at
values obeying the volume law. The final state of the subsystem (region) is a
partially thermalized state reminiscent of a generalized Gibbs ensemble. We
comment on application of our results to the question of when and how
cosmological perturbations decohere. |
Spectral functions of the Dirac operator under local boundary conditions: After a brief discussion of elliptic boundary problems and their properties,
we concentrate on a particular example: the Euclidean Dirac operator in two
dimensions, with its domain determined by local boundary conditions. We discuss
the meromorphic structure of the zeta function of the associated second order
problem, as well as the main characteristic of the first order problem, i.e.,
the boundary contribution to the spectral asymmetry, as defined through the eta
function. | Exceptional Groups and Physics: Quarks and leptons charges and interactions are derived from gauge theories
associated with symmetries. Their space-time labels come from representations
of the non-compact algebra of Special Relativity. Common to these descriptions
are the Lie groups stemming from their invariances. Does Nature use Exceptional
Groups, the most distinctive among them? We examine the case for and against
their use. They do indeed appear in charge space, as the Standard Model fits
naturally inside the exceptional group $E_6$. Further, the advent of the
$E_8\times E_8$ Heterotic Superstring theory adds credibility to this venue. On
the other hand, their use as space-time labels has not been as evident as they
link spinors and tensors under space rotations, which flies in the face of the
spin-statistics connection. We discuss a way to circumvent this difficulty in
trying to generalize eleven-dimensional supergravity. |
T-duality versus Gauge Symmetry: We review the recently constructed `double field theory' which introduces in
addition to the conventional coordinates associated to momentum modes
coordinates associated to winding modes. Thereby, T-duality becomes a global
symmetry of the theory, which can be viewed as an `O(D,D) covariantization' of
the low-energy effective space-time action of closed string theory. We discuss
its symmetries with a special emphasis on the relation between global duality
symmetries and local gauge symmetries. | Thermal Conformal Blocks: We study conformal blocks for thermal one-point-functions on the sphere in
conformal field theories of general dimension. These thermal conformal blocks
satisfy second order Casimir differential equations and have integral
representations related to AdS Witten diagrams. We give an analytic formula for
the scalar conformal block in terms of generalized hypergeometric functions. As
an application, we deduce an asymptotic formula for the three-point coeffcients
of primary operators in the limit where two of the operators are heavy. |
Mass Renormalization in String Theory: Special States: String theory gives a well defined procedure for computing the S-matrix of
BPS or a class of massless states, but similar calculation for general massive
states is plagued with difficulties due to mass renormalization effect. In this
paper we describe a procedure for computing the renormalized masses and
S-matrix elements in bosonic string theory for a special class of massive
states which do not mix with unphysical states under renormalization. Even
though this requires working with off-shell amplitudes which are ambiguous, we
show that the renormalized masses and S-matrix elements are free from these
ambiguities. We also argue that the masses and S-matrix elements for general
external states can be found by examining the locations of the poles and the
residues of the S-matrix of special states. Finally we discuss generalizations
to heterotic and superstring theories. | Geodesic Motions in AdS Soliton Background Space-time: We study both massive and massless particle's geodesic motion in the
background of general dimensional AdS-Sol space-time. We find that the massive
particles oscillate along the radial direction, while massless particles
experience one-time bouncing as they approach the "horizon" line of the
soliton. Our results provide a direct way to understand the negative
energy/masses leading to the AdS-Sol geometry. As a potential application, we
extend the point particle to a 3-brane and fix the background as a 5+1
dimension AdS-Sol, thus obtain a very natural bouncing/cyclic cosmological
model. |
Non-analyticities in three-dimensional gauge theories: Quantum fluctuations generate in three-dimensional gauge theories not only
radiative corrections to the Chern-Simons coupling but also non-analytic terms
in the effective action. We review the role of those terms in gauge theories
with massless fermions and Chern-Simons theories. The explicit form of
non-analytic terms turns out to be dependent on the regularization scheme and
in consequence the very existence of phenomena like parity and framing
anomalies becomes regularization dependent. In particular we find
regularization regimes where both anomalies are absent. Due to the presence of
non-analytic terms the effective action becomes not only discontinuous but also
singular for some background gauge fields which include sphalerons. The
appearence of this type of singularities is linked to the existence of nodal
configurations in physical states and tunneling suppression at some classical
field configurations. In the topological field theory the number of physical
states may also become regularization dependent. Another consequence of the
peculiar behaviour of three-dimensional theories under parity odd
regularizations is the existence of a simple mechanism of generation of a mass
gap in pure Yang-Mills theory by a suitable choice of regularization scheme.
