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Inflation induced by Gravitino Condensation in Supergravity: We discuss the emergence of an inflationary phase in supergravity with the
super-Higgs effect due to dynamical spontaneous breaking of supersymmetry, in
which the role of the inflaton is played by the gravitino condensate. Realistic
models compatible with the Planck satellite CMB data are found in conformal
supergravity scenarios with dynamical gravitino masses that are small compared
to the Planck mass, as could be induced by a non-trivial vacuum expectation
value of the dilaton superfield of appropriate magnitude.
|
Effects of the CPT-even and Lorentz violation on the Bhabha scattering
at finite temperature: In this paper a Lorentz-violating CPT-even non-minimal coupling term is
considered. A new interaction term between fermions and photons emerges. In
this context, the differential cross-section for Bhabha scattering at finite
temperature is calculated. The temperature effects are introduced using the
Thermo- Field Dynamics (TFD) formalism. It is shown that the differential
cross-section is changed due to both effects, Lorentz violation and finite
temperature.
|
Semi-infinite cohomology in conformal field theory and 2d gravity: We discuss various techniques for computing the semi-infinite cohomology of
highest weight modules which arise in the BRST quantization of two dimensional
field theories. In particular, we concentrate on two such theories -- the $G/H$
coset models and $2d$ gravity coupled to $c\leq 1$ conformal matter. (to appear
in the proceedings of the XXV Karpacz Winter School)
|
Feynman graph generation and calculations in the Hopf algebra of Feynman
graphs: Two programs for the computation of perturbative expansions of quantum field
theory amplitudes are provided. feyngen can be used to generate Feynman graphs
for Yang-Mills, QED and $\varphi^k$ theories. Using dedicated graph theoretic
tools feyngen can generate graphs of comparatively high loop orders. feyncop
implements the Hopf algebra of those Feynman graphs which incorporates the
renormalization procedure necessary to calculate finite results in perturbation
theory of the underlying quantum field theory. feyngen is validated by
comparison to explicit calculations of zero dimensional quantum field theories
and feyncop is validated using a combinatorial identity on the Hopf algebra of
graphs.
|
Describing Curved Spaces by Matrices: It is shown that a covariant derivative on any d-dimensional manifold M can
be mapped to a set of d operators acting on the space of functions on the
principal Spin(d)-bundle over M. In other words, any d-dimensional manifold can
be described in terms of d operators acting on an infinite dimensional space.
Therefore it is natural to introduce a new interpretation of matrix models in
which matrices represent such operators. In this interpretation the
diffeomorphism, local Lorentz symmetry and their higher-spin analogues are
included in the unitary symmetry of the matrix model. Furthermore the Einstein
equation is obtained from the equation of motion, if we take the standard form
of the action S=-tr([A_{a},A_{b}][A^{a},A^{b}]).
|
Gauss' Law and String-Localized Quantum Field Theory: The quantum Gauss Law as an interacting field equation is a prominent feature
of QED with eminent impact on its algebraic and superselection structure. It
forces charged particles to be accompanied by "photon clouds" that cannot be
realized in the Fock space, and prevents them from having a sharp mass. Because
it entails the possibility of "measurement of charges at a distance", it is
well-known to be in conflict with locality of charged fields in a Hilbert
space. We show how a new approach to QED advocated by the authors, that avoids
indefinite metric and ghosts, can secure causality and achieve Gauss' Law along
with all its nontrivial consequences. We explain why this is not at variance
with recent results in a paper by Buchholz et al.
|
Non-split singularities and conifold transitions in F-theory: In F-theory, if a fiber type of an elliptic fibration involves a condition
that requires an exceptional curve to split into two irreducible components, it
is called ``split'' or ``non-split'' type depending on whether it is globally
possible or not. In the latter case, the gauge symmetry is reduced to a
non-simply-laced Lie algebra due to monodromy. We show that this
split/non-split transition is, except for a special class of models, a conifold
transition from the resolved to the deformed side, associated with the conifold
singularities emerging where the codimension-one singularity is enhanced to
$D_{2k+2}$ $(k \geq 1)$ or $E_7$. We also examine how the previous proposal for
the origin of non-local matter can be actually implemented in our blow-up
analysis.
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Particles with distance dependent statistics at low temperatures: We consider a simplified model of particles with effectively distance
dependent statistics, that is particles coupled to a gauge field the Lagrangian
of which contains the Chern-Simons term. We analyze the low-lying states of the
two-particle system and show that under certain conditions they can exhibit
negative compressibility, hinting on a possible \`a la van der Vaals picture.
|
N=1 super sinh-Gordon model in the half line: Breather solutions: We examine the N=1 super sinh-Gordon (SShG) model restricted into the half
line through a reduction from the defect SShG model. The B\"acklund
transformations are employed to generate one-, two- and three-soliton solutions
as well as a class of breathers solution for this model. The parameters of such
classical solutions are shown to satisfy some contraints in order to preserve
both integrability and supersymmetry properties of the original bulk theory.
Additionally, previous results are recovered when performing the purely bosonic
limit.
|
Quantum Graphity: a model of emergent locality: Quantum graphity is a background independent model for emergent locality,
spatial geometry and matter. The states of the system correspond to dynamical
graphs on N vertices. At high energy, the graph describing the system is highly
connected and the physics is invariant under the full symmetric group acting on
the vertices. We present evidence that the model also has a low-energy phase in
which the graph describing the system breaks permutation symmetry and appears
to be ordered, low-dimensional and local. Consideration of the free energy
associated with the dominant terms in the dynamics shows that this low-energy
state is thermodynamically stable under local perturbations. The model can also
give rise to an emergent U(1) gauge theory in the ground state by the
string-net condensation mechanism of Levin and Wen. We also reformulate the
model in graph-theoretic terms and compare its dynamics to some common graph
processes.
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Duality between 1+1 dimensional Maxwell-Dilaton gravity and Liouville
field theory: We present an interesting reformulation of a collection of dilaton gravity
models in two space-time dimensions into a field theory of two decoupled
Liouville fields in flat space, in the presence of a Maxwell gauge field. An
effective action is also obtained, encoding the dynamics of the dilaton field
and the single gravitational degree of freedom in a decoupled regime. This
effective action represents an interesting starting point for future work,
including the canonical quantization of these classes of non trivial models of
gravity coupled matter systems.
|
BPS $M2$-branes in $AdS_4\times Q^{1, 1, 1}$ Dual to Loop Operators: In this paper, we first compute the Killing spinors of $AdS_4\times Q^{1, 1,
1}$ and its certain orbifolds. Based on this, two classes of $M2$-brane
solutions are found. The first class of solutions includes $M2$-branes dual to
Wilson loops in the fundamental representation as special cases. The second
class includes the candidates of the holographic description of vortex loops in
the dual field theories.
|
Classical/Quantum Duality: String theory requires two kinds of loop expansion: classical $(\alpha')$
worldsheet loops with expansion parameter $<T>$ where $T$ is a modulus field,
and quantum $(\hbar)$ spacetime loops with expansion parameter $<S>$ where $S$
is the dilaton field. Four-dimensional string/string duality (a corollary of
ten-dimensional string/fivebrane duality) interchanges the roles of $S$ and $T$
and hence interchanges classical and quantum.
|
LieART 2.0 -- A Mathematica Application for Lie Algebras and
Representation Theory: We present LieART 2.0 which contains substantial extensions to the
Mathematica application LieART (Lie Algebras and Representation Theory) for
computations frequently encountered in Lie algebras and representation theory,
such as tensor product decomposition and subalgebra branching of irreducible
representations. The basic procedure is unchanged: it computes root systems of
Lie algebras, weight systems and several other properties of irreducible
representations, but new features and procedures have been included to allow
the extensions to be seamless. The new version of LieART continues to be user
friendly. New extended tables of properties, tensor products and branching
rules of irreducible representations are included in the supplementary material
for use without Mathematica software. LieART 2.0 now includes the branching
rules to special subalgebras for all classical and exceptional Lie algebras up
to and including rank 15.
|
Noncommutative Instantons in 4k Dimensions: We consider Ward's generalized self-duality equations for U(2r) Yang-Mills
theory on R^{4k} and their Moyal deformation under self-dual noncommutativity.
Employing an extended ADHM construction we find two kinds of explicit
solutions, which generalize the 't Hooft and BPST instantons from R^4 to
noncommutative R^{4k}. The BPST-type configurations appear to be new even in
the commutative case.
|
All Or Nothing: On the Small Fluctuations of Two-Dimensional
String-Theoretic Black Holes: A comprehensive analysis of small fluctuations about two-dimensional
string-theoretic and string-inspired black holes is presented. It is shown with
specific examples that two-dimensional black holes behave in a radically
different way from all known black holes in four dimensions. For both the
$SL(2,R)/U(1)$ black hole and the two-dimensional black hole coupled to a
massive dilaton with constant field strength, it is shown that there are a {\it
continuous infinity} of solutions to the linearized equations of motion, which
are such that it is impossible to ascertain the classical linear response. It
is further shown that the two-dimensional black hole coupled to a massive,
linear dilaton admits {\it no small fluctuations at all}. We discuss possible
implications of our results for the Callan-Giddings-Harvey-Strominger black
hole.
|
R matrix and bicovariant calculus for the inhomogeneous quantum groups
IGL_q(n): We find the R matrix for the inhomogeneous quantum groups whose homogeneous
part is $GL_q(n)$, or its restrictions to $SL_q(n)$,$U_q(n)$ and $SU_q(n)$. The
quantum Yang-Baxter equation for R holds because of the Hecke relation for the
braiding matrix of the homogeneous subgroup. A bicovariant differential
calculus on $IGL_q(n)$ is constructed, and its application to the $D=4$
Poincar\'e group $ISL_q(2,\Cb)$ is discussed.
|
Collective coordinate model of kink-antikink collisions in $φ^4$
theory: The fractal velocity pattern in symmetric kink-antikink collisions in
$\phi^4$ theory is shown to emerge from a dynamical model with two effective
moduli, the kink-antikink separation and the internal shape mode amplitude. The
shape mode usefully approximates Lorentz contractions of the kink and antikink,
and the previously problematic null-vector in the shape mode amplitude at zero
separation is regularized.
|
E11 and exceptional field theory: We demonstrate that exceptional field theory is a truncation of the
non-linear realisation of the semi-direct product of E11 and its first
fundamental as proposed in 2003. Evaluating the simple equations of the E11
approach, and using the commutators of the E11 algebra, we find the equations
of exceptional field theory after making a radical truncation. This procedure
does not respect any of the higher level E11 symmetries and so these are lost.
We suggest that the need for the section condition in exceptional field theory
could be a consequence of the truncation.
|
Fine-tuning and the Wilson renormalization group: We use the Wilson renormalization group (RG) formulation to solve the
fine-tuning procedure needed in renormalization schemes breaking the gauge
symmetry. To illustrate this method we systematically compute the non-invariant
couplings of the ultraviolet action of the SU(2) pure Yang-Mills theory at
one-loop order.
|
Domain walls in supersymmetric QCD: We consider domain walls that appear in supersymmetric SU(N) with one massive
flavour. In particular, for N > 3 we explicitly construct the elementary domain
wall that interpolates between two contiguous vacua. We show that these
solutions are BPS saturated for any value of the mass of the matter fields. We
also comment on their large N limit and their relevance for supersymmetric
gluodynamics.
|
On interactions of massless integer high spin and scalar fields: We apply an unconstrained formulation of bosonic higher spin fields to study
interactions of these fields with a bosonic field using new method for the
deformation procedure. It is proved that local vertices of any order containing
one higher spin $s$ field and arbitrary number of scalar fields and being
invariant under original gauge transformations are described with the help of
one local totally symmetric $(s-2)$-rank tensor of scalar fields. This tensor
is explicitly constructed for particular cases related to cubic vertices for
spin $s$ and vertices of an arbitrary order for spin $s=4$.
|
Schild Action and Space-Time Uncertainty Principle in String Theory: We show that the path-integral quantization of relativistic strings with the
Schild action is essentially equivalent to the usual Polyakov quantization at
critical space-time dimensions. We then present an interpretation of the Schild
action which points towards a derivation of superstring theory as a theory of
quantized space-time where the squared string scale plays the role of the
minimum quantum for space-time areas. A tentative approach towards such a goal
is proposed, based on a microcanonical formulation of large N supersymmetric
matrix model.
|
Generalized Near Horizon Extreme Binary Black Hole Geometry: We present a new vacuum solution of Einstein's equations describing the near
horizon region of two neutral, extreme (zero-temperature), co-rotating,
non-identical Kerr black holes. The metric is stationary, asymptotically near
horizon extremal Kerr (NHEK), and contains a localized massless strut along the
symmetry axis between the black holes. In the deep infrared, it flows to two
separate throats which we call "pierced-NHEK" geometries: each throat is NHEK
pierced by a conical singularity. We find that in spite of the presence of the
strut for the pierced-NHEK geometries the isometry group SL(2,R)xU(1) is
restored. We find the physical parameters and entropy.
|
The Holographic Fluid on the Sphere Dual to the Schwarzschild Black Hole: We consider deformation of the d+2 dimensional asymptotically flat
Schwarzschild black hole spacetime with the induced metric on a d-sphere at
$r=r_c$ held fixed. This is done without taking the near horizon limit. The
deformation is determined so that the $\Lambda=0$ vacuum Einstein equation is
satisfied and the metric is regular on the horizon. In this paper the velocity
of a dual fluid $v^i$ is assumed to be a Killing field and small, and the
deformed metric is obtained up to $O(v^2)$. At this order of hydrodynamic
expansion the dual fluid is an ideal one. The structure of the metric is fairly
different from the near horizon result of Bredberg and Strominger in
arXiv:1106.3084.
|
Brick wall diagrams as a completely integrable system: We study the free energy of an integrable, planar, chiral and non-unitary
four-dimensional Yukawa theory, the bi-fermion fishnet theory discovered by
Pittelli and Preti. The typical Feynman-diagrams of this model are of regular
"brick-wall"-type, replacing the regular square lattices of standard fishnet
theory. We adapt A. B. Zamolodchikov's powerful classic computation of the
thermodynamic free energy of fishnet graphs to the brick-wall case in a
transparent fashion, and find the result in closed form. Finally, we briefly
discuss two further candidate integrable models in three and six dimensions
related to the brick wall model.
|
Quantum backreaction for overspinning BTZ geometries: We examine the semiclassical backreaction of a conformally coupled scalar
field on an overspinning BTZ geometry. This extends the work done on a similar
problem for ($2+1$)- AdS geometries of the BTZ family with $|M|>|J|$. The
overspinning classical solutions corresponds to $|M|<|J|$ and possess a naked
singularity at $r=0$. Using the renormalized quantum stress-energy tensor for a
conformally coupled scalar field on such a spacetime, we obtain the
semiclassical Einstein equations, which we attempt to solve perturbatively. We
show that the stress-energy tensor is non-renormalizable in this approach, and
consequently the perturbative solution to the semiclassical equations in the
overspinning case does not exist. This could be an indication of the fact that
the naked singularity at the center of an overspinning geometry is of a more
severe nature than the conical singularity found in the same family of BTZ
geometries.
