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Probing Supersymmetric Black Holes with Surface Defects: It has long been conjectured that the large $N$ deconfinement phase
transition of $\mathcal{N}=4$ ${\rm SU}(N)$ super-Yang-Mills corresponds via
AdS/CFT to the Hawking-Page transition in which black holes dominate the
thermal ensemble, and quantitative evidence of this has come through the recent
matching of the superconformal index of ${1\over 16}$-BPS states to the
supersymmetric black hole entropy. We introduce the half-BPS Gukov-Witten
surface defect as a probe of the superconformal index, which also serves as an
order parameter for the deconfinement transition. This can be studied directly
in field theory as a modification of the usual unitary matrix model or in the
dual description as a D3-brane probe in the background of a (complex)
supersymmetric black hole. Using a saddle point approximation, we determine our
defect index in the large $N$ limit as a simple function of the chemical
potentials and show independently that it is reproduced by the renormalized
action of the brane in the black hole background. Along the way, we also
comment on the Cardy limit and the thermodynamics of the D3-brane in the
generalized ensemble. The defect index sharply distinguishes between the
confining and the deconfining phases of the gauge theory and thus is a
supersymmetric non-perturbative order parameter for these large $N$ phase
transitions which deserves further investigation. Finally, our work provides an
example where the properties of a black hole coupled to an external system can
be analyzed precisely. | Non-Abelian Chern-Simons Particles and their Quantization: A many--body Schr\"odinger equation for non--Abelian Chern--Simons particles
is obtained from both point--particle and field--theoretic pictures. We present
a particle Lagrangian and a field theoretic Lagrange density, and discuss their
properties. Both are quantized by the symplectic method of Hamiltonian
reduction. An $N$--body Schr\"odinger equation for the particles is obtained
from both starting points. It is shown that the resulting interaction between
particles can be replaced by non--trivial boundary conditions. Also, the
equation is compared with the one given in the literature. |
Reconstruction of modified gravity with ghost dark energy models: In this work, we reconstruct the $f(R)$ modified gravity for different ghost
and generalized ghost dark energy models in FRW flat universe, which describe
the accelerated expansion of the universe. The equation of state of
reconstructed $f(R)$ - gravity has been calculated. We show that the
corresponding $f(R)$ gravity of ghost dark energy model can behave like phantom
or quintessence. We also show that the equation of state of reconstructed
$f(R)$ gravity for generalized ghost model can transit from quintessence regime
to the phantom regime as indicated by recent observations. | Berry phase for oscillating neutrinos: We show the presence of a topological (Berry) phase in the time evolution of
a mixed state. For the case of mixed neutrinos, the Berry phase is a function
of the mixing angle only. |
New N=2 Supersymmetric Membrane Flow In Eleven-Dimensional Supergravity: We construct the 11-dimensional lift of the known N=2 supersymmetric RG flow
solution in 4-dimensional N=8 gauged supergravity. The squashed and stretched
7-dimensional internal metric preserving SU(2) x U(1) x U(1)_R symmetry
contains an Einstein-Kahler 2-fold which is a base manifold of 5-dimensional
Sasaki-Einstein Y^{p, q} space found in 2004. The nontrivial r(transverse to
the domain wall)-dependence of the AdS_4 supergravity fields makes the
Einstein-Maxwell equations consistent not only at the critical points but also
along the supersymmetric whole RG flow connecting two critical points. With an
appropriate 3-form gauge field, we find an exact solution to the 11-dimensional
Einstein-Maxwell equations corresponding to the above lift of the SU(2) x U(1)
x U(1)_R-invariant RG flow. The particular limits of this solution give rise to
the previous solutions with SU(3) x U(1)_R or SU(2) x SU(2) x U(1)_R. | Cosmological Exact Solutions in Some Modified Gravitational Theories: In a homogenous and isotropic cosmology, we introduce general exact solutions
for some modified gravity models. In particular, we introduce exact solutions
for power-law $f(R)$ gravity and Brans-Dicke theory in Einstein and Jordan
conformal frames. In the Brans-Dicke case, the solutions are presented for both