The generic value of this mass does agree with the values obtained in
Hamiltonian and numerical analysis. Finally, the existence of different
regularization regimes unveils the difficulties of establishing a Zamolodchikov
c-theorem for three-dimensional field theories in terms of the induced
gravitational Chern-Simons couplings. | On the Evaluation of Compton Scattering Amplitudes in String Theory: We consider the Compton amplitude for the scattering of a photon and a
(massless) ``electron/positron'' at one loop (i.e. genus one) in a
four-dimensional fermionic heterotic string model. Starting from the
bosonization of the world-sheet fermions needed to explicitly construct the
spin-fields representing the space-time fermions, we present all the steps of
the computation which leads to the explicit form of the amplitude as an
integral of modular forms over the moduli space. |
T-dual RR couplings on D-branes from S-matrix elements: Using the linear T-dual ward identity associated with the NSNS gauge
transformations, some RR couplings on D$_p$-branes have been found at order
$O(\alpha'^2)$. We examine the $C^{(p-1)}$ couplings with the S-matrix elements
of one RR, one graviton and one antisymmetric B-field vertex operators. We find
the consistency of T-dual S-matrix elements and explicit results of scattering
string amplitude and show that the string amplitude reproduces these couplings
as well as some other couplings. This illustration is found for $C^{(p-3)}$
couplings in the literature which is extended to the $C^{(p-1)}$ couplings in
this paper. | A new AdS/CFT correspondence: We consider a geometric zero-radius limit for strings on $AdS_5\times S^5$,
where the anti-de Sitter hyperboloid becomes the projective lightcone. In this
limit the fifth dimension becomes nondynamical, yielding a different
"holographic" interpretation than the usual "bulk to boundary" one. When
quantized on the random lattice, the fifth coordinate acts as a new kind of
Schwinger parameter, producing Feynman rules with normal propagators at the
tree level: For example, in the bosonic case ordinary massless $\phi^4$ theory
is obtained. In the superstring case we obtain new, manifestly ${\cal N}=4$
supersymmetric rules for ${\cal N}=4$ super Yang-Mills. These gluons are also
different from those of the usual AdS/CFT correspondence: They are the
"partons" that make up the usual "hadrons" of the open and closed strings in
the familiar QCD string picture. Thus, their coupling $g_{YM}$ and rank $N$ of
the "color" gauge group are different from those of the "flavor" gauge group of
the open string. As a result we obtain different perturbation expansions in
radius, coupling, and 1/N. |
Chern-Simons Forms, Mickelsson-Faddeev Algebras and the P-Branes: In string theory, nilpotence of the BRS operator $\d$ for the string
functional relates the Chern-Simons term in the gauge-invariant antisymmetric
tensor field strength to the central term in the Kac-Moody algebra. We
generalize these ideas to p-branes with odd p and find that the Kac-Moody
algebra for the string becomes the Mickelsson-Faddeev algebra for the p-brane. | Infrared Behaviour, sources and the Schwinger action principle: The paper describes a dynamical analogy for the renormalization group which
leads to insights into its structure. |
Dressing operator approach to Moyal algebraic deformation of selfdual
gravity: Recently Strachan introduced a Moyal algebraic deformation of selfdual
gravity, replacing a Poisson bracket of the Plebanski equation by a Moyal
bracket. The dressing operator method in soliton theory can be extended to this
Moyal algebraic deformation of selfdual gravity. Dressing operators are defined
as Laurent series with coefficients in the Moyal (or star product) algebra, and
turn out to satisfy a factorization relation similar to the case of the KP and
Toda hierarchies. It is a loop algebra of the Moyal algebra (i.e., of a
$W_\infty$ algebra) and an associated loop group that characterize this
factorization relation. The nonlinear problem is linearized on this loop group
and turns out to be integrable. | Product of Boundary Distributions: 1) We identify new parameter branches for the ultra-local boundary Poisson
bracket in d spatial dimension with a (d-1)-dimensional spatial boundary. There
exist 2^{r(r-1)/2} r-dimensional parameter branches for each d-box, r-row Young
tableau. The already known branch (hep-th/9912017) corresponds to a vertical
1-column, d-box Young tableau. 2) We consider a local distribution product