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Antiparticle Contribution in the Cross Ladder Diagram for Two Boson
Propagation in the Light-front: In the light-front milieu, there is an implicit assumption that the vacuum is
trivial. By this " triviality " is meant that the Fock space of solutions for
equations of motion is sectorized in two, one of positive energy k- and the
other of negative one corresponding respectively to positive and negative
momentum k+. It is assumed that only one of the Fock space sector is enough to
give a complete description of the solutions, but in this work we consider an
example where we demonstrate that both sectors are necessary.
|
Handling Handles: Nonplanar Integrability in $\mathcal{N}=4$
Supersymmetric Yang-Mills Theory: We propose an integrability setup for the computation of correlation
functions of gauge-invariant operators in $\mathcal{N}=4$ supersymmetric
Yang-Mills theory at higher orders in the large $N_{\text{c}}$ genus expansion
and at any order in the 't Hooft coupling $g_{\text{YM}}^2N_{\text{c}}$. In
this multi-step proposal, one polygonizes the string worldsheet in all possible
ways, hexagonalizes all resulting polygons, and sprinkles mirror particles over
all hexagon junctions to obtain the full correlator. We test our
integrability-based conjecture against a non-planar four-point correlator of
large half-BPS operators at one and two loops.
|
Gauge fields - strings duality and the loop equation: We explore gauge fields - strings duality by means of the loop equations and
the zigzag symmetry. The results are striking and incomplete. Striking -
because we find that the string ansatz proposed in [A.M. Polyakov,
hep-th/9711002] satisfies gauge theory Schwinger-Dyson equations precisely at
the critical dimension D=4. Incomplete - since we get these results only in the
WKB approximation and only for a special class of contours. The ways to go
beyond these limitations and in particular the OPE for operators defined on the
loop are also discussed.
|
Five-point Superluminality Bounds: We investigate how the speed of propagation of physical excitations is
encoded in the coefficients of five-point interactions. This leads to a
superluminality bound on scalar five-point interactions, which we present here
for the first time. To substantiate our result, we also consider the case of
four-point interactions for which bounds from S-matrix sum rules exist and show
that these are parametrically equivalent to the bounds obtained within our
analysis. Finally, we extend the discussion to a class of higher-point
interactions.
|
A Kaehler Structure of the Triplectic Geometry: We study the geometry of the triplectic quantization of gauge theories. We
show that underlying the triplectic geometry is a Kaehler manifold N endowed
with a pair of transversal polarizations. The antibrackets can be brought to
the canonical form if and only if N admits a flat symmetric connection that is
compatible with the complex structure and the polarizations.
|
A class of two-dimensional Yang-Mills vacua and their relation to the
non-linear sigma model: Classical vacuum - pure gauge - solutions of Euclidean two-dimensional SU(2)
Yang-Mills theories are studied. Topologically non-trivial vacua are found in a
class of gauge group elements isomorphic to $S_2$. These solutions are
unexpectedly related to the solution of the non-linear O(3) model and to the
motion of a particle in a periodic potential.
|
General first-order mass ladder operators for Klein-Gordon fields: We study the ladder operator on scalar fields, mapping a solution of the
Klein-Gordon equation onto another solution with a different mass, when the
operator is at most first order in derivatives. Imposing the commutation
relation between the d'Alembertian, we obtain the general condition for the
ladder operator, which contains a non-trivial case which was not discussed in
the previous work [V. Cardoso, T. Houri and M. Kimura, Phys.Rev.D 96, 024044
(2017), arXiv:1706.07339]. We also discuss the relation with supersymmetric
quantum mechanics.
|
Entanglement Entropy with a Time-dependent Hamiltonian: The time evolution of entanglement tracks how information propagates in
interacting quantum systems. We study entanglement entropy in CFT$_2$ with a
time-dependent Hamiltonian. We perturb by operators with time-dependent source
functions and use the replica trick to calculate higher order corrections to
entanglement entropy. At first order, we compute the correction due to a metric
perturbation in AdS$_3$/CFT$_2$ and find agreement on both sides of the
duality. Past first order, we find evidence of a universal structure of
entanglement propagation to all orders. The central feature is that
interactions entangle unentangled excitations. Entanglement propagates
according to "entanglement diagrams," proposed structures that are motivated by
accessory spacetime diagrams for real-time perturbation theory. To illustrate
the mechanisms involved, we compute higher-order corrections to free fermion
entanglement entropy. We identify an unentangled operator, one which does not
change the entanglement entropy to any order. Then, we introduce an interaction
and find it changes entanglement entropy by entangling the unentangled
excitations. The entanglement propagates in line with our conjecture. We
compute several entanglement diagrams. We provide tools to simplify the
computation of loop entanglement diagrams, which probe UV effects in
entanglement propagation in CFT and holography.
|
Non-geometric heterotic backgrounds and 6D SCFTs/LSTs: We study ${\mathcal N}=(1,0)$ six-dimensional theories living on defects of
non-geometric backgrounds of the $E_8\times E_8$ and the
$\text{Spin}(32)/{\mathbb Z}_2$ heterotic strings. Such configurations can be
analyzed by dualizing to F-theory on elliptic K3-fibered non-compact Calabi-Yau
threefolds. The majority of the resulting dual threefolds turn out to contain
singularities which do not admit a crepant resolution. When the singularities
can be resolved crepantly, the theories living on the defect are explicitly
determined and reveal a form of duality in which distinct defects are described
by the same IR fixed point. In particular, a subclass of non-geometric defects
corresponds to SCFTs/LSTs arising from small heterotic instantons on ADE
singularities.
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Black hole thermodynamics is extensive with variable Newton constant: Inspired by the recent studies on the thermodynamics of AdS black holes in
the restricted phase space formalism, we propose a similar formalism for the
thermodynamics of non-AdS black holes with variable Newton constant. It is
shown that, by introducing the new variables $N,\mu$, where $N$ is proportional
to the inverse Newton constant and $\mu$ its conjugate variable, referred to as
the chemical potential, the black hole thermodynamics can be formulated in a
form which is consistent with the standard extensive thermodynamics for open
macroscopic systems, with the first law and the Euler relation hold
simultaneously. This formalism has profound implications, in particular, the
mass is a homogeneous function of the first order in the extensive variables
and the intensive variables are zeroth order homogeneous functions. The
chemical potential is shown to be closely related to the Euclidean action
evaluated at the black hole configuration.
|
Strict deformations of quantum field theory in de Sitter spacetime: We propose a new deformed Rieffel product for functions in de Sitter
spacetime, and study the resulting deformation of quantum field theory in de
Sitter using warped convolutions. This deformation is obtained by embedding de
Sitter in a higher-dimensional Minkowski spacetime, deforming there using the
action of translations and subsequently projecting back to de Sitter. We
determine the two-point function of a deformed free scalar quantum field, which
differs from the undeformed one, in contrast to the results in deformed
Minkowski spacetime where they coincide. Nevertheless, we show that in the
limit where de Sitter spacetime becomes flat, we recover the well-known
non-commutative Minkowski spacetime.
|
Wavelet regularization of Euclidean QED: The regularization of quantum electrodynamics in the space of functions
$\psi_a(x)$, which depend on both the position $x$ and the scale $a$, is
presented. The scale-dependent functions are defined in terms of the continuous
wavelet transform in $\mathbb{R}^4$ Euclidean space, with the derivatives of
Gaussian served as basic wavelets. The vacuum polarization and the dependence
of the effective coupling constant on the scale parameters are calculated in
one-loop approximation in the limit $p^2 \gg 4m^2$.
|
Thermodynamics of Taub-NUT/Bolt-AdS Black Holes in Einstein-Gauss-Bonnet
Gravity: We give a review of the existence of Taub-NUT/bolt solutions in Einstein
Gauss-Bonnet gravity with the parameter $\alpha $ in six dimensions. Although
the spacetime with base space $S^{2}\times S^{2}$ has curvature singularity at
$r=N$, which does not admit NUT solutions, we may proceed with the same
computations as in the $\mathbb{CP}^{2}$ case. The investigation of
thermodynamics of NUT/Bolt solutions in six dimensions is carried out. We
compute the finite action, mass, entropy, and temperature of the black hole.
Then the validity of the first law of thermodynamics is demonstrated. It is
shown that in NUT solutions all thermodynamic quantities for both base spaces
are related to each other by substituting
$\alpha^{\mathbb{CP}^{k}}=[(k+1)/k]\alpha^{S^{2} \times S^{2}\times
>...S_{k}^{2}}$. So no further information is given by investigating NUT
solution in the $S^{2}\times S^{2}$ case. This relation is not true for bolt
solutions. A generalization of the thermodynamics of black holes to arbitrary
even dimensions is made using a new method based on the Gibbs-Duhem relation
and Gibbs free energy for NUT solutions. According to this method, the finite
action in Einstein Gauss-Bonnet is obtained by considering the generalized
finite action in Einstein gravity with an additional term as a function of
$\alpha$. Stability analysis is done by investigating the heat capacity and
entropy in the allowed range of $\alpha$, $\Lambda$ and $N$. For NUT solutions
in $d$ dimensions, there exist a stable phase at a narrow range of $\alpha$. In
six-dimensional Bolt solutions, metric is completely stable for
$\mathcal{B}=S^{2}\times S^{2}$, and is completely unstable for
$\mathcal{B}=\mathbb{CP}^{2}$ case.
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Poisson-Lie T-Duality of WZW Model via Current Algebra Deformation: Poisson-Lie T-duality of the Wess-Zumino-Witten (WZW) model having the group
manifold of $SU(2)$ as target space is investigated. The whole construction
relies on the deformation of the affine current algebra of the model, the
semi-direct sum $\mathfrak{su}(2)(\mathbb{R}) \, \dot{\oplus} \, \mathfrak{a}$,
to the fully semisimple Kac-Moody algebra
$\mathfrak{sl}(2,\mathbb{C})(\mathbb{R})$. A two-parameter family of models
with $SL(2,\mathbb{C})$ as target phase space is obtained so that Poisson-Lie
T-duality is realised as an $O(3,3)$ rotation in the phase space. The dual
family shares the same phase space but its configuration space is
$SB(2,\mathbb{C})$, the Poisson-Lie dual of the group $SU(2)$. A parent action
with doubled degrees of freedom on $SL(2,\mathbb{C})$ is defined, together with
its Hamiltonian description.
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Non-perturbative BRST quantization of Euclidean Yang-Mills theories in
Curci-Ferrari gauges: In this paper we address the issue of the non-perturbative quantization of
Euclidean Yang-Mills theories in the Curci-Ferrari gauge. In particular, we
construct a Refined Gribov-Zwanziger action for this gauge which takes into
account the presence of gauge copies as well as the dynamical formation of
dimension two condensates. This action enjoys a non-perturbative BRST symmetry
recently proposed in \cite{Capri:2015ixa}. Finally, we give attention to the
gluon propagator in different space-time dimensions.
|
Classical solutions in the Einstein-Born-Infeld-Abelian-Higgs model: We consider the classical equations of the Born-Infeld-Abelian-Higgs model
(with and without coupling to gravity) in an axially symmetric ansatz. A
numerical analysis of the equations reveals that the (gravitating)
Nielsen-Olesen vortices are smoothly deformed by the Born-Infeld interaction,
characterized by a coupling constant $\beta^2$, and that these solutions cease
to exist at a critical value of $\beta^2$. When the critical value is
approached, the length of the magnetic field on the symmetry axis becomes
infinite.
|
Physics of String Flux Compactifications: We provide a qualitative review of flux compactifications of string theory,
focusing on broad physical implications and statistical methods of analysis.
|
Long-lived oscillons from asymmetric bubbles: The possibility that extremely long-lived, time-dependent, and localized
field configurations (``oscillons'') arise during the collapse of asymmetrical
bubbles in 2+1 dimensional phi^4 models is investigated. It is found that
oscillons can develop from a large spectrum of elliptically deformed bubbles.
Moreover, we provide numerical evidence that such oscillons are: a) circularly
symmetric; and b) linearly stable against small arbitrary radial and angular
perturbations. The latter is based on a dynamical approach designed to
investigate the stability of nonintegrable time-dependent configurations that
is capable of probing slowly-growing instabilities not seen through the usual
``spectral'' method.
|
High-temperature expansion of the grand thermodynamic potential for
scalar particles in crossed electromagnetic fields: The problem of a scalar particle in a constant crossed electromagnetic field
($\mathbf{E}\perp\mathbf{H}$ and $|\mathbf{E}|=|\mathbf{H}|$) is examined. The
high-temperature expansion of the grand thermodynamic potential and vacuum
energy with account for non-perturbative corrections are derived. The
contribution from particles and antiparticles is considered separately. It is
shown that the non-perturbative corrections depend on boundary conditions but
do not depend on fields.
|
String Theory and the Donaldson Polynomial: It is shown that the scattering of spacetime axions with fivebrane solitons
of heterotic string theory at zero momentum is proportional to the Donaldson
polynomial.
|
Light Cone Bootstrap in General 2D CFTs and Entanglement from Light Cone
Singularity: The light cone OPE limit provides a significant amount of information
regarding the conformal field theory (CFT), like the high-low temperature limit
of the partition function. We started with the light cone bootstrap in the {\it
general} CFT ${}_2$ with $c>1$. For this purpose, we needed an explicit
asymptotic form of the Virasoro conformal blocks in the limit $z \to 1$, which
was unknown until now. In this study, we computed it in general by studying the
pole structure of the {\it fusion matrix} (or the crossing kernel). Applying
this result to the light cone bootstrap, we obtained the universal total twist
(or equivalently, the universal binding energy) of two particles at a large
angular momentum. In particular, we found that the total twist is saturated by
the value $\frac{c-1}{12}$ if the total Liouville momentum exceeds beyond the
{\it BTZ threshold}. This might be interpreted as a black hole formation in
AdS${}_3$. As another application of our light cone singularity, we studied the
dynamics of entanglement after a global quench and found a Renyi phase
transition as the replica number was varied. We also investigated the dynamics
of the 2nd Renyi entropy after a local quench. We also provide a universal form
of the Regge limit of the Virasoro conformal blocks from the analysis of the
light cone singularity. This Regge limit is related to the general $n$-th Renyi
entropy after a local quench and out of time ordered correlators.
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BRST symmetry of SU(2) Yang-Mills theory in Cho--Faddeev--Niemi
decomposition: We determine the nilpotent BRST and anti-BRST transformations for the
Cho--Faddeev-Niemi variables for the SU(2) Yang-Mills theory based on the new
interpretation given in the previous paper of the Cho--Faddeev-Niemi
decomposition. This gives a firm ground for performing the BRST quantization of
the Yang--Mills theory written in terms of the Cho--Faddeev-Niemi variables. We
propose also a modified version of the new Maximal Abelian gauge which could
play an important role in the reduction to the original Yang-Mills theory.
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The Structure of the Non-SUSY Baryonic Branch of Klebanov-Strassler: We study the two-dimensional space of supergravity solutions corresponding to
non-supersymmetric deformations of the baryonic branch of Klebanov-Strassler.
By combining analytical methods with a numerical survey of the parameter space,
we find that this solution space includes as limits the softly-broken N=1
solutions of Gubser et al. and those of Dymarsky and Kuperstein. We also
identify a one-dimensional family of solutions corresponding to a natural
non-supersymmetric generalisation of Klebanov-Strassler, and one corresponding
to the limit in which supersymmetry is completely absent, even in the far UV.
For almost all of the parameter space we find indications that much of the
structure of the supersymmetric baryonic branch survives.
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Vacuum energy for a scalar field with self-interaction in (1+1)
dimensions: We calculate the vacuum (Casimir) energy for a scalar field with $\phi^4$
self-interaction in (1+1) dimensions non perturbatively, i.e., in all orders of
the self-interaction. We consider massive and massless fields in a finite box
with Dirichlet boundary conditions and on the whole axis as well. For strong
coupling, the vacuum energy is negative indicating some instability.
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Level truncation and the tachyon in open bosonic string field theory: The tachyonic instability of the open bosonic string is analyzed using the
level truncation approach to string field theory. We have calculated all terms
in the cubic action of the string field theory describing zero-momentum
interactions of up to level 20 between scalars of level 10 or less. These
results are used to study the tachyon effective potential and the
nonperturbative stable vacuum. We find that the energy gap between the unstable
and stable vacua converges much more quickly than the coefficients of the
effective tachyon potential. By including fields up to level 10, 99.91% of the
energy from the bosonic D-brane tension is cancelled in the nonperturbative
stable vacuum. It appears that the perturbative expansion of the effective
tachyon potential around the unstable vacuum has a small but finite radius of
convergence. We find evidence for a critical point in the tachyon effective
potential at a small negative value of the tachyon field corresponding to this
radius of convergence. We study the branch structure of the effective potential
in the vicinity of this point and speculate that the tachyon effective
potential is globally nonnegative.
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More on effective composite metrics: In this work we study different classes of effective composite metrics
proposed in the context of one-loop quantum corrections in bimetric gravity.
For this purpose we consider contributions of the matter loops in form of
cosmological constants and potential terms yielding two types of effective
composite metrics. This guarantees a nice behaviour at the quantum level.
However, the theoretical consistency at the classical level needs to be ensured
additionally. It turns out that among all these possible couplings only one
unique effective metric survives this criteria at the classical level.
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Feynman Integrals and Intersection Theory: We introduce the tools of intersection theory to the study of Feynman
integrals, which allows for a new way of projecting integrals onto a basis. In
order to illustrate this technique, we consider the Baikov representation of
maximal cuts in arbitrary space-time dimension. We introduce a minimal basis of
differential forms with logarithmic singularities on the boundaries of the
corresponding integration cycles. We give an algorithm for computing a basis
decomposition of an arbitrary maximal cut using so-called intersection numbers
and describe two alternative ways of computing them. Furthermore, we show how
to obtain Pfaffian systems of differential equations for the basis integrals
using the same technique. All the steps are illustrated on the example of a
two-loop non-planar triangle diagram with a massive loop.