single and double exponential potentials in Einstein frame which correspond to
power-law potentials in Jordan frame. Our analysis for extracting general exact
solutions can also be generalized to those scalar-tensor theories in which the
scalar field has an exponential coupling to Ricci scalar. |
On the 6th Mode in Massive Gravity: Generic massive gravity models in the unitary gauge correspond to a
self-gravitating medium with six degrees of freedom. It is widely believed that
massive gravity models with six degrees of freedom have an unavoidable
ghost-like instability; however, the corresponding medium has stable
phonon-like excitations. The apparent contradiction is solved by the presence
of a non-vanishing background pressure and energy density of the medium that
opens up a stability window. The result is confirmed by looking at linear
stability on an expanding Universe, recovering the flat space stability
conditions in the small wavelength limit. Moreover, one can show that under
rather mild conditions, no ghost-like instability is present for any
wavelength. As a result, exploiting the medium interpretation, a generic
massive gravity model with six degrees of freedom is perfectly viable. | QED with external field: Hamiltonian treatment for anisotropic medium
formed by the Lorentz-non-invariant vacuum: Nonlinear electrodynamics, QED included, is considered against the
Lorentz-noninvariant external field background, treated as an anisotropic
medium. Hamiltonian formalism is applied to electromagnetic excitations over
the background, and entities of electrodynamics of media, such as field
inductions and intensities, are made sense of in terms of canonical variables.
Both conserved and nonconserved generators of space-time translations and
rotations are defined on the phase space, and their Hamiltonian equations of
motion and Dirac bracket relations, different from the Poincar\'e algebra, are
established. Nonsymmetric, but--in return--gauge-invariant, energy-momentum
tensor suggests a canonical momentum density other than the Poynting vector. A
photon magnetic moment is found to govern the evolution of the photon angular
momentum. It is determined by the antisymmetric part of the energy-momentum
tensor. |
Power to Integral Forms: A novel reformulation of D=4, N=1 supergravity action in the language of
integral forms is given. We illustrate the construction of the Berezinian in
the supergeometric framework, providing a useful dictionary between mathematics
and physics. We present a unified framework for Berezin-Lebesgue integrals for
functions and for integral forms. As an application, we discuss Volkov-Akulov
theory and its coupling to supergravity from this new perspective. | Membrane Quantum Mechanics: We consider the multiple M2-branes wrapped on a compact Riemann surface and
study the arising quantum mechanics by taking the limit where the size of the
Riemann surface goes to zero. The IR quantum mechanical models resulting from
the BLG-model and the ABJM-model compactified on a torus are N = 16 and N = 12
superconformal gauged quantum mechanics. After integrating out the auxiliary
gauge fields we find OSp(16|2) and SU(1,1|6) quantum mechanics from the reduced
systems. The curved Riemann surface is taken as a holomorphic curve in a
Calabi-Yau space to preserve supersymmetry and we present a prescription of the
topological twisting. We find the N = 8 superconformal gauged quantum mechanics
that may describe the motion of two wrapped M2-branes in a K3 surface. |
Effective String Theories (EST) of Yang-Mills Flux Tubes: This chapter explains the concept of \emph{Effective String Theories}(EST),
and their success in explaining the results that Yang-Mills flux tubes behave,
to a high degree of accuracy, like Bosonic Strings(BST). It describes EST's of
L\"uscher and Weisz, and their principal conclusions. It then discusses the
Polchinski-Strominger EST's. which are valid in all dimensions. It then
describes the works by Drummond, and, the author and Peter Matlock, which
extended the analysis to $R^{-3}$ order and showed, that even at that order the
spectrum is that of BST. The chapter analyses the issues of string momentum in
higher orders. It discusses at length the powerful covariant calculus, to
systematically construct EST's to arbitrary orders. The most general actions to
$R^{-7}$ order are shown to be governed by just two parameters. The works of
Aharony and collaborators on the spectrum of EST's, both in static and