among the so-called boundary distributions. The product is required to respect
the associativity and the Leibnitz rule. We show that the consistency
requirements on this product correspond to the Jacobi identity conditions for
the boundary Poisson bracket. In other words, the restrictions on forming a
boundary Poisson bracket can be related to the more fundamental distribution
product construction. 3) The definition of the higher functional derivatives is
made independent of the choice of integral kernel representative for a
functional. |
Transition Amplitudes in de Sitter Space: Maldacena has shown that the wavefunction of the universe in de Sitter space
can be viewed as the partition function of a conformal field theory. In this
paper, we investigate this approach to the dS/CFT correspondence in further
detail. We emphasize that massive bulk fields are dual to two primary operators
on the boundary, which encode information about the two independent behaviors
of bulk expectation values at late times. An operator statement of the duality
is given, and it is shown that the resulting boundary correlators can be
interpreted as transition amplitudes from the Bunch-Davies vacuum to an excited
state in the infinite future. We also explain how these scattering amplitudes
can be used to compute late-time Bunch-Davies expectation values, and comment
on the effects of anomalies in the dual CFT on such expectation values. | A General Solution of the Master Equation for a Class of First Order
Systems: Inspired by the formulation of the Batalin-Vilkovisky method of quantization
in terms of ``odd time'', we show that for a class of gauge theories which are
first order in the derivatives, the kinetic term is bilinear in the fields, and
the interaction part satisfies some properties, it is possible to give the
solution of the master equation in a very simple way. To clarify the general
procedure we discuss its application to Yang-Mills theory, massive (abelian)
theory in the Stueckelberg formalism, relativistic particle and to the
self-interacting antisymmetric tensor field. |
Non-minimally coupled canonical, phantom and quintom models of
holographic dark energy: We investigate canonical, phantom and quintom models, with the various fields
being non-minimally coupled to gravity, in the framework of holographic dark
energy. We classify them and we discuss their cosmological implications. In
particular, we examine the present value of the dark energy equation-of-state
parameter and the crossing through the phantom divide, and we extract the
conditions for a future cosmological singularity. The combined scenarios are in
agreement with observations and reveal interesting cosmological behaviors. | Anomaly inflow and thermal equilibrium: Using the anomaly inflow mechanism, we compute the flavor/Lorentz
non-invariant contribution to the partition function in a background with a
U(1) isometry. This contribution is a local functional of the background
fields. By identifying the U(1) isometry with Euclidean time we obtain a
contribution of the anomaly to the thermodynamic partition function from which
hydrostatic correlators can be efficiently computed. Our result is in line
with, and an extension of, previous studies on the role of anomalies in a
hydrodynamic setting. Along the way we find simplified expressions for
Bardeen-Zumino polynomials and various transgression formulae |
Space-time Schrödinger symmetries of a post-Galilean particle: We study the space-time symmetries of the actions obtained by expanding the
action for a massive free relativistic particle around the Galilean action. We
obtain all the point space-time symmetries of the post-Galilean actions by
working in canonical space. We also construct an infinite collection of
generalized Schr\"odinger algebras parameterized by an integer $M$, with $M=0$
corresponding to the standard Schr\"odinger algebra. We discuss the
Schr\"odinger equations associated to these algebras, their solutions and
projective phases. | The Giant Graviton Expansion: We propose and test a novel conjectural relation satisfied by the
superconformal index of maximally supersymmetric $U(N)$ gauge theory in four
dimensions. Analogous relations appear to be also valid for the superconformal
indices of a large collection of other gauge theories, as well as for a broad
class of index-like generating functions. The relation expresses the finite $N$
index as a systematic series of corrections to a large $N$ answer. Individual
corrections have an holographic interpretation as the analytic continuation of