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Exact self-gravitating N-body motion in the CGHS model: In the asymptotically flat two-dimensional dilaton gravity, we present an
N-body particle action which has a dilaton coupled mass term for the exact
solubility. This gives nonperturbative exact solutions for the N-body
self-gravitating system, so the infalling particles form a black hole and their
trajectories are exactly described. In our two-dimensional case, the critical
mass for the formation of black holes does not exist, so even a single particle
forms a black hole, which means that we can treat many black holes. The
infalling particles give additional time-like singularities in addition to the
space-like black hole singularity. However, the latter singularities can be
properly cloaked by the future horizons within some conditions.
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Proper incorporation of self-adjoint extension method to Green's
function formalism : one-dimensional $δ^{'}$-function potential case: One-dimensional $\delta^{'}$-function potential is discussed in the framework
of Green's function formalism without invoking perturbation expansion. It is
shown that the energy-dependent Green's function for this case is crucially
dependent on the boundary conditions which are provided by self-adjoint
extension method. The most general Green's function which contains four real
self-adjoint extension parameters is constructed. Also the relation between the
bare coupling constant and self-adjoint extension parameter is derived.
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Tachyonic Resonance Preheating in Expanding Universe: In this paper the tachyonic resonance preheating generated from the bosonic
trilinear $\phi\chi^2$ interactions in an expanding Universe is studied. In
$\lambda\phi^4/4$ inflationary model the trilinear interaction, in contrast to
the four-legs $\phi^2\chi^2$, breaks the conformal symmetry explicitly and the
resonant source term becomes non-periodic, making the Floquet theorem
inapplicable. We find that the occupation number of the produced
$\chi$-particles has a non-linear exponential growth with exponent $\sim
x^{3/2}$, where $x$ is the conformal time. This should be contrasted with
preheating from a periodic resonant source, arising for example from the
four-legs $\phi^2\chi^2$ interaction, where the occupation number has a linear
exponential growth. We present an analytic method to compute the interference
term coming from phases accumulated in non-tachyonic scattering regions and
show that the effects of the interference term causes ripples on $x^{3/2}$
curve, a result which is confirmed by numerical analysis. Studying the effects
of back-reaction of the $\chi$-particles, we show that tachyonic resonance
preheating in our model can last long enough to transfer most of the energy
from the background inflation field $\phi$, providing an efficient model for
preheating in the chaotic inflation models.
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Spiky strings in $\varkappa$-deformed $AdS$: We study rigidly rotating strings in $\varkappa$-deformed $AdS$ background.
We probe this classically integrable background with `spiky' strings and
analyze the string profiles in the large charge limit systematically. We also
discuss the dispersion relation among the conserved charges for these solutions
in long string limit.
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Statistical Mechanics of Vortices from D-branes and T-duality: We propose a novel and simple method to compute the partition function of
statistical mechanics of local and semi-local BPS vortices in the Abelian-Higgs
model and its non-Abelian extension on a torus. We use a D-brane realization of
the vortices and T-duality relation to domain walls. We there use a special
limit where domain walls reduce to gas of hard (soft) one-dimensional rods for
Abelian (non-Abelian) cases. In the simpler cases of the Abelian-Higgs model on
a torus, our results agree with exact results which are geometrically derived
by an explicit integration over the moduli space of vortices. The equation of
state for U(N) gauge theory deviates from van der Waals one, and the second
virial coefficient is proportional to 1/sqrt{N}, implying that non-Abelian
vortices are "softer" than Abelian vortices. Vortices on a sphere are also
briefly discussed.
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Generally Covariant Actions for Multiple D-branes: We develop a formalism that allows us to write actions for multiple D-branes
with manifest general covariance. While the matrix coordinates of the D-branes
have a complicated transformation law under coordinate transformations, we find
that these may be promoted to (redundant) matrix fields on the transverse space
with a simple covariant transformation law. Using these fields, we define a
covariant distribution function (a matrix generalization of the delta function
which describes the location of a single brane). The final actions take the
form of an integral over the curved space of a scalar single-trace action built
from the covariant matrix fields, tensors involving the metric, and the
covariant distribution function. For diagonal matrices, the integral localizes
to the positions of the individual branes, giving N copies of the single-brane
action.
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The holographic map as a conditional expectation: We study the holographic map in AdS/CFT, as modeled by a quantum error
correcting code with exact complementary recovery. We show that the map is
determined by local conditional expectations acting on the operator algebras of
the boundary/physical Hilbert space. Several existing results in the literature
follow easily from this perspective. The Black Hole area law, and more
generally the Ryu-Takayanagi area operator, arises from a central sum of
entropies on the relative commutant. These entropies are determined in a state
independent way by the conditional expectation. The conditional expectation can
also be found via a minimization procedure, similar to the minimization
involved in the RT formula. For a local net of algebras associated to connected
boundary regions, we show the complementary recovery condition is equivalent to
the existence of a standard net of inclusions -- an abstraction of the
mathematical structure governing QFT superselection sectors given by Longo and
Rehren. For a code consisting of algebras associated to two disjoint regions of
the boundary theory we impose an extra condition, dubbed dual-additivity, that
gives rise to phase transitions between different entanglement wedges.
Dual-additive codes naturally give rise to a new split code subspace, and an
entropy bound controls which subspace and associated algebra is
reconstructable. We also discuss known shortcomings of exact complementary
recovery as a model of holography. For example, these codes are not able to
accommodate holographic violations of additive for overlapping regions. We
comment on how approximate codes can fix these issues.
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Strings in Yang-Mills-Higgs theory coupled to gravity: Non-Abelian strings for an Einstein-Yang-Mills-Higgs theory are explicitly
constructed. We consider N_f Higgs fields in the fundamental representation of
the U(1)xSU(N_c) gauge group in order to have a color-flavor SU(N_c) group
remaining unbroken. Choosing a suitable ansatz for the metric, Bogomol'nyi-like
first order equations are found and rotationally symmetric solutions are
proposed. In the N_f = N_c case, solutions are local strings and are shown to
be truly non-Abelian by parameterizing them in terms of orientational
collective coordinates. When N_f > N_c, the solutions correspond to semilocal
strings which, beside the orientational degrees of freedom, acquire additional
collective coordinates parameterizing their transverse size. The low-energy
effective theories for the correspondent moduli are found, showing that all
zero modes are normalizable in presence of gravity, even in the semilocal case.
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Towards gravitational QNM spectrum from quantum spacetime: The effective potential for the axial mode of gravitational wave on
noncommutative Schwarzschild background is presented.
Noncommutativity is introduced via deformed Hopf algebra of diffeomorphisms
by means of a semi-Killing Drinfeld twist.
The analysis is performed up to the first order in perturbation of the metric
and noncommutativity parameter.
This results in a modified Regge-Wheeler potential with the strongest
differences in comparison to the classical Regge-Wheeler potential being near
the horizon.
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The mass formula for a fundamental string as a BPS solution of a
D-brane's worldvolume: We propose a (generalized) ``mass formula'' for a fundamental string
described as a BPS solution of a D-brane's worldvolume. The mass formula is
obtained by using the Hamiltonian density on the worldvolume, based on
transformation properties required for it. Its validity is confirmed by
investigating the cases of point charge solutions of D-branes in a D-8-brane
(i.e. curved) background, where the mass of each of the corresponding strings
is proportional to the geodesic distance from the D-brane to the point
parametrized by the (regularized) value of a transverse scalar field. It is
also shown that the mass of the string agrees with the energy defined on the
D-brane's worldvolume only in the flat background limit, but the agreement does
not always hold when the background is curved.
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GR uniqueness and deformations: In the metric formulation gravitons are described with the parity symmetric
$S_+^2\otimes S_-^2$ representation of Lorentz group. General Relativity is
then the unique theory of interacting gravitons with second order field
equations. We show that if a chiral $S_+^3\otimes S_-$ representation is used
instead, the uniqueness is lost, and there is an infinite-parametric family of
theories of interacting gravitons with second order field equations. We use the
language of graviton scattering amplitudes, and show how the uniqueness of GR
is avoided using simple dimensional analysis. The resulting distinct from GR
gravity theories are all parity asymmetric, but share the GR MHV amplitudes.
They have new all same helicity graviton scattering amplitudes at every
graviton order. The amplitudes with at least one graviton of opposite helicity
continue to be determinable by the BCFW recursion.
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Coupling supergravity to non-supersymmetric matter: By introducing a nonlinearly transforming goldstino field
non-super\-sym\-metric matter can be coupled to supergravity. This implies the
possibility of coupling a standard model with one Higgs to supergravity.
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Limits on the integration constant of the dark radiation term in Brane
Cosmology: We consider the constraints from primordial Helium abundances on the constant
of integration of the dark radiation term of the brane-world generalized
Friedmann equation derived from the Randall-Sundrum Single brane model. We
found that -- using simple, approximate and semianalytical Method -- that the
constant of integration is limited to be between -8.9 and 2.2 which limits the
possible contribution from dark radiation term to be approximately between -27%
to 7% of the background photon energy density.
|
Evolution equation for 3-quark Wilson loop operator: The evolution equation for the 3 quark Wilson loop operator has been derived
in the leading logarithm approximation within Balitsky high energy operator
expansion.
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6D Supersymmetry, Projective Superspace and 4D, N=1 Superfields: In this note, we establish the formulation of 6D, N=1 hypermultiplets in
terms of 4D chiral-nonminimal (CNM) scalar multiplets. The coupling of these to
6D, N=1 Yang-Mills multiplets is described. A 6D, N=1 projective superspace
formulation is given in which the above multiplets naturally emerge. The
covariant superspace quantization of these multiplets is studied in details.
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Quantum Field Theory on Star Graphs: We discuss some basic aspects of quantum fields on star graphs, focusing on
boundary conditions, symmetries and scale invariance in particular. We
investigate the four-fermion bulk interaction in detail. Using bosonization and
vertex operators, we solve the model exactly for scale invariant boundary
conditions, formulated in terms of the fermion current and without dissipation.
The critical points are classified and determined explicitly. These results are
applied for deriving the charge and spin transport, which have interesting
physical features.
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Vacuum Structure of Two-Dimensional Gauge Theories on the Light Front: We discuss the problem of vacuum structure in light-front field theory in the
context of (1+1)-dimensional gauge theories. We begin by reviewing the known
light-front solution of the Schwinger model, highlighting the issues that are
relevant for reproducing the $\theta$-structure of the vacuum. The most
important of these are the need to introduce degrees of freedom initialized on
two different null planes, the proper incorporation of gauge field zero modes
when periodicity conditions are used to regulate the infrared, and the
importance of carefully regulating singular operator products in a
gauge-invariant way. We then consider SU(2) Yang-Mills theory in 1+1 dimensions
coupled to massless adjoint fermions. With all fields in the adjoint
representation the gauge group is actually SU(2)$/Z_2$, which possesses
nontrivial topology. In particular, there are two topological sectors and the
physical vacuum state has a structure analogous to a $\theta$ vacuum. We
formulate the model using periodicity conditions in $x^\pm$ for infrared
regulation, and consider a solution in which the gauge field zero mode is
treated as a constrained operator. We obtain the expected $Z_2$ vacuum
structure, and verify that the discrete vacuum angle which enters has no effect
on the spectrum of the theory. We then calculate the chiral condensate, which
is sensitive to the vacuum structure. The result is nonzero, but inversely
proportional to the periodicity length, a situation which is familiar from the
Schwinger model. The origin of this behavior is discussed.
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Stochastic Analysis of an Accelerated Charged Particle -Transverse
Fluctuations-: An accelerated particle sees the Minkowski vacuum as thermally excited, and
the particle moves stochastically due to an interaction with the thermal bath.
This interaction fluctuates the particle's transverse momenta like the Brownian
motion in a heat bath. Because of this fluctuating motion, it has been
discussed that the accelerated charged particle emits extra radiation (the
Unruh radiation) in addition to the classical Larmor radiation, and experiments
are under planning to detect such radiation by using ultrahigh intensity lasers
constructed in near future. There are, however, counterarguments that the
radiation is canceled by an interference effect between the vacuum fluctuation
and the fluctuating motion. In fact, in the case of an internal detector where
the Heisenberg equation of motion can be solved exactly, there is no additional
radiation after the thermalization is completed. In this paper, we revisit the
issue in the case of an accelerated charged particle in the scalar-field analog
of QED. We prove the equipartition theorem of transverse momenta by
investigating a stochastic motion of the particle, and show that the Unruh
radiation is partially canceled by an interference effect.
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Dualities and loops on squashed $S^3$: We consider $\mathcal{N}=4$ supersymmetric gauge theories on the squashed
three-sphere with six preserved supercharges. We first discuss how Wilson and
vortex loops preserve up to four of the supercharges and we find squashing
independence for the expectation values of these $\frac{2}{3}$-BPS loops. We
then show how the additional supersymmetries facilitate the analytic matching
of partition functions and loop operator expectation values to those in the
mirror dual theory, allowing one to lift all the results that were previously
established on the round sphere to the squashed sphere. Additionally, on the
squashed sphere with four preserved supercharges, we numerically evaluate the
partition functions of ABJM and its dual super-Yang-Mills at low ranks of the
gauge group. We find matching values of their partition functions, prompting us
to conjecture the general equality on the squashed sphere. From the numerics we
also observe the squashing dependence of the Lee-Yang zeros and of the
non-perturbative corrections to the all order large $N$ expression for the ABJM
partition function.
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Electron neutrino mass scale in spectrum of Dirac equation with the
5-form flux term on the AdS(5)xS(5) background: Dimensional reduction from 10 to 5 dimensions of the IIB supergravity Dirac
equation written down on the AdS(5)xS(5) (+ self-dual 5-form) background
provides the unambiguous values of bulk masses of Fermions in the effective 5D
Randall Sundrum theory. The use of "untwisted" and "twisted" (hep-th/0012378)
boundary conditions at the UV and IR ends of the warped space-time results in
two towers of spectrum of Dirac equation: the ordinary one which is linear in
spectral number and the "twisted" one exponentially decreasing with growth of
spectral number. Taking into account of the Fermion-5-form interaction
(hep-th/9811106) gives the electron neutrino mass scale in the "twisted"
spectrum of Dirac equation. Profiles in extra space of the eigenfunctions of
left and right "neutrinos" drastically differ which may result in the extremely
small coupling of light right neutrino with ordinary matter thus joining it to
plethora of candidates for Dark Matter.
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Comment on ``A New Symmetry for QED'' and ``Relativistically Covariant
Symmetry in QED'': We show that recently found symmetries in QED are just non-local versions of
standard BRST symmetry.
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Hydrodynamic manifestations of gravitational chiral anomaly: The conservation of an axial current modified by the gravitational chiral
anomaly implies the universal transport phenomenon (Kinematical Vortical
Effect) dependent solely on medium vorticity and acceleration but not dependent
explicitly on its temperature and density. This general analysis is verified
for the case of massless fermions with spin 1/2.
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Integrability and MHV diagrams in N=4 supersymmetric Yang-Mills theory: We apply MHV diagrams to the derivation of the one-loop dilatation operator
of N=4 super Yang-Mills in the SO(6) sector. We find that in this approach the
calculation reduces to the evaluation of a single MHV diagram in dimensional
regularisation. This provides the first application of MHV diagrams to an
off-shell quantity. We also discuss other applications of the method and future
directions.
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The Multi-Regge limit of NMHV Amplitudes in N=4 SYM Theory: We consider the multi-Regge limit for N=4 SYM NMHV leading color amplitudes
in two different formulations: the BFKL formalism for multi-Regge amplitudes in
leading logarithm approximation, and superconformal N=4 SYM amplitudes. It is
shown that the two approaches agree to two-loops for the 2->4 and 3->3
six-point amplitudes. Predictions are made for the multi-Regge limit of three
loop 2->4 and 3->3 NMHV amplitudes, as well as a particular sub-set of two loop
2 ->2 +n N^kMHV amplitudes in the multi-Regge limit in the leading logarithm
approximation from the BFKL point of view.
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An Introduction to Spontaneous Symmetry Breaking: Perhaps the most important aspect of symmetry in physics is the idea that a
state does not need to have the same symmetries as the theory that describes
it. This phenomenon is known as spontaneous symmetry breaking. In these lecture
notes, starting from a careful definition of symmetry in physics, we introduce
symmetry breaking and its consequences. Emphasis is placed on the physics of
singular limits, showing the reality of symmetry breaking even in small-sized
systems. Topics covered include Nambu-Goldstone modes, quantum corrections,
phase transitions, topological defects and gauge fields. We provide many
examples from both high energy and condensed matter physics. These notes are
suitable for graduate students.