conformal gauges,to $R^{-5}$ order, and their results that even at that order
the ground state energy remains the same as that of BST, but the excited
spectrum gets corrected for $D\,>\,3$, are explained. It discusses the
simulation results for excited states. It also discusses the AdS-CFT approaches
and thickness of flux tubes.Recent works on the path-integral approaches to
this issue are also discussed and compared with the other approaches. It
concludes with remarks on the significance of the results for QCD. | String/Gauge Correspondence; View from the High Energy Side: We briefly review the recent progress concerning the application of the
hidden integrability to the derivation of the stringy/brane picture for the
high energy QCD. |
Equivalence between the Lovelock-Cartan action and a constrained gauge
theory: We show that the four-dimensional Lovelock-Cartan action can be derived from
a massless gauge theory for the $SO(1,3)$ group with an additional BRST trivial
part. The model is originally composed by a topological sector and a BRST exact
piece and has no explicit dependence on the metric, the vierbein or a mass
parameter. The vierbein is introduced together with a mass parameter through
some BRST trivial constraints. The effect of the constraints is to identify the
vierbein with some of the additional fields, transforming the original action
into the Lovelock-Cartan one. In this scenario, the mass parameter is
identified with Newton's constant while the gauge field is identified with the
spin-connection. The symmetries of the model are also explored. Moreover, the
extension of the model to a quantum version is qualitatively discussed. | Stochastic Quantization vs. KdV Flows in 2D Quantum Gravity: We consider the stochastic quantization scheme for a non-perturbative
stabilization of 2D quantum gravity and prove that it does not satisfy the KdV
flow equations. It therefore differs from a recently suggested matrix model
which allows real solutions to the KdV equations. The behaviour of the Fermi
energy, the free energy and macroscopic loops in the stochastic quantization
scheme are elucidated. |
Supersymmetry then and now: A brief description of some salient aspects of four-dimensional
supersymmetry: early history, supermanifolds, the MSSM, cold dark matter, the
cosmological constant and the string landscape. | Invariants of 2+1 Quantum Gravity: In [1,2] we established and discussed the algebra of observables for 2+1
gravity at both the classical and quantum level. Here our treatment broadens
and extends previous results to any genus $g$ with a systematic discussion of
the centre of the algebra. The reduction of the number of independent
observables to $6g-6 (g > 1)$ is treated in detail with a precise
classification for $g = 1$ and $g = 2$. |
Conformal Mechanics and the Virasoro Algebra: We demonstrate that any scale-invariant mechanics of one variable exhibits
not only 0+1 conformal symmetry, but also the symmetries of a full Virasoro
algebra. We discuss the implications for the adS/CFT correspondence. | Superfield Approach To Nilpotent Symmetries For QED From A Single
Restriction: An Alternative To The Horizontality Condition: We derive together the exact local, covariant, continuous and off-shell
nilpotent Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry
transformations for the U(1) gauge field (A_\mu), the (anti-)ghost fields
((\bar C)C) and the Dirac fields (\psi, \bar\psi) of the Lagrangian density of
a four (3 + 1)-dimensional QED by exploiting a single restriction on the six
(4, 2)-dimensional supermanifold. A set of four even spacetime coordinates
x^\mu (\mu = 0, 1, 2, 3) and two odd Grassmannian variables \theta and
\bar\theta parametrize this six dimensional supermanifold. The new gauge
invariant restriction on the above supermanifold owes its origin to the (super)
covariant derivatives and their intimate relations with the (super) 2-form
curvatures (\tilde F^{(2)})F^{(2)} constructed with the help of (super) 1-form
gauge connections (\tilde A^{(1)})A^{(1)} and (super) exterior derivatives
(\tilde d)d. The results obtained separately by exploiting (i) the
horizontality condition, and (ii) one of its consistent extensions, are shown
to be a simple consequence of this new single restriction on the above
supermanifold. Thus, our present endeavour provides an alternative to (and, in
some sense, generalization of) the horizontality condition of the usual
superfield formalism applied to the derivation of BRST symmetries. |