contributions from "giant graviton" branes fixed by a specific symmetry
generator. |
More on Heavy-Light Bootstrap up to Double-Stress-Tensor: We investigate the heavy-light four-point function up to
double-stress-tensor, supplementing 1910.06357. By using the OPE coefficients
of lowest-twist double-stress-tensor in the literature, we find the Regge
behavior for lowest-twist double-stress-tensor in general even dimension within
the large impact parameter regime. In the next, we perform the Lorentzian
inversion formula to obtain both the OPE coefficients and anomalous dimensions
of double-twist operators $[\mathcal{O}_H\mathcal{O}_L]_{n,J}$ with finite spin
$J$ in $d=4$. We also extract the anomalous dimensions of double-twist
operators with finite spin in general dimension, which allows us to address the
cases that $\Delta_L$ is specified to the poles in lowest-twist
double-stress-tensors where certain double-trace operators
$[\mathcal{O}_L\mathcal{O}_L]_{n,J}$ mix with lowest-twist
double-stress-tensors. In particular, we verify and discuss the Residue
relation that determines the product of the mixed anomalous dimension and the
mixed OPE. We also present the double-trace and mixed OPE coefficients
associated with $\Delta_L$ poles in $d=6,8$. In the end, we turn to discuss
CFT$_2$, we verify the uniqueness of double-stress-tensor that is consistent
with Virasoso symmetry. | Black hole collision with a scalar particle in four, five and seven
dimensional anti-de Sitter spacetimes: ringing and radiation: In this work we compute the spectra, waveforms and total scalar energy
radiated during the radial infall of a small test particle coupled to a scalar
field into a $d$-dimensional Schwarzschild-anti-de Sitter black hole. We focus
on $d=4, 5$ and 7, extending the analysis we have done for $d=3$. For small
black holes, the spectra peaks strongly at a frequency $\omega \sim d-1$, which
is the lowest pure anti-de Sitter (AdS) mode. The waveform vanishes
exponentially as $t \to \infty$, and this exponential decay is governed
entirely by the lowest quasinormal frequency. This collision process is
interesting from the point of view of the dynamics itself in relation to the
possibility of manufacturing black holes at LHC within the brane world
scenario, and from the point of view of the AdS/CFT conjecture, since the
scalar field can represent the string theory dilaton, and 4, 5, 7 are
dimensions of interest for the AdS/CFT correspondence. |
D-Branes in Field Theory: Certain gauge theories in four dimensions are known to admit semi-classical
D-brane solitons. These are domain walls on which vortex flux tubes may end.
The purpose of this paper is to develop an open-string description of these
D-branes. The dynamics of the domain walls is shown to be governed by a
Chern-Simons-Higgs theory which, at the quantum level, captures the classical
"closed string" scattering of domain wall solitons. | Generalized Coordinate Gauge, Nonabelian Stokes Theorem and Dual QCD
Lagrangian: This paper is an extended version of hep-th/9802134. Dual QCD Lagrangian is
derived by making use of the generalized coordinate gauge, where 1-form (vector
potential) is expressed as an integral of the 2-form (field strength) along an
(arbitrary) contour. As another application a simple proof of the nonabelian
Stokes theorem is given. |
General Metrics of G_2 and Spin(7) Holonomy: Using a method introduced by Hitchin we obtain the system of first order
differential equations that determine the most general cohomogeniety one G_2
holonomy metric with S^3 \times S^3 principal orbits. The method is then
applied to G_2 metric with S^3 \times T^3 principal orbits in which an analytic
solution is obtained. The generalized metric has more free parameters than that
previously constructed. After showing that the generalization is non-trivial a
system of first order equations is obtained for new Spin(7) metric with
principal orbits S^7. | How to Stop (Worrying and Love) the Bubble: Boundary Changing Solutions: We discover that a class of bubbles of nothing are embedded as time dependent
scaling limits of previous spacelike-brane solutions. With the right initial
conditions, a near-bubble solution can relax its expansion and open the compact
circle. Thermodynamics of the new class of solutions is discussed and the
relationships between brane/flux transitions, tachyon condensation and
imaginary D-branes are outlined. Finally, a related class of simultaneous
connected S-branes are also examined. |
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