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Leading low-energy effective action in the 6D hypermultiplet theory on a
vector/tensor background: We consider a six dimensional (1,0) hypermultiplet model coupled to an
external field of vector/tensor system and study the structure of the
low-energy effective action of this model. Manifestly a (1,0) supersymmetric
procedure of computing the effective action is developed in the framework of
the superfield proper-time technique. The leading low-energy contribution to
the effective action is calculated.
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Towards a Big Crunch Dual: We show there exist smooth asymptotically anti-de Sitter initial data which
evolve to a big crunch singularity in a low energy supergravity limit of string
theory. This opens up the possibility of using the dual conformal field theory
to obtain a fully quantum description of the cosmological singularity. A
preliminary study of this dual theory suggests that the big crunch is an
endpoint of evolution even in the full string theory. We also show that any
theory with scalar solitons must have negative energy solutions. The results
presented here clarify our earlier work on cosmic censorship violation in N=8
supergravity.
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The boundary state for a class of analytic solutions in open string
field theory: We construct a boundary state for a class of analytic solutions in the
Witten's open string field theory. The result is consistent with the property
of the zero limit of a propagator's length, which was claimed in [19]. And we
show that our boundary state becomes expected one for the perturbative vacuum
solution and the tachyon vacuum solution. We also comment on possible presence
of multi-brane solutions and ghost brane solutions from our boundary state.
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Bounded solutions of fermions in the background of mixed vector-scalar
inversely linear potentials: The problem of a fermion subject to a general mixing of vector and scalar
potentials in a two-dimensional world is mapped into a Sturm-Liouville problem.
Isolated bounded solutions are also searched. For the specific case of an
inversely linear potential, which gives rise to an effective Kratzer potential
in the Sturm-Liouville problem, exact bounded solutions are found in closed
form. The case of a pure scalar potential with their isolated zero-energy
solutions, already analyzed in a previous work, is obtained as a particular
case. The behaviour of the upper and lower components of the Dirac spinor is
discussed in detail and some unusual results are revealed. The nonrelativistic
limit of our results adds a new support to the conclusion that even-parity
solutions to the nonrelativistic one-dimensional hydrogen atom do not exist.
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Beyond Triality: Dual Quiver Gauge Theories and Little String Theories: The web of dual gauge theories engineered from a class of toric Calabi-Yau
threefolds is explored. In previous work, we have argued for a triality
structure by compiling evidence for the fact that every such manifold $X_{N,M}$
(for given $(N,M)$) engineers three a priori different, weakly coupled quiver
gauge theories in five dimensions. The strong coupling regime of the latter is
in general described by Little String Theories. Furthermore, we also
conjectured that the manifold $X_{N,M}$ is dual to $X_{N',M'}$ if $NM=N'M'$ and
$\text{gcd}(N,M)=\text{gcd}(N',M')$. Combining this result with the triality
structure, we currently argue for a large number of dual quiver gauge theories,
whose instanton partition functions can be computed explicitly as specific
expansions of the topological partition function $\mathcal{Z}_{N,M}$ of
$X_{N,M}$. We illustrate this web of dual theories by studying explicit
examples in detail. We also undertake first steps in further analysing the
extended moduli space of $X_{N,M}$ with the goal of finding other dual gauge
theories.
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The relativistic fluid dual to vacuum Einstein gravity: We present a construction of a (d+2)-dimensional Ricci-flat metric
corresponding to a (d+1)-dimensional relativistic fluid, representing
holographically the hydrodynamic regime of a (putative) dual theory. We show
how to obtain the metric to arbitrarily high order using a relativistic
gradient expansion, and explicitly carry out the computation to second order.
The fluid has zero energy density in equilibrium, which implies
incompressibility at first order in gradients, and its stress tensor (both at
and away from equilibrium) satisfies a quadratic constraint, which determines
its energy density away from equilibrium. The entire dynamics to second order
is encoded in one first order and six second order transport coefficients,
which we compute. We classify entropy currents with non-negative divergence at
second order in relativistic gradients. We then verify that the entropy current
obtained by pulling back to the fluid surface the area form at the null horizon
indeed has a non-negative divergence. We show that there are distinct
near-horizon scaling limits that are equivalent either to the relativistic
gradient expansion we discuss here, or to the non-relativistic expansion
associated with the Navier-Stokes equations discussed in previous works. The
latter expansion may be recovered from the present relativistic expansion upon
taking a specific non-relativistic limit.
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Further studies on holographic insulator/superconductor phase
transitions from Sturm-Liouville eigenvalue problems: We take advantage of the Sturm-Liouville eigenvalue problem to analytically
study the holographic insulator/superconductor phase transition in the probe
limit. The interesting point is that this analytical method can not only
estimate the most stable mode of the phase transition, but also the second
stable mode. We find that this analytical method perfectly matches with other
numerical methods, such as the shooting method. Besides, we argue that only
Dirichlet boundary condition of the trial function is enough under certain
circumstances, which will lead to a more precise estimation. This relaxation
for the boundary condition of the trial function is first observed in this
paper as far as we know.
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Comments on lump solutions in SFT: We analyze a recently proposed scheme to construct analytic lump solutions in
open SFT. We argue that in order for the scheme to be operative and guarantee
background independence it must be implemented in the same 2D conformal field
theory in which SFT is formulated. We outline and discuss two different
possible approaches. Next we reconsider an older proposal for analytic lump
solutions and implement a few improvements. In the course of the analysis we
formulate a distinction between regular and singular gauge transformations and
advocate the necessity of defining a topology in the space of string fields.
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Axion decay constants at special points in type II string theory: We propose the mechanism to disentangle the decay constant of closed string
axion from the string scale in the framework of type II string theory on
Calabi-Yau manifold. We find that the quantum and geometrical corrections in
the prepotential that arise at some special points in the moduli space widen
the window of axion decay constant. In particular, around the small complex
structure points, the axion decay constant becomes significantly lower than the
string scale. We also discuss the moduli stabilization leading to the
phenomenologically attractive low-scale axion decay constant.
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Domain wall junctions in a generalized Wess-Zumino model: We investigate domain wall junctions in a generalized Wess-Zumino model with
a Z(N) symmetry. We present a method to identify the junctions which are
potentially BPS saturated. We then use a numerical simulation to show that
those junctions indeed saturate the BPS bound for N=4. In addition, we study
the decay of unstable non-BPS junctions.
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Cuscuton: A Causal Field Theory with an Infinite Speed of Sound: We introduce a model of scalar field dark energy, Cuscuton, which can be
realized as the incompressible (or infinite speed of sound) limit of a scalar
field theory with a non-canonical kinetic term (or k-essence). Even though
perturbations of Cuscuton propagate superluminally, we show that they have a
locally degenerate phase space volume (or zero entropy), implying that they
cannot carry any microscopic information, and thus the theory is causal. Even
coupling to ordinary scalar fields cannot lead to superluminal signal
propagation. Furthermore, we show that the family of constant field
hypersurfaces are the family of Constant Mean Curvature (CMC) hypersurfaces,
which are the analogs of soap films (or soap bubbles) in a Euclidian space.
This enables us to find the most general solution in 1+1 dimensions, whose
properties motivate conjectures for global degeneracy of the phase space in
higher dimensions. Finally, we show that the Cuscuton action can model the
continuum limit of the evolution of a field with discrete degrees of freedom
and argue why it is protected against quantum corrections at low energies.
While this paper mainly focuses on interesting features of Cuscuton in a
Minkowski spacetime, a companion paper (astro-ph/0702002) examines cosmology
with Cuscuton dark energy.
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QCD strings and the thermodynamics of the metastable phase of QCD at
large $N_c$: The thermodyanmics of a metastable hadronic phase of QCD at large $N_C$ are
related to properties of an effective QCD string. In particular, it is shown
that in the large $N_c$ limit and near the maximum hadronic temperature, $T_H$,
the energy density and pressure of the metastable phase scale as ${\cal E} \sim
(T_H-T)^{-(D_\perp-6)/2}$ (for $D_\perp <6$) and $P \sim
(T_H-T)^{-(D_\perp-4)/2}$ (for $D_\perp <4$) where $D_\perp$ is the effective
number of transverse dimensions of the string theory. It is shown, however,
that for the thermodynamic quantities of interest the limits $T \to T_H$ and
$N_c \to \infty$ do not commute. The prospect of extracting $D_\perp$ via
lattice simulations of the metastable hadronic phase at moderately large $N_c$
is discussed.
|
Quantum Theory in Accelerated Frames of Reference: The observational basis of quantum theory in accelerated systems is studied.
The extension of Lorentz invariance to accelerated systems via the hypothesis
of locality is discussed and the limitations of this hypothesis are pointed
out. The nonlocal theory of accelerated observers is briefly described.
Moreover, the main observational aspects of Dirac's equation in noninertial
frames of reference are presented. The Galilean invariance of nonrelativistic
quantum mechanics and the mass superselection rule are examined in the light of
the invariance of physical laws under inhomogeneous Lorentz transformations.
|
de Sitter Spacetimes from Warped Compactifications of IIB String Theory: We continue our study of codimension two solutions of warped space-time
varying compactifications of string theory. In this letter we discuss a
non-supersymmetric solution of the classical type IIB string theory with de
Sitter gravity on a codimension two uncompactified part of spacetime. A
non-zero positive value of the cosmological constant is induced by the presence
of non-trivial stringy moduli, such as the axion-dilaton system for the type
IIB string theory. Furthermore, the naked singularity of the codimension two
solution is resolved by the presence of a small but non-zero cosmological
constant.
|
Self-duality and vacuum selection: I propose that self-duality in quantum phase-space provides the criteria for
the selection of the quantum gravity vacuum. The evidence for this assertion
arises from two independent considerations. The first is the phenomenological
success of the free fermionic heterotic-string models, which are constructed in
the vicinity of the self-dual point under T-duality. The relation between the
free fermionic models and the underlying Z2 X Z2 toroidal orbifolds is
discussed. Recent analysis revealed that the Z2 X Z2 free fermionic orbifolds
utilize an asymmetric shift in the reduction to three generations, which
indicates that the untwisted geometrical moduli are fixed near the self-dual
point. The second consideration arises from the recent formulation of quantum
mechanics from an equivalence postulate and its relation to phase-space
duality. In this context it is demonstrated that the trivial state, with
V(q)=E=0, is identified with the self-dual state under phase-space duality.
These observations suggest a more general mathematical principle in operation.
In physical systems that exhibit a duality structure, the self-dual states
under the given duality transformations correspond to critical points.
|
A Solvable 2D Quantum Gravity Model with $\GAMMA >0$: We consider a model of discretized 2d gravity interacting with Ising spins
where phase boundaries are restricted to have minimal length and show
analytically that the critical exponent $\gamma= 1/3$ at the spin transition
point. The model captures the numerically observed behavior of standard
multiple Ising spins coupled to 2d gravity.
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Noncommutativity and the lightfront: We discuss various limits which transform configuration space into phase
space, with emphasis on those related to lightfront field theory, and show that
they are unified by spectral flow. Examples include quantising in `almost
lightfront' coordinates and the appearance of lightlike noncommutativity from a
strong background laser field. We compare this with the limit of a strong
magnetic field, and investigate the role played by lightfront zero modes.
|
Noncommutative Geometry and Matrix Theory: Compactification on Tori: We study toroidal compactification of Matrix theory, using ideas and results
of non-commutative geometry. We generalize this to compactification on the
noncommutative torus, explain the classification of these backgrounds, and
argue that they correspond in supergravity to tori with constant background
three-form tensor field. The paper includes an introduction for mathematicians
to the IKKT formulation of Matrix theory and its relation to the BFSS Matrix
theory.
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2k-dimensional N=8 supersymmetric quantum mechanics: We demonstrate that two-dimensional N=8 supersymmetric quantum mechanics
which inherits the most interesting properties of $N=2, d=4$ SYM can be
constructed if the reduction to one dimension is performed in terms of the
basic object, i.e. the $N=2, d=4$ vector multiplet. In such a reduction only
complex scalar fields from the $N=2, d=4$ vector multiplet become physical
bosons in $d=1$, while the rest of the bosonic components are reduced to
auxiliary fields, thus giving rise to the {\bf (2, 8, 6)} supermultiplet in
$d=1$. We construct the most general action for this supermultiplet with all
possible Fayet-Iliopoulos terms included and explicitly demonstrate that the
action possesses duality symmetry extended to the fermionic sector of theory.
In order to deal with the second--class constraints present in the system, we
introduce the Dirac brackets for the canonical variables and find the
supercharges and Hamiltonian which form a N=8 super Poincar\`{e} algebra with
central charges. Finally, we explicitly present the generalization of
two-dimensional N=8 supersymmetric quantum mechanics to the $2k$-dimensional
case with a special K\"{a}hler geometry in the target space.
|
Hilbert series and mixed branches of $T[SU(N)]$ theory: We consider mixed branches of 3d $\mathcal{N}=4$ $T[SU(N)]$ theory. We
compute the Hilbert series of the Coulomb branch part of the mixed branch from
a restriction rule acting on the Hilbert series of the full Coulomb branch that
will truncate the magnetic charge summation only to the subset of BPS dressed
monopole operators that arise in the Coulomb branch sublocus where the mixed
branch stems. This restriction can be understood directly from the type IIB
brane picture by a relation between the magnetic charges of the monopoles and
brane position moduli. We also apply the restriction rule to the Higgs branch
part of a given mixed branch by exploiting 3d mirror symmetry. Both cases show
complete agreement with the results calculated by different methods.
|
Matter-coupled de Sitter Supergravity: De Sitter supergravity describes interaction of supergravity with general
chiral and vector multiplets as well as one nilpotent chiral multiplet. The
extra universal positive term in the potential due to the nilpotent multiplet,
corresponding to the anti-D3 brane in string theory, supports de Sitter vacua
in these supergravity models. In the flat space limit these supergravity models
include the Volkov-Akulov model with a non-linearly realized supersymmetry. The
rules for constructing pure de Sitter supergravity action are generalized here
in presence of other matter multiplets. We present a strategy to derive the
complete closed form general supergravity action with a given Kahler potential
$K$, superpotential $W$ and vector matrix $f_{AB}$ interacting with a nilpotent
chiral multiplet. It has the potential $V=e^K(|F^2 |+ |DW|^2 - 3 |W|^2)$, where
$F$ is a necessarily non-vanishing value of the auxiliary field of the
nilpotent multiplet. De Sitter vacua are present under simple condition that
$|F^2|- 3|W|^2>0$. A complete explicit action in the unitary gauge is
presented.
|
A generalized photon propagator: A covariant gauge independent derivation of the generalized dispersion
relation of electromagnetic waves in a medium with local and linear
constitutive law is presented. A generalized photon propagator is derived. For
Maxwell constitutive tensor, the standard light cone structure and the standard
Feynman propagator are reinstated.
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On the impact of Majorana masses in gravity-matter systems: We investigate the Higgs-Yukawa system with Majorana masses of a fermion
within asymptotically safe quantum gravity. Using the functional
renormalization group method we derive the beta functions of the Majorana
masses and the Yukawa coupling constant and discuss the possibility of a
non-trivial fixed point for the Yukawa coupling constant. In the gravitational
sector we take into account higher derivative terms such as $R^2$ and
$R_{\mu\nu}R^{\mu\nu}$ in addition to the Einstein-Hilbert term for our
truncation. For a certain value of the gravitational coupling constants and the
Majorana masses, the Yukawa coupling constant has a non-trivial fixed point
value and becomes an irrelevant parameter being thus a prediction of the
theory. We also discuss consequences due to the Majorana mass terms to the
running of the quartic coupling constant in the scalar sector.
|
Classical polymerization of the Schwarzschild metric: We study a spherically symmetric setup consisting of a Schwarzschild metric
as the background geometry in the framework of classical polymerization. This
process is an extension of the polymeric representation of quantum mechanics in
such a way that a transformation maps classical variables to their polymeric
counterpart. We show that the usual Schwarzschild metric can be extracted from
a Hamiltonian function which in turn, gets modifications due to the classical
polymerization. Then, the polymer corrected Schwarzschild metric may be
obtained by solving the polymer-Hamiltonian equations of motion. It is shown
that while the conventional Schwarzschild space-time is a vacuum solution of
the Einstein equations, its polymer-corrected version corresponds to an
energy-momentum tensor that exhibits the features of dark energy. We also use
the resulting metric to investigate some thermodynamical quantities associated
to the Schwarzschild black hole, and in comparison with the standard
Schwarzschild metric the similarities and differences are discussed.
|
Quantum Spacetime and Algebraic Quantum Field Theory: We review the investigations on the quantum structure of spactime, to be
found at the Planck scale if one takes into account the operational limitations
to localization of events which result from the concurrence of Quantum
Mechanics and General Relativity. We also discuss the different approaches to
(perturbative) Quantum Field Theory on Quantum Spacetime, and some of the
possible cosmological consequences.
|
Heterotic fluxes and supersymmetry: We show that the formal alpha' expansion for heterotic flux vacua is only
sensible when flux quantization and the appearance of string scale cycles in
the geometry are carefully taken into account. We summarize a number of
properties of solutions with N=1 and N=2 space-time supersymmetry.
|
Notes on renormalization: We outline the proofs of several principal statements in conventional
renormalization theory. This may be of some use in the light of new trends and
new techniques (Hopf algebras, etc.) recently introduced in the field.
|
Gauged Linear Sigma Model for Exotic Five-brane: We study an N=(4,4) supersymmetric gauged linear sigma model which gives rise
to the nonlinear sigma model for multi-centered KK-monopoles. We find a new
T-duality transformation of the model even in the presence of F-terms.