High energy scattering amplitudes in matrix string theory: High energy fixed angle scattering is studied in matrix string theory. The
saddle point world sheet configurations, which give the dominant contributions
to the string theory amplitude, are taken as classical backgrounds in matrix
string theory. A one loop fluctuation analysis about the classical background
is performed. An exact treatment of the fermionic and bosonic zero modes is
shown to lead to all of the expected structure of the scattering amplitude. The
ten dimensional Lorentz invariant kinematical structure is obtained from the
fermion zero modes, and the correct factor of the string coupling constant is
obtained from the abelian gauge field zero modes. Up to a numerical factor we
reproduce, from matrix string theory, the high energy limit of the tree level,
four graviton scattering amplitude. | The quantum Neumann model: refined semiclassical results: We extend the semiclassical study of the Neumann model down to the deep
quantum regime. A detailed study of connection formulae at the turning points
allows to get good matching with the exact results for the whole range of
parameters. |
How Low Can Vacuum Energy Go When Your Fields Are Finite-Dimensional?: According to the holographic bound, there is only a finite density of degrees
of freedom in space when gravity is taken into account. Conventional quantum
field theory does not conform to this bound, since in this framework,
infinitely many degrees of freedom may be localized to any given region of
space. In this paper, we explore the viewpoint that quantum field theory may
emerge from an underlying theory that is locally finite-dimensional, and we
construct a locally finite-dimensional version of a Klein-Gordon scalar field
using generalized Clifford algebras. Demanding that the finite-dimensional
field operators obey a suitable version of the canonical commutation relations
makes this construction essentially unique. We then find that enforcing local
finite dimensionality in a holographically consistent way leads to a huge
suppression of the quantum contribution to vacuum energy, to the point that the
theoretical prediction becomes plausibly consistent with observations. | A-twisted heterotic Landau-Ginzburg models: In this paper, we apply the methods developed in recent work for constructing
A-twisted (2,2) Landau-Ginzburg models to analogous (0,2) models. In
particular, we study (0,2) Landau-Ginzburg models on topologically non-trivial
spaces away from large-radius limits, where one expects to find correlation
function contributions akin to (2,2) curve corrections. Such heterotic theories
admit A- and B-model twists, and exhibit a duality that simultaneously
exchanges the twists and dualizes the gauge bundle. We explore how this duality
operates in heterotic Landau-Ginzburg models, as well as other properties of
these theories, using examples which RG flow to heterotic nonlinear sigma
models as checks on our methods. |
Exactly solvable charged dilaton gravity theories in two dimensions: We find exactly solvable dilaton gravity theories containing a U(1) gauge
field in two dimensional space-time. The classical general solutions for the
gravity sector (the metric plus the dilaton field) of the theories coupled to a
massless complex scalar field are obtained in terms of the stress-energy tensor
and the U(1) current of the scalar field. We discuss issues that arise when we
attempt to use these models for the study of the gravitational back-reaction. | Application of Bootstrap to $θ$-term: Recently, novel numerical computation on quantum mechanics by using a
bootstrap method was proposed by Han, Hartnoll, and Kruthoff. We consider
whether this method works in systems with a $\theta$-term, where the standard
Monte-Carlo computation may fail due to the sign problem. As a starting point,
we study quantum mechanics of a charged particle on a circle in which a
constant gauge potential is a counterpart of a $\theta$-term. We find that it
is hard to determine physical quantities as functions of $\theta$ such as
$E(\theta)$, except at $\theta=0$ and $\pi$. On the other hand, the
correlations among observables for energy eigenstates are correctly reproduced
for any $\theta$. Our results suggest that the bootstrap method may work not
perfectly but sufficiently well, even if a $\theta$-term exists in the system. |
Renormalizable Abelian-projected effective gauge theory derived from
Quantum Chromodynamics: We show that an effective Abelian gauge theory can be obtained as a