Performing T-duality, we find the gauged linear sigma model whose IR limit
describes the exotic 522-brane with B-field.
|
Type I vacua with brane supersymmetry breaking: We show how chiral type I models whose tadpole conditions have no
supersymmetric solution can be consistently defined introducing antibranes with
non-supersymmetric world volumes. At tree level, the resulting stable non-BPS
configurations correspond to tachyon-free spectra, where supersymmetry is
broken at the string scale on some (anti)branes but is exact in the bulk, and
can be further deformed by the addition of brane-antibrane pairs of the same
type. As a result, a scalar potential is generated, that can stabilize some
radii of the compact space. This setting has the novel virtue of linking
supersymmetry breaking to the consistency requirements of an underlying
fundamental theory.
|
Photon Self-Energy and Electric Susceptibility in a Magnetized
Three-flavor Color Superconductor: We study the photon self-energy for the in-medium photon in a three-flavor
color superconductor in the presence of a magnetic field. At strong magnetic
field, the quark dynamics becomes $(1+1)$-dimensional and the self-energy
tensor only has longitudinal components. In this approximation there is no
Debye or Meissner screenings at zero temperature, but the electric
susceptibility is nonzero and highly anisotropic. In the direction transverse
to the applied field, the electric susceptibility is the same as in vacuum,
while in the longitudinal direction it depends on the magnitude of the magnetic
field. Such a behavior is a realization in cold-dense QCD of the
magnetoelectric effect, which was first discovered in condensed matter physics.
The magnetic permeability remains equal to that in vacuum for both transverse
and longitudinal components. We discuss the importance of the Pauli-Villars
regularization to get meaningful physical results in the infrared limit of the
polarization operator. We also find the covariant form of the polarization
operator in the reduced (1+1)-D space of the lowest Landau level and proves its
transversality.
|
The Constrained State of Minimum Energy and the Effective Equation of
Motion: We define the state of minimum energy while the expectation values of the
field operators and their time derivatives in a determined moment in such a
state are constrained. As an axiom, we consider such a state as the background
of the quantum field theory. As an example, we consider the scalar field with
{\lambda}/4!{\Phi}4 interaction. To the third order of perturbation, we obtain
the equation of motion of the dynamic expectation value of the scalar field in
the defined state.
|
Maximally supersymmetric G-backgrounds of IIB supergravity: We classify the geometry of all supersymmetric IIB backgrounds which admit
the maximal number of $G$-invariant Killing spinors. For compact stability
subgroups $G=G_2, SU(3)$ and SU(2), the spacetime is locally isometric to a
product $X_n\times Y_{10-n}$ with $n=3,4,6$, where $X_n$ is a maximally
supersymmetric solution of a $n$-dimensional supergravity theory and $Y_{10-n}$
is a Riemannian manifold with holonomy $G$. For non-compact stability
subgroups, $G=K\ltimes\bR^8$, $K=Spin(7)$, SU(4), $Sp(2)$, $SU(2)\times SU(2)$
and $\{1\}$, the spacetime is a pp-wave propagating in an eight-dimensional
manifold with holonomy $K$. We find new supersymmetric pp-wave solutions of IIB
supergravity.
|
Massive mixed symmetry field dynamics in open bosonic string theory: We consider the sigma-model description of an open string interacting with
massive fields of the fourth (third massive) level. Equations of motion for the
background fields are obtained by demanding that the renormalized operator of
the energy-momentum tensor trace vanishes.
|
The large N limit of quiver matrix models and Sasaki-Einstein manifolds: We study the matrix models that result from localization of the partition
functions of N=2 Chern-Simons-matter theories on the three-sphere. A large
class of such theories are conjectured to be holographically dual to M-theory
on Sasaki-Einstein seven-manifolds. We study the M-theory limit (large N and
fixed Chern-Simons levels) of these matrix models for various examples, and
show that in this limit the free energy reproduces the expected AdS/CFT result
of N^{3/2}/Vol(Y)^{1/2}, where Vol(Y) is the volume of the corresponding
Sasaki-Einstein metric. More generally we conjecture a relation between the
large N limit of the partition function, interpreted as a function of trial
R-charges, and the volumes of Sasakian metrics on links of Calabi-Yau four-fold
singularities. We verify this conjecture for a family of U(N)^2 Chern-Simons
quivers based on M2 branes at hypersurface singularities, and for a U(N)^3
theory based on M2 branes at a toric singularity.
|
New universality classes of the non-Hermitian Dirac operator in QCD-like
theories: In non-Hermitian random matrix theory there are three universality classes
for local spectral correlations: the Ginibre class and the nonstandard classes
$\mathrm{AI}^\dagger$ and $\mathrm{AII}^\dagger$. We show that the continuum
Dirac operator in two-color QCD coupled to a chiral $\mathrm{U}(1)$ gauge field
or an imaginary chiral chemical potential falls in class $\mathrm{AI}^\dagger$
($\mathrm{AII}^\dagger$) for fermions in pseudoreal (real) representations of
$\mathrm{SU}(2)$. We introduce the corresponding chiral random matrix theories
and verify our predictions in lattice simulations with staggered fermions, for
which the correspondence between representation and universality class is
reversed. Specifically, we compute the complex eigenvalue spacing ratios
introduced recently. We also derive novel spectral sum rules.
|
Two-dimensional Quantum-Corrected Eternal Black Hole: The one-loop quantum corrections to geometry and thermodynamics of black hole
are studied for the two-dimensional RST model. We chose boundary conditions
corresponding to the eternal black hole being in the thermal equilibrium with
the Hawking radiation. The equations of motion are exactly integrated. The one
of the solutions obtained is the constant curvature space-time with dilaton
being a constant function. Such a solution is absent in the classical theory.
On the other hand, we derive the quantum-corrected metric (\ref{solution})
written in the Schwarzschild like form which is a deformation of the classical
black hole solution \cite{5d}. The space-time singularity occurs to be milder
than in classics and the solution admits two asymptotically flat black hole
space-times lying at "different sides" of the singularity. The thermodynamics
of the classical black hole and its quantum counterpart is formulated. The
thermodynamical quantities (energy, temperature, entropy) are calculated and
occur to be the same for both the classical and quantum-corrected black holes.
So, no quantum corrections to thermodynamics are observed. The possible
relevance of the results obtained to the four-dimensional case is discussed.
|
Graphene properties from curved space Dirac equation: A mathematical formulation for particle states and electronic properties of a
curved graphene sheet is provided, exploiting a massless Dirac spectrum
description for charge carriers living in a curved bidimensional background. In
particular, we study how the new description affects the characteristics of the
sample, writing an appropriate conductivity Kubo formula for the modified
background. Finally, we provide a theoretical analysis for the particular case
of a cylindrical graphene sample.
|
Bäcklund transformation for non-relativistic Chern-Simons vortices: A B\"acklund transformation yielding the static non-relativistic Chern-Simons
vortices of Jackiw and Pi is presented.
|
Consistency Conditions of the Faddeev-Niemi-Periwal Ansatz for the SU(N)
Gauge Field: The consistency condition of the Faddeev-Niemi ansatz for the gauge-fixed
massless SU(2) gauge field is discussed. The generality of the ansatz is
demonstrated by obtaining a sufficient condition for the existence of the
three-component field introduced by Faddeev and Niemi. It is also shown that
the consistency conditions determine this three-component field as a functional
of two arbitrary functions. The consistency conditions corresponding to the
Periwal ansatz for the SU(N) gauge field with N larger than 2 are also
obtained. It is shown that the gauge field obeying the Periwal ansatz must
satisfy extra (N-1)(N-2)/2 conditions.
|
Confining complex ghost degrees of freedom: We show a theorem proving that a non-local bosonic field upon a covariant
interaction with a confining gauge field undergoes the confinement of its
degrees of freedom present in the free theory changing completely the physical
mass spectrum following Kugo-Ojima criterion. This is applicable to an infinite
number of excitations of the bosonic field including ghosts whereas we pay
special attention to the modes with the complex conjugate masses, states
appearing in the string field theory motivated infinite-derivative models. The
same recipe will obviously work for the Lee-Wick models.
|
Duality and higher Buscher rules in p-form gauge theory and linearized
gravity: We perform an in-depth analysis of the transformation rules under duality for
couplings of theories containing multiple scalars, $p$-form gauge fields,
linearized gravitons or $(p,1)$ mixed symmetry tensors. Following a similar
reasoning to the derivation of the Buscher rules for string background fields
under T-duality, we show that the couplings for all classes of aforementioned
multi-field theories transform according to one of two sets of duality rules.
These sets comprise the ordinary Buscher rules and their higher counterpart;
this is a generic feature of multi-field theories in spacetime dimensions where
the field strength and its dual are of the same degree. Our analysis takes into
account topological theta terms and generalized $B$-fields, whose behavior
under duality is carefully tracked. For a 1-form or a graviton in 4D, this
reduces to the inversion of the complexified coupling or generalized metric
under electric/magnetic duality. Moreover, we write down an action for
linearized gravity in the presence of $\theta$-term from which we obtain
previously suggested on-shell duality and double duality relations. This also
provides an explanation for the origin of theta in the gravitational duality
relations as a specific additional sector of the linearized gravity action.
|
Entanglement Entropy Near Cosmological Singularities: We investigate the behavior of the entanglement entropy of a confining gauge
theory near cosmological singularities using gauge/gravity duality. As
expected, the coefficients of the UV divergent terms are given by simple
geometric properties of the entangling surface in the time-dependent
background. The finite (universal) part of the entanglement entropy either
grows without bound or remains bounded depending on the nature of the
singularity and entangling region. We also discuss a confinement/deconfinement
phase transition as signaled by the entanglement entropy.
|
Oscillating instanton solutions in curved space: We investigate oscillating instanton solutions of a self-gravitating scalar
field between degenerate vacua. We show that there exist O(4)-symmetric
oscillating solutions in a de Sitter background. The geometry of this solution
is finite and preserves the $Z_{2}$ symmetry. The nontrivial solution
corresponding to tunneling is possible only if the effect of gravity is taken
into account. We present numerical solutions of this instanton, including the
phase diagram of solutions in terms of the parameters of the present work and
the variation of energy densities. Our solutions can be interpreted as
solutions describing an instanton-induced domain wall or braneworld-like object
rather than a kink-induced domain wall or braneworld. The oscillating instanton
solutions have a thick wall and the solutions can be interpreted as a mechanism
providing nucleation of the thick wall for topological inflation. We remark
that $Z_{2}$ invariant solutions also exist in a flat and anti-de Sitter
background, though the physical significance is not clear.
|
From Electromagnetic Duality to Extended Electrodynamics: This paper presents the transition from Classical Electrodynamics (CED) to
Extended Electrodynamics (EED) from the electromagnetic duality point of view,
and emphasizes the role of the canonical complex structure in ${\cal R}^2$ in,
both, nonrelativistic and relativistic formulations of CED and EED. We begin
with summarizing the motivations for passing to EED, as well as we motivate and
outline the way to be followed in pursuing the right extension of Maxwell
equations. Further we give the nonrelativistic and relativistic approaches to
the extension and give explicitly the new equations as well as some properties
of the nonlinear vacuum solutions.
|
Black holes in presence of cosmological constant: Second order in 1/D: We have extended the results of arXiv:1704.06076 upto second subleading order
in an expansion around large dimension D. Unlike the previous case, there are
non-trivial metric corrections at this order. Due to our `background-covariant'
formalism, the dependence on Ricci and the Riemann curvature tensor of the
background is manifest here. The gravity system is dual to a dynamical membrane
coupled with a velocity field. The dual membrane is embedded in some smooth
background geometry that also satisfies the Einstein equation in presence of
cosmological constant. We explicitly computed the corrections to the equation
governing the membrane-dynamics. Our results match with earlier derivations in
appropriate limits. We calculated the spectrum of QNM from our membrane
equations and matched them against similar results derived from gravity.
|
Generalized N=2 Topological Amplitudes and Holomorphic Anomaly Equation: In arXiv:0905.3629 we described a new class of N=2 topological amplitudes
that depends both on vector and hypermultiplet moduli. Here we find that this
class is actually a particular case of much more general topological amplitudes
which appear at higher loops in heterotic string theory compactified on K3 x
T^2. We analyze their effective field theory interpretation and derive
particular (first order) differential equations as a consequence of
supersymmetry Ward identities and the 1/2-BPS nature of the corresponding
effective action terms. In string theory the latter get modified due to
anomalous world-sheet boundary contributions, generalizing in a non-trivial way
the familiar holomorphic and harmonicity anomalies studied in the past. We
prove by direct computation that the subclass of topological amplitudes studied
in arXiv:0905.3629 forms a closed set under these anomaly equations and that
these equations are integrable.
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The Schwarzian Theory - A Wilson Line Perspective: We provide a holographic perspective on correlation functions in Schwarzian
quantum mechanics, as boundary-anchored Wilson line correlators in
Jackiw-Teitelboim gravity. We first study compact groups and identify the
diagrammatic representation of bilocal correlators of the particle-on-a-group
model as Wilson line correlators in its 2d holographic BF description. We
generalize to the Hamiltonian reduction of SL(2,R) and derive the Schwarzian
correlation functions. Out-of-time ordered correlators are determined by
crossing Wilson lines, giving a 6j-symbol, in agreement with 2d CFT results.
|
Ergodic Equilibration of Rényi Entropies and Replica Wormholes: We study the behavior of R\'enyi entropies for pure states from standard
assumptions about chaos in the high-energy spectrum of the Hamiltonian of a
many-body quantum system. We compute the exact long-time averages of R\'enyi
entropies and show that the quantum noise around these values is exponentially
suppressed in the microcanonical entropy. For delocalized states over the
microcanonical band, the long-time average approximately reproduces the
equilibration proposal of H. Liu and S. Vardhan, with extra structure arising
at the order of non-planar permutations. We analyze the equilibrium
approximation for AdS/CFT systems describing black holes in equilibrium in a
box. We extend our analysis to the situation of an evaporating black hole, and
comment on the possible gravitational description of the new terms in our
approximation.
|
Topological first-order vortices in a gauged CP(2) model: We study time-independent radially symmetric first-order solitons in a CP(2)
model interacting with an Abelian gauge field whose dynamics is controlled by
the usual Maxwell term. In this sense, we develop a consistent first-order
framework verifying the existence of a well-defined lower bound for the
corresponding energy. We saturate such a lower bound by focusing on those
solutions satisfying a particular set of coupled first-order differential
equations. We solve these equations numerically using appropriate boundary
conditions giving rise to regular structures possessing finite-energy. We also
comment the main features these configurations exhibit. Moreover, we highlight
that, despite the different solutions we consider for an auxiliary function
$\beta \left( r\right) $ labeling the model (therefore splitting our
investigation in two a priori distinct branches), all resulting scenarios
engender the very same phenomenology, being physically equivalent.
|
Matrix Bases for Star Products: a Review: We review the matrix bases for a family of noncommutative $\star$ products
based on a Weyl map. These products include the Moyal product, as well as the
Wick-Voros products and other translation invariant ones. We also review the
derivation of Lie algebra type star products, with adapted matrix bases. We
discuss the uses of these matrix bases for field theory, fuzzy spaces and
emergent gravity.
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Brezin-Gross-Witten model as "pure gauge" limit of Selberg integrals: The AGT relation identifies the Nekrasov functions for various N=2 SUSY gauge
theories with the 2d conformal blocks, which possess explicit Dotsenko-Fateev
matrix model (beta-ensemble) representations the latter being polylinear
combinations of Selberg integrals. The "pure gauge" limit of these matrix
models is, however, a non-trivial multiscaling large-N limit, which requires a
separate investigation. We show that in this pure gauge limit the Selberg
integrals turn into averages in a Brezin-Gross-Witten (BGW) model. Thus, the
Nekrasov function for pure SU(2) theory acquires a form very much reminiscent
of the AMM decomposition formula for some model X into a pair of the BGW
models. At the same time, X, which still has to be found, is the pure gauge
limit of the elliptic Selberg integral. Presumably, it is again a BGW model,
only in the Dijkgraaf-Vafa double cut phase.
|
Unquenched QCD Dirac Operator Spectra at Nonzero Baryon Chemical
Potential: The microscopic spectral density of the QCD Dirac operator at nonzero baryon
chemical potential for an arbitrary number of quark flavors was derived
recently from a random matrix model with the global symmetries of QCD. In this
paper we show that these results and extensions thereof can be obtained from
the replica limit of a Toda lattice equation. This naturally leads to a
factorized form into bosonic and fermionic QCD-like partition functions. In the
microscopic limit these partition functions are given by the static limit of a
chiral Lagrangian that follows from the symmetry breaking pattern. In
particular, we elucidate the role of the singularity of the bosonic partition
function in the orthogonal polynomials approach. A detailed discussion of the
spectral density for one and two flavors is given.
|
3D superconformal theories from Sasakian seven-manifolds: new nontrivial
evidences for AdS_4/CFT_3: In this paper we discuss candidate superconformal N=2 gauge theories that
realize the AdS/CFT correspondence with M--theory compactified on the
homogeneous Sasakian 7-manifolds M^7 that were classified long ago. In
particular we focus on the two cases M^7=Q^{1,1,1} and M^7=M^{1,1,1}, for the
latter the Kaluza Klein spectrum being completely known. We show how the toric
description of M^7 suggests the gauge group and the supersingleton fields. The
conformal dimensions of the latter can be independently calculated by
comparison with the mass of baryonic operators that correspond to 5-branes
wrapped on supersymmetric 5-cycles and are charged with respect to the Betti
multiplets. The entire Kaluza Klein spectrum of short multiplets agrees with
these dimensions. Furthermore, the metric cone over the Sasakian manifold is a
conifold algebraically embedded in some C^p. The ring of chiral primary fields
is defined as the coordinate ring of C^p modded by the ideal generated by the
embedding equations; this ideal has a nice characterization by means of
representation theory. The entire Kaluza Klein spectrum is explained in terms
of these vanishing relations. We give the superfield interpretation of all
short multiplets and we point out the existence of many long multiplets with
rational protected dimensions, whose presence and pattern seem to be universal
in all compactifications.
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Non-Perturbative Two-Dimensional Dilaton Gravity: We present a review of the canonical quantization approach to the problem of
non-perturbative 2d dilaton gravity. In the case of chiral matter we describe a
method for solving the constraints by constructing a Kac-Moody current algebra.
For the models of interest, the relevant Kac-Moody algebras are based on
SL(2,R) X U(1) group and on an extended 2d Poincare group. As a consequence,
the constraints become free-field Virasoro generators with background charges.
We argue that the same happens in the non-chiral case. The problem of the
corresponding BRST cohomology is discussed as well as the unitarity of the
theory. One can show that the theory is unitary by chosing a physical gauge,
and hence the problem of transitions from pure into mixed sates is absent.
Implications for the physics of black holes are discussed. (Based on the talks
presented at Trieste conference on Gauge Theories, Applied Supersymmetry and
Quantum Gravity, May 1993 and at Danube '93 Workshop, Belgrade, Yugoslavia,
June 1993)
|
Gaugeon formalism for the two-form gauge fields: We present a BRST symmetric gaugeon formalism for the two-form gauge fields.
A set of vector gaugeon fields is introduced as a quantum gauge freedom. One of
the gaugeon fields satisfies a higher derivative field equation; this property
is necessary to change the gauge-fixing parameter of the two-form gauge field.
A naive Lagrangian for the vector gaugeon fields is itself invariant under a
gauge transformation for the vector gaugeon field. The Lagrangian of our theory
includes the gauge-fixing terms for the gaugeon fields and corresponding
Faddeev--Popov ghosts terms.
|
DDF and Pohlmeyer invariants of (super)string: We show how the Pohlmeyer invariants of the bosonic string are expressible in
terms of DDF invariants. Quantization of the DDF observables in the usual way
yields a consistent quantization of the algebra of Pohlmeyer invariants.
Furthermore it becomes straightforward to generalize the Pohlmeyer invariants
to the superstring as well as to all backgrounds which allow a free field
realization of the worldsheet theory.
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Teleparallelism in the algebraic approach to extended geometry: Extended geometry is based on an underlying tensor hierarchy algebra. We
extend the previously considered $L_\infty$ structure of the local symmetries
(the diffeomorphisms and their reducibility) to incorporate physical fields,
field strengths and Bianchi identities, and identify these as elements of the
tensor hierarchy algebra. The field strengths arise as generalised torsion, so
the naturally occurring complex in the $L_\infty$ algebra is $\ldots\leftarrow$
torsion BI's $\leftarrow$ torsion $\leftarrow$ vielbein $\leftarrow$
diffeomorphism parameters $\leftarrow\ldots$ In order to obtain equations of
motion, which are not in this complex, (pseudo-)actions, quadratic in torsion,
are given for a large class of models. This requires considering the dual
complex. We show how local invariance under the compact subgroup locally
defined by a generalised metric arises as a "dual gauge symmetry" associated
with a certain torsion Bianchi identity, generalising Lorentz invariance in the
teleparallel formulation of gravity. The analysis is performed for a large
class of finite-dimensional structure groups, with $E_5$ as a detailed example.
The continuation to infinite-dimensional cases is discussed.
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On the symmetries of BF models and their relation with gravity: The perturbative finiteness of various topological models (e.g. BF models)
has its origin in an extra symmetry of the gauge-fixed action, the so-called
vector supersymmetry. Since an invariance of this type also exists for gravity
and since gravity is closely related to certain BF models, vector supersymmetry
should also be useful for tackling various aspects of quantum gravity. With
this motivation and goal in mind, we first extend vector supersymmetry of BF
models to generic manifolds by incorporating it into the BRST symmetry within
the Batalin-Vilkovisky framework. Thereafter, we address the relationship
between gravity and BF models, in particular for three-dimensional space-time.
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Self-dual solitons in N=2 supersymmetric semilocal Chern-Simons theory: We embed the semilocal Chern-Simons-Higgs theory into an N=2 supersymmetric
system. We construct the corresponding conserved supercharges and derive the
Bogomol'nyi equations of the model from supersymmetry considerations. We show
that these equations hold provided certain conditions on the coupling constants
as well as on the Higgs potential of the system, which are a consequence of the
huge symmetry of the theory, are satisfied. They admit string-like solutions
which break one half of the supersymmetries --BPS Chern-Simons semilocal cosmic
strings-- whose magnetic flux is concentrated at the center of the vortex. We
study such solutions and show that their stability is provided by supersymmetry
through the existence of a lower bound for the energy, even though the manifold
of the Higgs vacuum does not contain non-contractible loops.
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Fluxes, Brane Charges and Chern Morphisms of Hyperbolic Geometry: The purpose of this paper is to provide the reader with a collection of
results which can be found in the mathematical literature and to apply them to
hyperbolic spaces that may have a role in physical theories. Specifically we
apply K-theory methods for the calculation of brane charges and RR-fields on
hyperbolic spaces (and orbifolds thereof). It is known that by tensoring
K-groups with the rationals, K-theory can be mapped to rational cohomology by
means of the Chern character isomorphisms. The Chern character allows one to
relate the analytic Dirac index with a topological index, which can be
expressed in terms of cohomological characteristic classes. We obtain explicit
formulas for Chern character, spectral invariants, and the index of a twisted
Dirac operator associated with real hyperbolic spaces. Some notes for a
bivariant version of topological K-theory (KK-theory) with its connection to
the index of the twisted Dirac operator and twisted cohomology of hyperbolic
spaces are given. Finally we concentrate on lower K-groups useful for
description of torsion charges.
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Conformal symmetry, chiral fermions and semiclassical approximation: The explicit form of conformal generators is found which provides the
extension of Poincare symmetry for massless particles of arbitrary helicity.
The helicity 1/2 particles are considered as the particular example. The
realization of conformal symmetry in the semiclassical regime of Weyl equation
is obtained.
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On Open String Sigma-Model and Noncommutative Gauge Fields: We consider the ordinary and noncommutative Dirac-Born-Infeld theories within
the open string sigma-model. First, we propose a renormalization scheme, hybrid
point splitting regularization, that leads directly to the Seiberg-Witten
description including their two-form. We also show how such a form appears
within the standard renormalization scheme just by some freedom in changing
variables. Second, we propose a Wilson factor which has the noncommutative
gauge invariance on the classical level and then compute the sigma-model
partition function within one of the known renormalization scheme that
preserves the noncommutative gauge invariance. As a result, we find the
noncommutative Yang-Mills action.
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A heterotic sigma model with novel target geometry: We construct a (1,2) heterotic sigma model whose target space geometry
consists of a transitive Lie algebroid with complex structure on a Kaehler
manifold. We show that, under certain geometrical and topological conditions,
there are two distinguished topological half--twists of the heterotic sigma
model leading to A and B type half--topological models. Each of these models is
characterized by the usual topological BRST operator, stemming from the
heterotic (0,2) supersymmetry, and a second BRST operator anticommuting with
the former, originating from the (1,0) supersymmetry. These BRST operators
combined in a certain way provide each half--topological model with two
inequivalent BRST structures and, correspondingly, two distinct perturbative
chiral algebras and chiral rings. The latter are studied in detail and
characterized geometrically in terms of Lie algebroid cohomology in the
quasiclassical limit.
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Two-Dimensional Dilaton Gravity: I briefly summarize recent results on classical and quantum dilaton gravity
in 1+1 dimensions.
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Quantum Entropy for the Fuzzy Sphere and its Monopoles: Using generalized bosons, we construct the fuzzy sphere $S_F^2$ and monopoles
on $S_F^2$ in a reducible representation of $SU(2)$. The corresponding quantum
states are naturally obtained using the GNS-construction. We show that there is
an emergent non-abelian unitary gauge symmetry which is in the commutant of the
algebra of observables. The quantum states are necessarily mixed and have
non-vanishing von Neumann entropy, which increases monotonically under a
bistochastic Markov map. The maximum value of the entropy has a simple relation
to the degeneracy of the irreps that constitute the reducible representation
that underlies the fuzzy sphere.
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Categorical Distributions of Maximum Entropy under Marginal Constraints: The estimation of categorical distributions under marginal constraints
summarizing some sample from a population in the most-generalizable way is key
for many machine-learning and data-driven approaches. We provide a
parameter-agnostic theoretical framework that enables this task ensuring (i)
that a categorical distribution of Maximum Entropy under marginal constraints
always exists and (ii) that it is unique. The procedure of iterative
proportional fitting (IPF) naturally estimates that distribution from any
consistent set of marginal constraints directly in the space of probabilities,
thus deductively identifying a least-biased characterization of the population.
The theoretical framework together with IPF leads to a holistic workflow that
enables modeling any class of categorical distributions solely using the
phenomenological information provided.
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Quantum discord and entropic measures of two relativistic fermions: In the present work, we study the interplay between relativistic effects and
quantumness in the system of two relativistic fermions. In particular, we
explore entropic measures of quantum correlations and quantum discord before
and after application of a boost and subsequent Wigner rotation. We also study
the positive operator-valued measurements (POVM) invasiveness before and after
the boosts. While the relativistic principle is universal and requires Lorentz
invariance of quantum correlations in the entire system, we have found specific
partitions where quantum correlations stored in particular subsystems are not
invariant. We calculate quantum discords corresponding of the states before and
after applying a boost, and observe that the state gains extra discord after
the boost. When analyzing the invasiveness of the POVMs, we have found that the
POVM applied to the initial entangled state reduces the discord to zero.
However, discord of the boosted state survives after the same POVM. Thus we
conclude that the quantum discord generated by Lorentz boost is robust
concerning the protective POVM, while the measurement exerts an invasive effect
on the discord of the initial state. Finally, we discuss potential
implementation of the ideas of this work using top quarks as a benchmark
scenario.
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Eleven dimensional supergravity and the E10/KE10 sigma-model at low A9
levels: Recently, the concept of a nonlinear sigma-model over a coset space G/H was
generalized to the case where the group G is an infinite-dimensional Kac-Moody
group, and H its (formal) `maximal compact subgroup'. Here, we study in detail
the one-dimensional (geodesic) sigma-model with G = E10 and H=KE10. We
re-examine the construction of this sigma-model and its relation to the bosonic
sector of eleven-dimensional supergravity, up to height 30, by using a new
formulation of the equations of motion. Specifically, we make systematic use of
KE10-orthonormal local frames, in the sense that we decompose the `velocity' on
E10/KE10 in terms of objects which are representations of the compact subgroup
KE10. This new perspective may help in extending the correspondence between the
E10/KE10 sigma-model and supergravity beyond the level currently checked.
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Topological Mass Generation in Three-Dimensional String Theory: The effective action of string theory in three dimensions is investigated,
incorporating the Lorentz and gauge Chern-Simons terms in the definition of the
Kalb-Ramond axion field strength. Since in three dimensions any three-form is
trivial, the action can be reformulated by properly integrating the axion out.
The circumstances under which it can be recast in form of topologically massive
gravity coupled to a topologically massive gauge theory are pointed out.
Finally, the strong coupling limit of the resulting action is inspected, with
the focus on the roles played by the axion and dilaton fields.
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Model building with the non-supersymmetric heterotic SO(16)xSO(16)
string: In this talk we review recent investigations of the non-supersymmetric
heterotic SO(16)xSO(16) string on orbifolds and smooth Calabi-Yaus. Using such
supersymmetry preserving backgrounds allows one to re-employ commonly known
model building techniques. We will argue that tachyons do not appear on smooth
Calabi-Yaus to leading order in alpha' and g_s. Twisted tachyons may arise on
singular orbifolds, where some of these approximations break down. However,
they get lifted in full blow-up. Finally, we show that model searches is viable
by identifying over 12,000 of SM-like models on various orbifold geometries.
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Tree-level Scattering Amplitudes via Homotopy Transfer: We formalize the computation of tree-level scattering amplitudes in terms of
the homotopy transfer of homotopy algebras, illustrating it with scalar
$\phi^3$ and Yang-Mills theory. The data of a (gauge) field theory with an
action is encoded in a cyclic homotopy Lie or $L_{\infty}$ algebra defined on a
chain complex including a space of fields. This $L_{\infty}$ structure can be
transported, by means of homotopy transfer, to a smaller space that, in the
massless case, consists of harmonic fields. The required homotopy maps are
well-defined since we work with the space of finite sums of plane-wave
solutions. The resulting $L_{\infty}$ brackets encode the tree-level scattering
amplitudes and satisfy generalized Jacobi identities that imply the Ward
identities. We further present a method to compute color-ordered scattering
amplitudes for Yang-Mills theory, using that its $L_{\infty}$ algebra is the
tensor product of the color Lie algebra with a homotopy commutative associative
or $C_{\infty}$ algebra. The color-ordered scattering amplitudes are then
obtained by homotopy transfer of $C_{\infty}$ algebras.
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A Canonical Approach to the Einstein-Hilbert Action in Two Spacetime
Dimensions: The canonical structure of the Einstein-Hilbert Lagrange density
$L=\sqrt{-g}R$ is examined in two spacetime dimensions, using the metric
density $h^{\mu \nu}\equiv \sqrt{-g}g^{\mu \nu}$ and symmetric affine
connection $\Gamma_{\sigma \beta}^\lambda $ as dynamical variables. The
Hamiltonian reduces to a linear combination of three first class constraints
with a local SO(2,1) algebra. The first class constraints are used to find a
generator of gauge transformations that has a closed off-shell algebra and
which leaves the Lagrangian and $\det (h^{\mu \nu})$ invariant. These
transformations are distinct from diffeomorphism invariance, and are gauge
transformations characterized by a symmetric matrix $\zeta_{\mu \nu}$.
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Orbifolds by 2-groups and decomposition: In this paper we study three-dimensional orbifolds by 2-groups with a
trivially-acting one-form symmetry group BK. These orbifolds have a global
two-form symmetry, and so one expects that they decompose into (are equivalent
to) a disjoint union of other three-dimensional theories, which we demonstrate.