renormalizable theory from QCD in the maximal Abelian gauge. The derivation
improves in a systematic manner the previous version that was obtained by one
of the authors and was referred to as the Abelian-projected effective gauge
theory. This result supports the view that we can construct an effective
Abelian gauge theory from QCD without losing characteristic features of the
original non-Abelian gauge theory. In fact, it is shown that the effective
coupling constant in the resulting renormalizable theory has a
renormalization-scale dependence governed by the $\beta$-function that is
exactly the same as that of the original Yang-Mills theory, irrespective of the
choice of gauge fixing parameters of the maximal Abelian gauge and the
parameters used for identifying the dual variables. Moreover, we evaluate the
anomalous dimensions of the fields and parameters in the resultant theory. By
choosing the renormalized parameters appropriately, we can switch the theory
into an electric or a magnetic theory. | Gravitational Waveform: A Tale of Two Formalisms: We revisit the quantum-amplitude-based derivation of the gravitational
waveform emitted by the scattering of two spinless massive bodies at the third
order in Newton's constant, $h \sim G+G^2+G^3$ (one-loop level), and
correspondingly update its comparison with its classically-derived
multipolar-post-Minkowskian counterpart. A spurious-pole-free reorganization of
the one-loop five-point amplitude substantially simplifies the post-Newtonian
expansion. We find complete agreement between the two results up to the fifth
order in the small velocity expansion after taking into account three subtle
aspects of the amplitude derivation: (1) in agreement with [arXiv:2312.07452
[hep-th]], the term quadratic in the amplitude in the observable-based
formalism [JHEP 02, 137 (2019)] generates a frame rotation by half the
classical scattering angle; (2) the dimensional regularization of the infrared
divergences of the amplitude introduces an additional $(d-4)/(d-4)$ finite
term; and (3) zero-frequency gravitons are found to contribute additional terms
both at order $h \sim G^1$ and at order $h \sim G^3$ when including
disconnected diagrams in the observable-based formalism. |
Coordinate-free quantization of first-class constrained systems: The coordinate-free formulation of canonical quantization, achieved by a
flat-space Brownian motion regularization of phase-space path integrals, is
extended to a special class of closed first-class constrained systems that is
broad enough to include Yang-Mills type theories with an arbitrary compact
gauge group. Central to this extension are the use of coherent state path
integrals and of Lagrange multiplier integrations that engender projection
operators onto the subspace of gauge invariant states. | Orientation matters for NIMreps: The problem of finding boundary states in CFT, often rephrased in terms of
"NIMreps" of the fusion algebra, has a natural extension to CFT on
non-orientable surfaces. This provides extra information that turns out to be
quite useful to give the proper interpretation to a NIMrep. We illustrate this
with several examples. This includes a rather detailed discussion of the
interesting case of the simple current extension of A_2 level 9, which is
already known to have a rich structure. This structure can be disentangled
completely using orientation information. In particular we find here and in
other cases examples of diagonal modular invariants that do not admit a NIMrep,
suggesting that there does not exist a corresponding CFT. We obtain the
complete set of NIMreps (plus Moebius and Klein bottle coefficients) for many
exceptional modular invariants of WZW models, and find an explanation for the
occurrence of more than one NIMrep in certain cases. We also (re)consider the
underlying formalism, emphasizing the distinction between oriented and
unoriented string annulus amplitudes, and the origin of orientation-dependent
degeneracy matrices in the latter. |
Killing-Yano tensor and supersymmetry of the self-dual
Plebanski-Demianski solution: We explore various aspects of the self-dual Pleba\'nski-Demia\'nski family in
the Euclidean Einstein-Maxwell-$\Lambda$ system. The Killing-Yano tensor which
was recently found by Yasui and one of the present authors allows us to prove
that the self-dual Pleba\'nski-Demia\'nski metric can be brought into the
self-dual Carter metric by an orientation-reversing coordinate transformation.