These theories can be interpreted as sigma models on 2-gerbes, whose formal
structures reflect properties of the orbifold construction.
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Rotating Black Branes wrapped on Einstein Spaces: We present new rotating black brane solutions which solve Einstein's
equations with cosmological constant $\Lambda$ in arbitrary dimension $d$. For
negative $\Lambda$, the branes naturally appear in AdS supergravity
compactifications, and should therefore play some role in the AdS/CFT
correspondence. The spacetimes are warped products of a four-dimensional part
and an Einstein space of dimension $d-4$, which is not necessarily of constant
curvature. As a special subcase, the solutions contain the higher dimensional
generalization of the Kerr-AdS metric recently found by Hawking et al.
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Multiloop Amplitudes and Vanishing Theorems using the Pure Spinor
Formalism for the Superstring: A ten-dimensional super-Poincare covariant formalism for the superstring was
recently developed which involves a BRST operator constructed from superspace
matter variables and a pure spinor ghost variable. A super-Poincare covariant
prescription was defined for computing tree amplitudes and was shown to
coincide with the standard RNS prescription.
In this paper, picture-changing operators are used to define functional
integration over the pure spinor ghosts and to construct a suitable $b$ ghost.
A super-Poincare covariant prescription is then given for the computation of
N-point multiloop amplitudes. One can easily prove that massless N-point
multiloop amplitudes vanish for N<4, confirming the perturbative finiteness of
superstring theory. One can also prove the Type IIB S-duality conjecture that
$R^4$ terms in the effective action receive no perturbative contributions above
one loop.
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A Three-Family Standard-like Orientifold Model: Yukawa Couplings and
Hierarchy: We discuss the hierarchy of Yukawa couplings in a supersymmetric three family
Standard-like string Model. The model is constructed by compactifying Type IIA
string theory on a Z_2 x Z_2 orientifold in which the Standard Model matter
fields arise from intersecting D6-branes. When lifted to M theory, the model
amounts to compactification of M-theory on a G_2 manifold. While the actual
fermion masses depend on the vacuum expectation values of the multiple Higgs
fields in the model, we calculate the leading worldsheet instanton
contributions to the Yukawa couplings and examine the implications of the
Yukawa hierarchy.
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Conformal sector of Quantum Einstein Gravity in the local potential
approximation: non-Gaussian fixed point and a phase of unbroken
diffeomorphism invariance: We explore the nonperturbative renormalization group flow of Quantum Einstein
Gravity (QEG) on an infinite dimensional theory space. We consider "conformally
reduced" gravity where only fluctuations of the conformal factor are quantized
and employ the Local Potential Approximation for its effective average action.
The requirement of "background independence" in quantum gravity entails a
partial differential equation governing the scale dependence of the potential
for the conformal factor which differs significantly from that of a scalar
matter field. In the infinite dimensional space of potential functions we find
a Gaussian as well as a non-Gaussian fixed point which provides further
evidence for the viability of the asymptotic safety scenario. The analog of the
invariant cubic in the curvature which spoils perturbative renormalizability is
seen to be unproblematic for the asymptotic safety of the conformally reduced
theory. The scaling fields and dimensions of both fixed points are obtained
explicitly and possible implications for the predictivity of the theory are
discussed. Spacetime manifolds with $R^d$ as well as $S^d$ topology are
considered. Solving the flow equation for the potential numerically we obtain
examples of renormalization group trajectories inside the ultraviolet critical
surface of the non-Gaussian fixed point. The quantum theories based upon some
of them show a phase transition from the familiar (low energy) phase of gravity
with spontaneously broken diffeomorphism invariance to a new phase of unbroken
diffeomorphism invariance; the latter phase is characterized by a vanishing
expectation value of the metric.
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Non-commutative resolutions as mirrors of singular Calabi--Yau varieties: It has been conjectured that the hemisphere partition function
arXiv:1308.2217, arXiv:1308.2438 in a gauged linear sigma model (GLSM) computes
the central charge arXiv:math/0212237 of an object in the bounded derived
category of coherent sheaves for Calabi--Yau (CY) manifolds. There is also
evidence in arXiv:alg-geom/ 9511001, arXiv:hep-th/0007071. On the other hand,
non-commutative resolutions of singular CY varieties have been studied in the
context of abelian GLSMs arXiv:0709.3855. In this paper, we study an analogous
construction of abelian GLSMs for non-commutative resolutions and propose they
can be used to study a class of recently discovered mirror pairs of singular CY
varieties. Our main result shows that the hemisphere partition functions
(a.k.a.~$A$-periods) in the new GLSM are in fact period integrals
(a.k.a.~$B$-periods) of the singular CY varieties. We conjecture that the two
are completely equivalent: $B$-periods are the same as $A$-periods. We give
some examples to support this conjecture and formulate some expected
homological mirror symmetry (HMS) relation between the GLSM theory and the CY.
As shown in arXiv:2003.07148, the $B$-periods in this case are precisely given
by a certain fractional version of the $B$-series of arXiv:alg-geom/9511001.
Since a hemisphere partition function is defined as a contour integral in a
cone in the complexified secondary fan (or FI-theta parameter space)
arXiv:1308.2438, it can be reduced to a sum of residues (by theorems of
Passare-Tsikh-Zhdanov and Tsikh-Zhdanov). Our conjecture shows that this
residue sum may now be amenable to computations in terms of the $B$-series.
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Vibrational modes of Q-balls: We study linear perturbations of classically stable Q-balls in theories
admitting analytic solutions. Although the corresponding boundary value problem
is non-Hermitian, the analysis of perturbations can also be performed
analytically in certain regimes. We show that in theories with the flat
potential, large Q-balls possess soft excitations. We also find a specific
vibrational mode for Q-balls with a near-critical charge, where the
perturbation theory for excitations can be developed. Comparing with the
results on stability of Q-balls provides additional checks of our analysis.
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Heat-kernel coefficients for oblique boundary conditions: We calculate the heat-kernel coefficients, up to $a_2$, for a U(1) bundle on
the 4-Ball for boundary conditions which are such that the normal derivative of
the field at the boundary is related to a first-order operator in boundary
derivatives acting on the field. The results are used to place restrictions on
the general forms of the coefficients. In the specific case considered, there
can be a breakdown of ellipticity.
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Sampling in AdS/CFT: Recently, it has been proposed by Kempf a generalization of the Shannon
sampling theory to the physics of curved spacetimes. With the aim of exploring
the possible links between Holography and Information Theory we argue about the
similitude of the reconstruction formula in the sampling theory and
bulk-to-boundary relations found in the AdS/CFT context.
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On universal knot polynomials: We present a universal knot polynomials for 2- and 3-strand torus knots in
adjoint representation, by universalization of appropriate Rosso-Jones formula.
According to universality, these polynomials coincide with adjoined colored
HOMFLY and Kauffman polynomials at SL and SO/Sp lines on Vogel's plane, and
give their exceptional group's counterparts on exceptional line. We demonstrate
that [m,n]=[n,m] topological invariance, when applicable, take place on the
entire Vogel's plane. We also suggest the universal form of invariant of figure
eight knot in adjoint representation, and suggest existence of such
universalization for any knot in adjoint and its descendant representation.
Properties of universal polynomials and applications of these results are
discussed.
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Topology, Entropy and Witten Index of Dilaton Black Holes: We have found that for extreme dilaton black holes an inner boundary must be
introduced in addition to the outer boundary to give an integer value to the
Euler number. The resulting manifolds have (if one identifies imaginary time)
topology $S^1 \times R \times S^2 $ and Euler number $\chi = 0$ in contrast to
the non-extreme case with $\chi=2$. The entropy of extreme $U(1)$ dilaton black
holes is already known to be zero. We include a review of some recent ideas due
to Hawking on the Reissner-Nordstr\"om case. By regarding all extreme black
holes as having an inner boundary, we conclude that the entropy of {\sl all}
extreme black holes, including $[U(1)]^2$ black holes, vanishes. We discuss the
relevance of this to the vanishing of quantum corrections and the idea that the
functional integral for extreme holes gives a Witten Index. We have studied
also the topology of ``moduli space'' of multi black holes. The quantum
mechanics on black hole moduli spaces is expected to be supersymmetric despite
the fact that they are not HyperK\"ahler since the corresponding geometry has
torsion unlike the BPS monopole case. Finally, we describe the possibility of
extreme black hole fission for states with an energy gap. The energy released,
as a proportion of the initial rest mass, during the decay of an
electro-magnetic black hole is 300 times greater than that released by the
fission of an ${}^{235} U$ nucleus.
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Counting states in a model of replica wormholes: We study the Hilbert space of a system of $n$ black holes with an inner
product induced by replica wormholes. This takes the form of a sum over
permutations, which we interpret in terms of a gauge symmetry. The resulting
inner product is degenerate, with null states lying in representations
corresponding to Young diagrams with too many rows. We count the remaining
states in a large $n$ limit, which is governed by an emergent collective
Coulomb gas description describing the shape of typical Young diagrams. This
exhibits a third-order phase transition when the null states become numerous.
We find that the dimension of the black hole Hilbert space accords with a
microscopic interpretation of Bekenstein-Hawking entropy.
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Seiberg-Witten curves and double-elliptic integrable systems: An old conjecture claims that commuting Hamiltonians of the double-elliptic
integrable system are constructed from the theta-functions associated with
Riemann surfaces from the Seiberg-Witten family, with moduli treated as
dynamical variables and the Seiberg-Witten differential providing the
pre-symplectic structure. We describe a number of theta-constant equations
needed to prove this conjecture for the $N$-particle system. These equations
provide an alternative method to derive the Seiberg-Witten prepotential and we
illustrate this by calculating the perturbative contribution. We provide
evidence that the solutions to the commutativity equations are exhausted by the
double-elliptic system and its degenerations (Calogero and Ruijsenaars
systems). Further, the theta-function identities that lie behind the Poisson
commutativity of the three-particle Hamiltonians are proven.
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A rigorous lower bound on the scattering amplitude at large angle: We prove a lower bound for the modulus of the amplitude for a two-body
process at large scattering angle. This is based on the interplay of the
analyticity of the amplitude and the positivity properties of its absorptive
part. The assumptions are minimal, namely those of local quantum field theory
(in the case when dispersion relations hold). In Appendix A, lower bounds for
the forward particle-particle and particle-antiparticle amplitudes are
obtained. This is of independent interest.
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Noncommutative Geometry and Spacetime Gauge Symmetries of String Theory: We illustrate the various ways in which the algebraic framework of
noncommutative geometry naturally captures the short-distance spacetime
properties of string theory. We describe the noncommutative spacetime
constructed from a vertex operator algebra and show that its algebraic
properties bear a striking resemblence to some structures appearing in M
Theory, such as the noncommutative torus. We classify the inner automorphisms
of the space and show how they naturally imply the conventional duality
symmetries of the quantum geometry of spacetime. We examine the problem of
constructing a universal gauge group which overlies all of the dynamical
symmetries of the string spacetime. We also describe some aspects of toroidal
compactifications with a light-like coordinate and show how certain generalized
Kac-Moody symmetries, such as the Monster sporadic group, arise as gauge
symmetries of the resulting spacetime and of superstring theories.
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OPE for XXX: We explain a new method for finding the correlation functions for the XXX
model which is based on the concepts of Operator Product Expansion of Quantum
Field Theory on one hand and of fermionic bases for the XXX spin chain on the
other. With this method we are able to perform computations for up to 11
lattice sites. We show that these "experimental" data allow to guess exact
formulae for the OPE coefficients.
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Irrational Monodromies of Vacuum Energy: We present a theory with axion flux monodromies coupled to gravity, that
reduces to the local vacuum energy sequester below the axion mass scales. If
the axion potentials include a term generated by nonperturbative couplings to
gauge sectors, with a decay constant incommensurate with monodromy periods, the
low energy potential germinates a landscape of irrational axion vacua, with
arbitrarily small cosmological constants. The sensitivity of the values of
cosmological constants to unknown UV physics can be greatly reduced. The
variation of the cosmological constant in each vacuum, from one order in
perturbation theory to the next, can be much smaller than the na\"ive cutoff.
The nonperturbative transitions in the early universe between the vacua
populate this landscape, similar to the case of irrational axion. In such a
landscape of vacua a small cosmological constant can naturally emerge.
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Supersymmetry and Gravitational Duality: We study how the supersymmetry algebra copes with gravitational duality. As a
playground, we consider a charged Taub-NUT solution of D=4, N=2 supergravity.
We find explicitly its Killing spinors, and the projection they obey provides
evidence that the dual magnetic momenta necessarily have to appear in the
supersymmetry algebra. The existence of such a modification is further
supported using an approach based on the Nester form. In the process, we find
new expressions for the dual magnetic momenta, including the NUT charge. The
same expressions are then rederived using gravitational duality.
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Principal Tensor Strikes Again: Separability of Vector Equations with
Torsion: Many black hole spacetimes with a 3-form field exhibit a hidden symmetry
encoded in a torsion generalization of the principal Killing--Yano tensor. This
tensor determines basic properties of such black holes while also underlying
the separability of the Hamilton--Jacobi, Klein--Gordon, and (torsion-modified)
Dirac field equations in their background. As a specific example, we consider
the Chong--Cveti\v{c}--L\"u--Pope black hole of $D=5$ minimal gauged
supergravity and show that the torsion-modified vector field equations can also
be separated, with the principal tensor playing a key role in the separability
ansatz. For comparison, separability of the Proca field in higher-dimensional
Kerr--NUT--AdS spacetimes (including new explicit formulae in odd dimensions)
is also presented.
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On T-duality transformations for the three-sphere: We study collective T-duality transformations along one, two and three
directions of isometry for the three-sphere with H-flux. Our aim is to obtain
new non-geometric backgrounds along lines similar to the example of the
three-torus. However, the resulting backgrounds turn out to be geometric in
nature. To perform the duality transformations, we develop a novel procedure
for non-abelian T-duality, which follows a route different compared to the
known literature, and which highlights the underlying structure from an
alternative point of view.
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Wiener Process of Fractals and Path-Integrals II: Emergent
Einstein-Hilbert Action in Stochastic Process of Quantum Fields along with
the Ricci Flow of the Space Geometry: This is the second paper of a series of researches (that commenced with [66]
and is followed by [67]) that aims to interpret the gravitational effects of
nature within some consistent stochastic fractal-based (intrinsically
conformal) path-integral formulation. In the present work, the Wiener
stochastic process is employed to study the Brownian motion of fractal
functions on a closed Riemannian manifold with dynamical geometry due to the
Ricci flow. It has been shown that the Wiener measure automatically leads to
the Einstein-Hilbert action and the path-integral formulation of scalar quantum
field theory at the first local approximation. This would be interpreted as the
more fundamental formulation of quantum field theory in presence of gravity.
However, we establish that the emergence of Einstein-Hilbert action is
independent of the matter field interactions and is a merely entropic effect
stemming from the nature of the Ricci flow. We also extract an explicit formula
for the cosmological constant in terms of the Ricci flow and Hamilton's theorem
for 3-manifold. Then, we discuss the cosmological features of the FLRW solution
in $\Lambda$CDM Model via the derived equations of the Ricci flow. We also
argue the correlation between our formulations and the entropic aspects of
gravity. Finally, we establish some theoretical evidence that proves that the
second law of thermodynamics is the basic source of and more fundamental than
gravity.
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Englert-Brout-Higgs Mechanism in Nonrelativistic Systems: We study the general theory of Englert-Brout-Higgs mechanism without assuming
Lorentz invariance. In the presence of a finite expectation value of
non-Abelian matter charges, gauging those symmetries always results in
spontaneous breaking of spatial rotation. If we impose the charge neutrality by
assuming a background with the opposite charges, the dynamics of the background
cannot be decoupled and has to be fully taken into account. In either case, the
spectrum is continuous as the gauge coupling is switched off.
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The Return of the Phoenix Universe: Georges Lemaitre introduced the term "phoenix universe" to describe an
oscillatory cosmology with alternating periods of gravitational collapse and
expansion. This model is ruled out observationally because it requires a
supercritical mass density and cannot accommodate dark energy. However, a new
cyclic theory of the universe has been proposed that evades these problems. In
a recent elaboration of this picture, almost the entire universe observed today
is fated to become entrapped inside black holes, but a tiny region will emerge
from these ashes like a phoenix to form an even larger smooth, flat universe
filled with galaxies, stars, planets, and, presumably, life. Survival depends
crucially on dark energy and suggests a reason why its density is small and
positive today.