We show that the self-dual Pleba\'nski-Demia\'nski solution admits two
independent Killing spinors in the framework of $N=2$ minimal gauged
supergravity, whereas the non-self-dual solution admits only a single Killing
spinor. This can be demonstrated by casting the self-dual
Pleba\'nski-Demia\'nski metric into two distinct Przanowski-Tod forms. As a
by-product, a new example of the three-dimensional Einstein-Weyl space is
presented. We also prove that the self-dual Pleba\'nski-Demia\'nski metric
falls into two different Calderbank-Pedersen families, which are determined by
a single function subjected to a linear equation on the two dimensional
hyperbolic space. Furthermore, we consider the hyper-K\"ahler case for which
the metric falls into the Gibbons-Hawking class. We find that the condition for
the nonexistence of Dirac-Misner string enforces the solution with a
nonvanishing acceleration parameter to the Eguchi-Hanson space. | Comments on "On the Origin of Gravity and the Laws of Newton", by Erik
Verlinde: We argue that the relativistic Unruh temperature cannot be associated with
the bits on the screen, in the form considered by Verlinde. The acceleration
$a$ is a scalar quantity (the modulus of the acceleration four vecor) and not a
vector. When the mass $m$ approaches the holographic screen, viewed as a
stretched horizon, the shift $\Delta x$ from Verlinde's Eq. (3.15) becomes
$c^{2}/a$ and the entropy variation equals $(1/2) k_{B} \Delta N$, in
accordance with Gao's calculations. Using the Heisenberg Principle we show that
the energy on the causal horizon (viewed as a holographic screen) of an
inertial observer is proportional to its radius, as for a black hole. |
d=4 Black Hole Attractors in N=2 Supergravity with Fayet-Iliopoulos
Terms: We generalize the description of the d=4 Attractor Mechanism based on an
effective black hole (BH) potential to the presence of a gauging which does not
modify the derivatives of the scalars and does not involve hypermultiplets. The
obtained results do not rely necessarily on supersymmetry, and they can be
extended to d>4, as well. Thence, we work out the example of the stu model of
N=2 supergravity in the presence of Fayet-Iliopoulos terms, for the
supergravity analogues of the magnetic and D0-D6 BH charge configurations, and
in three different symplectic frames: the SO(1,1)^{2}, SO(2,2) covariant and
SO(8)-truncated ones. The attractive nature of the critical points, related to
the semi-positive definiteness of the Hessian matrix, is also studied. | Supertubes connecting D4 branes: We find and explore a class of dyonic instanton solutions which can be
identified as the supertubes connecting two D4 branes. They correspond to a
single monopole string and a pair of monopole antimonopole strings from the
worldvolume view point of D4 branes. |
1992 Trieste Lectures on Topological Gauge Theory and Yang-Mills Theory: In these lecture notes we explain a connection between Yang-Mills theory on
arbitrary Riemann surfaces and two types of topological field theory, the so
called $BF$ and cohomological theories. The quantum Yang-Mills theory is solved
exactly using path integral techniques. Explicit expressions, in terms of group
representation theory, are obtained for the partition function and various
correlation functions. In a particular limit the Yang-Mills theory devolves to
the topological models and the previously determined correlation functions give
topological information about the moduli spaces of flat connections. In
particular, the partition function yields the volume of the moduli space for
which an explicit expression is derived. These notes are self contained, with a
basic introduction to the various ideas underlying the topological field
theories. This includes some relatively new work on handling problems that
arise in the presence of reducible connections which in turn forms the bridge
between the various models under consideration. These notes are identical to
those made available to participants of the 1992 summer school in Trieste,
except for one or two additions added circa January 1993. | Superstring Amplitudes, Unitarity, and Hankel Determinants of Multiple
Zeta Values: The interplay of unitarity and analyticity has long been known to impose
strong constraints on scattering amplitudes in quantum field theory and string
theory. This has been highlighted in recent times in a number of papers and
lecture notes. Here we examine such conditions in the context of superstring
tree-level scattering amplitudes, leading to positivity constraints on
determinants of Hankel matrices involving polynomials of multiple zeta values.