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Index theorem in spontaneously symmetry-broken gauge theories on a fuzzy
2-sphere: We consider a gauge-Higgs system on a fuzzy 2-sphere and study the
topological structure of gauge configurations, when the U(2) gauge symmetry is
spontaneously broken to U(1) times U(1) by the vev of the Higgs field. The
topology is classified by the index of the Dirac operator satisfying the
Ginsparg-Wilson relation, which turns out to be a noncommutative analog of the
topological charge introduced by 't Hooft. It can be rewritten as a form whose
commutative limit becomes the winding number of the Higgs field. We also study
conditions which assure the validity of the formulation, and give a
generalization of the admissibility condition. Finally we explicitly calculate
the topological charge of a one-parameter family of configurations.
|
Gaussian Effective Potential and the Coleman's normal-ordering
Prescription : the Functional Integral Formalism: For a class of system, the potential of whose Bosonic Hamiltonian has a
Fourier representation in the sense of tempered distributions, we calculate the
Gaussian effective potential within the framework of functional integral
formalism. We show that the Coleman's normal-ordering prescription can be
formally generalized to the functional integral formalism.
|
Ultraviolet Finiteness or Asymptotic Safety in Higher Derivative
Gravitational Theories: We present and discuss well known conditions for ultraviolet finiteness and
asymptotic safety. The requirements for complete absence of ultraviolet
divergences in quantum field theories and existence of a non-trivial fixed
point for renormalization group flow in the ultraviolet regime are compared
based on the example of a six-derivative quantum gravitational theory in $d=4$
spacetime dimensions. In this model, it is possible for the first time to have
fully UV-finite quantum theory without adding matter or special symmetry, but
by inclusion of additional terms cubic in curvatures. We comment on
similarities and some apparent differences between the two approaches, but we
show that they are both compatible to each other. Finally, we motivate the
claim that actually asymptotic safety needs UV-finite models for providing
explicit form of the ultraviolet limit of Wilsonian effective actions
describing special situations at fixed points.
|
On the classical equivalence of monodromy matrices in squashed sigma
model: We proceed to study the hybrid integrable structure in two-dimensional
non-linear sigma models with target space three-dimensional squashed spheres. A
quantum affine algebra and a pair of Yangian algebras are realized in the sigma
models and, according to them, there are two descriptions to describe the
classical dynamics 1) the trigonometric description and 2) the rational
description, respectively. For every description, a Lax pair is constructed and
the associated monodromy matrix is also constructed. In this paper we show the
gauge-equivalence of the monodromy matrices in the trigonometric and rational
description under a certain relation between spectral parameters and the
rescalings of sl(2) generators.
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Axion-dilaton-modulus gravity theory of Brans-Dicke-type and conformal
symmetry: Conformal symmetry is investigated within the context of
axion-dilaton-modulus theory of gravity of Brans-Dicke-type. A distinction is
made between general conformal symmetry and invariance under transformations of
the physical units. The conformal degree of symmetry of the theory is studied
when quantum fermion (lepton) modes with electromagnetic interaction are
considered. Based on the requirement of invariance of the physical laws under
general transformations of the units of measure, arguments are given that point
at a matter action with non-minimal coupling of the dilaton to the matter
fields as the most viable description of the world within the context of the
model studied. The geometrical implications of the results obtained are
discussed.
|
Component twist method for higher twists in D1D5 CFT: The deformation operator of the D1D5 orbifold CFT, a twist 2 operator, drives
the CFT towards the black hole dual and its physics is key to understanding
thermalization in the D1D5 system. To further study this deformation, we extend
previous work on the effect of twist 2 operators to a method that works for
higher orders, in the continuum limit. Our component twist method works by
building higher twist operators out of twist 2 operators together with
knowledge of Bogoliubov transformations. Consequently, this method sidesteps
limitations in Lunin-Mathur technology by avoiding lifts to the covering space.
We verify the method by reproducing results obtainable with Lunin-Mathur
technology. Going further, our method upholds a previously conjectured scaling
law in the continuum limit that applies to any generic configuration of twists.
We illustrate this with computations for a new configuration of two twist 2
operators that twists three copies together.
|
Eluding SUSY at every genus on stable closed string vacua: In closed string vacua, ergodicity of unipotent flows provide a key for
relating vacuum stability to the UV behavior of spectra and interactions.
Infrared finiteness at all genera in perturbation theory can be rephrased in
terms of cancelations involving only tree-level closed strings scattering
amplitudes. This provides quantitative results on the allowed deviations from
supersymmetry on perturbative stable vacua. From a mathematical perspective,
diagrammatic relations involving closed string amplitudes suggest a relevance
of unipotent flows dynamics for the Schottky problem and for the construction
of the superstring measure.
|
Three dimensional noncommutative bosonization: We consider the extension of the 2+1-dimensional bosonization process in
Non-Commutative (NC) spacetime. We show that the large mass limit of the
effective action obtained by integrating out the fermionic fields in NC
spacetime leads to the NC Chern-Simons action. The present result is valid to
all orders in the noncommutative parameter $\theta$. We also discuss how the NC
Yang-Mills action is induced in the next to leading order.
|
On an inconsistency in path integral bosonization: A critically discerning discussion of path integral bosonization is given.
Successively evaluating the conventional path integral bosonization of QCD it
is shown without any approximations that gluons must be composed of two quarks.
This contradicts the fundamentals of QCD, where quarks and gluons are
independent fields. Furthermore, bosonizing the Fierz reordered effective four
quark interaction term yields gluons, too. Colorless ``mesons'' are shown to be
Fierz equivalent to a submanifold of gluons. The results obtained are not
specific to QCD, but apply to other models as well.
|
Curvature actions on Spin(n) bundles: We compute the number of linearly independent ways in which a tensor of Weyl
type may act upon a given irreducible tensor-spinor bundle V over a Riemannian
manifold. Together with the analogous but easier problem involving actions of
tensors of Einstein type, this enumerates the possible curvature actions on V.
|
On DBI Textures with Generalized Hopf Fibration: In this letter we show numerical existence of O(4) Dirac-Born-Infeld (DBI)
Textures living in (N +1) dimensional spacetime. These defects are
characterized by $S^N\rightarrow S^3$ mapping, generalizing the well-known Hopf
fibration into ?$\pi_N (S^3)$, for all N > 3. The nonlinear nature of DBI
kinetic term provides stability against size perturbation and thus renders the
defects having natural scale.
|
`Desert' in Energy or Transverse Space?: I review the issue of string and compactification scales in the weak-coupling
regimes of string theory. I explain how in the Brane World scenario a
(effectively) two-dimensional transverse space that is hierarchically larger
than the string length may replace the conventional `energy desert' described
by renormalizable supersymmetric QFT. I comment on the puzzle of unification in
this context.
|
Aspects of finite electrodynamics in D=3 dimensions: We study the impact of a minimal length on physical observables for a
three-dimensional axionic electrodynamics. Our calculation is done within the
framework of the gauge-invariant, but path-dependent, variables formalism which
is alternative to the Wilson loop approach. Our result shows that the
interaction energy contains a regularised Bessel function and a linear
confining potential. This calculation involves no theta expansion at all. Once
again, the present analysis displays the key role played by the new quantum of
length.
|
Emergent non-invertible symmetries in $\mathcal{N}=4$ Super-Yang-Mills
theory: One of the simplest examples of non-invertible symmetries in higher
dimensions appears in 4d Maxwell theory, where its $SL(2,\mathbb{Z})$ duality
group can be combined with gauging subgroups of its electric and magnetic
1-form symmetries to yield such defects at many different values of the
coupling. Even though $\mathcal{N}=4$ Super-Yang-Mills (SYM) theory also has an
$SL(2,\mathbb{Z})$ duality group, it only seems to share two types of such
non-invertible defects with Maxwell theory (known as duality and triality
defects). Motivated by this apparent difference, we begin our investigation of
the fate of these symmetries by studying the case of 4d $\mathcal{N}=4$ $U(1)$
gauge theory which contains Maxwell theory in its content. Surprisingly, we
find that the non-invertible defects of Maxwell theory give rise, when combined
with the standard $U(1)$ symmetry acting on the free fermions, to defects which
act on local operators as elements of the $U(1)$ outer-automorphism of the
$\mathcal{N}=4$ superconformal algebra, an operation that was referred to in
the past as the "bonus symmetry". Turning to the nonabelian case of
$\mathcal{N}=4$ SYM, the bonus symmetry is not an exact symmetry of the theory
but is known to emerge at the supergravity limit. Based on this observation we
study this limit and show that if it is taken in a certain way, non-invertible
defects that realize different elements of the bonus symmetry emerge as
approximate symmetries, in analogy to the abelian case.
|
RG flow between $W_3$ minimal models by perturbation and domain wall
approaches: We explore the RG flow between neighboring minimal CFT models with $W_3$
symmetry. After computing several classes of OPE structure constants we were
able to find the matrices of anomalous dimensions for three classes of RG
invariant sets of local fields. Each set from the first class consists of a
single primary field, the second one of three primaries, while sets in the
third class contain six primary and four secondary fields. We diagonalize their
matrices of anomalous dimensions and establish the explicit maps between UV and
IR fields (mixing coefficients).
While investigating the three point functions of secondary fields we have
encountered an interesting phenomenon, namely violation of holomorphic
anti-holomorphic factorization property, something that does not happen in
ordinary minimal models with Virasoro symmetry solely.
Furthermore, the perturbation under consideration preserves a non-trivial
subgroup of $W$ transformations. We have derived the corresponding conserved
current explicitly. We used this current to define a notion of anomalous
$W$-weights in perturbed theory: the analog for matrix of anomalous dimensions.
For RG invariant sets with primary fields only we have derived a formula for
this quantity in terms of structure constants. This allowed us to compute
anomalous $W$-weights for the first and second classes explicitly.
The same RG flow we investigate also with the domain wall approach for the
second RG invariant class and find complete agreement with the perturbative
approach.
|
Supersymmetric Analogs of the Gordon-Andrews Identities, and Related TBA
Systems: The Gordon-Andrews identities, which generalize the Rogers-Ramanujan-Schur
identities, provide product and fermionic forms for the characters of the
minimal conformal field theories (CFTs) M(2,2k+1). We discuss/conjecture
identities of a similar type, providing two different fermionic forms for the
characters of the models SM(2,4k) in the minimal series of N=1 super-CFTs.
These two forms are related to two families of thermodynamic Bethe Ansatz (TBA)
systems, which are argued to be associated with the $\hat{\phi}_{1,3}^{\rm
top}$- and $\hat{\phi}_{1,5}^{\rm bot}$-perturbations of the models SM(2,4k).
Certain other q-series identities and TBA systems are also discussed, as well
as a possible representation-theoretical consequence of our results, based on
Andrews's generalization of the Gollnitz-Gordon theorem.
|
Supersymmetric Warped Conformal Field Theory: In this work, we study the supersymmetric warped conformal field theory in
two dimensions. We show that the Hofman-Strominger theorem on symmetry
enhancement could be generalized to the supersymmetric case. More precisely, we
find that within a chiral superspace $(x^+,\th)$, a two-dimensional field
theory with two translational invariance and a chiral scaling symmetry can have
enhanced local symmetry, under the assumption that the dilation spectrum is
discrete and non-negative. Similar to the pure bosonic case, there are two
kinds of minimal models, one being $N=(1,0)$ supersymmetric conformal field
theories, while the other being $N=1$ supersymmetric warped conformal field
theories (SWCFT). We study the properties of SWCFT, including the
representations of the algebra, the space of states and the correlation
functions of the superprimaries.
|
Unitarity, Locality, and Scale versus Conformal Invariance in Four
Dimensions: In four dimensional unitary scale invariant theories, arguments based on the
proof of the a-theorem suggest that the trace of the energy-momentum tensor T
vanishes when the momentum is light-like, p^2=0. We show that there exists a
local operator O such that the trace is given as T=\partial^2 O, which
establishes the equivalence of scale and conformal invariance. We define the
operator as O=\partial^{-2} T, and explain why this is a well-defined local
operator. Our argument is based on the assumptions that: (1) A kind of crossing
symmetry for vanishing matrix elements holds regardless of the existence of the
S-matrix. (2) Correlation functions in momentum space are analytic functions
other than singularities and branch cuts coming from on-shell processes. (3)
The Wightman axioms are sufficient criteria of the locality of an operator.
|
Killing scalar of non-linear sigma models on G/H realizing the classical
exchange algebra: The Poisson brackets for non-linear sigma models on G/H are set up on the
light-like plane. A quantity which transforms irreducibly by the Killing
vectors, called Killing scalar, is constructed in an arbitrary representation
of G. It is shown to satisfy the classical exchange algebra.
|
Are Extremal 2D Black Holes Really Frozen ?: In the standard methodology for evaluating the Hawking radiation emanating
from a black hole, the background geometry is fixed. Trying to be more
realistic we consider a dynamical geometry for a two-dimensional charged black
hole and we evaluate the Hawking radiation as tunneling process. This
modification to the geometry gives rise to a nonthermal part in the radiation
spectrum. We explore the consequences of this new term for the extremal case.
|
2D Supergravity and Integrable Systems: Integrable hierarchy based on the constrained Osp(2$\mid%2) connection is
considered. The connection with 2D supergravity and some analogies with the
W$_3^{(2)}$ case are given. It is shown that super Virasoro transformations are
symmetries of tha hierarchy.
|
Gluonic evanescent operators: negative-norm states and complex anomalous
dimensions: In this paper, we build on our previous work to further investigate the role
of evanescent operators in gauge theories, with a particular focus on their
contribution to violations of unitarity. We develop an efficient method for
calculating the norms of gauge-invariant operators in Yang-Mills (YM) theory by
employing on-shell form factors. Our analysis, applicable to general spacetime
dimensions, reveals the existence of negative norm states among evanescent
operators. We also explore the one-loop anomalous dimensions of these operators
and find complex anomalous dimensions. We broaden our analysis by considering
YM theory coupled with scalar fields and we observe similar patterns of
non-unitarity. The presence of negative norm states and complex anomalous
dimensions across these analyses provides compelling evidence that general
gauge theories are non-unitary in non-integer spacetime dimensions.
|
Recurrent Acceleration in Dilaton-Axion Cosmology: A class of Einstein-dilaton-axion models is found for which almost all flat
expanding homogeneous and isotropic universes undergo recurrent periods of
acceleration. We also extend recent results on eternally accelerating open
universes.
|
p-p' System with B-field, Branes at Angles and Noncommutative Geometry: We study the generic $p-p^\prime$ system in the presence of constant NS
2-form $B_{ij}$ field. We derive properties concerning with the
noncommutativity of D-brane worldvolume, the Green functions and the spectrum
of this system. In the zero slope limit, a large number of light states appear
as the lowest excitations in appropriate cases. We are able to relate the
energies of the lowest states after the GSO projection with the configurations
of branes at angles. Through analytic continuation, the system is compared with
the branes with relative motion.
|
Gauge Field, Parity and Uncertainty Relation of Quantum Mechanics on S^1: We consider the uncertainty relation between position and momentum of a
particle on $ S^1 $ (a circle). Since $ S^1 $ is compact, the uncertainty of
position must be bounded. Consideration on the uncertainty of position demands
delicate treatment. Recently Ohnuki and Kitakado have formulated quantum
mechanics on $ S^D $ (a $D$-dimensional sphere). Armed with their formulation,
we examine this subject. We also consider parity and find a phenomenon similar
to the spontaneous symmetry breaking. We discuss problems which we encounter
when we attempt to formulate quantum mechanics on a general manifold.
|
Nonabelian Faddeev-Niemi Decomposition of the SU(3) Yang-Mills Theory: Faddeev and Niemi (FN) have introduced an abelian gauge theory which
simulates dynamical abelianization in Yang-Mills theory (YM). It contains both
YM instantons and Wu-Yang monopoles and appears to be able to describe the
confining phase. Motivated by the meson degeneracy problem in dynamical
abelianization models, in this note we present a generalization of the FN
theory. We first generalize the Cho connection to dynamical symmetry breaking
pattern SU(N+1) -> U(N), and subsequently try to complete the Faddeev-Niemi
decomposition by keeping the missing degrees of freedom. While it is not
possible to write an on-shell complete FN decomposition, in the case of SU(3)
theory of physical interest we find an off-shell complete decomposition for
SU(3) -> U(2) which amounts to partial gauge fixing, generalizing naturally the
result found by Faddeev and Niemi for the abelian scenario SU(N+1) -> U(1)^N.
We discuss general topological aspects of these breakings, demonstrating for
example that the FN knot solitons never exist when the unbroken gauge symmetry
is nonabelian, and recovering the usual no-go theorems for colored dyons.
|
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