These generalise certain constraints on polynomials of single zeta values in
the mathematics literature. |
Non Self-conjugate Strings, Singular Strings and Rigged Configurations
in the Heisenberg Model: We observe a different type of complex solutions in the isotropic spin-1/2
Heisenberg chain starting from N=12, where the central rapidity of some of the
odd-length strings becomes complex making not all the strings self-conjugate
individually. We show that there are at most (N-2)/2 singular solutions for
M=4, M=5 down-spins and at most (N^2-6N+8)/8 singular solutions for M=6, M=7
down-spins in an even-length chain with N \geq 2M. Correspondence of the non
self-conjugate string solutions and the singular string solutions to the rigged
configurations has also been shown. | Constructible reality condition of pseudo entropy via pseudo-Hermiticity: As a generalization of entanglement entropy, pseudo entropy is not always
real. The real-valued pseudo entropy has promising applications in holography
and quantum phase transition. We apply the notion of pseudo-Hermticity to
formulate the reality condition of pseudo entropy. We find the general form of
the transition matrix for which the eigenvalues of the reduced transition
matrix possess real or complex pairs of eigenvalues. Further, we construct a
class of transition matrices for which the pseudo (R\'enyi) entropies are
non-negative. Some known examples which give real pseudo entropy in quantum
field theories can be explained in our framework. Our results offer a novel
method to generate the transition matrix with real pseudo entropy. Finally, we
show the reality condition for pseudo entropy is related to the Tomita-Takesaki
modular theory for quantum field theory. |
Integrable properties of sigma-models with non-symmetric target spaces: It is well-known that sigma-models with symmetric target spaces are
classically integrable. At the example of the model with target space the flag
manifold U(3)/U(1)^3 -- a non-symmetric space -- we show that the introduction
of torsion allows to cast the equations of motion in the form of a
zero-curvature condition for a one-parametric family of connections, which can
be a sign of integrability of the theory. We also elaborate on geometric
aspects of the proposed model. | Gapped Fermions in Top-down Holographic Superconductors: We use holography to compute spectral functions of certain fermionic
operators in three different finite-density, zero-temperature states of ABJM
theory with a broken U(1) symmetry. In each of the three states, dual to
previously studied domain wall solutions of four-dimensional gauged
supergravity, we find that the fermionic operators have gapped spectra. In one
case the gap can be traced to the small charge of the fermions, while in the
other cases it is due to a particular interaction that mixes particles and
holes. |
Black Branes as Piezoelectrics: We find a realization of linear electroelasticity theory in gravitational
physics by uncovering a new response coefficient of charged black branes,
exhibiting their piezoelectric behavior. Taking charged dilatonic black strings
as an example and using the blackfold approach we measure their elastic and
piezolectric moduli. We also use our results to draw predictions about the
equilibrium condition of charged dilatonic black rings in dimensions higher
than six. | Non-planar one-loop Parke-Taylor factors in the CHY approach for
quadratic propagators: In this work we have studied the Kleiss-Kuijf relations for the recently
introduced Parke-Taylor factors at one-loop in the CHY approach, that reproduce
quadratic Feynman propagators. By doing this, we were able to identify the
non-planar one-loop Parke-Taylor factors. In order to check that, in fact,
these new factors can describe non-planar amplitudes, we applied them to the
bi-adjoint $\Phi^3$ theory. As a byproduct, we found a new type of graphs that
we called the non-planar CHY-graphs. These graphs encode all the information
for the subleading order at one-loop, and there is not an equivalent of these
in the Feynman formalism. |
Multi-Flux Warped Throats and Cascading Gauge Theories: We describe duality cascades and their infrared behavior for systems of
D3-branes at singularities given by complex cones over del Pezzo surfaces (and
related examples), in the presence of fractional branes. From the gauge field
theory viewpoint, we show that D3-branes probing the infrared theory have a
quantum deformed moduli space, given by a complex deformation of the initial
geometry to a simpler one. This implies that for the dual supergravity
viewpoint, the gauge theory strong infrared dynamics smoothes out the naked
singularities of the recently constructed warped throat solutions with 3-form
fluxes, describing the cascading RG flow of the gauge theory. This behavior
thus generalizes the Klebanov-Strassler deformation of the conifold. We
describe several explicit examples, including models with several scales of
strong gauge dynamics. In the regime of widely separated scales, the dual
supergravity solutions should correspond to throats with several radial regions
with different exponential warp factors. These rich throat geometries are
expected to have interesting applications in compactification and model
building. Along our studies, we also construct explicit duality cascades for
gauge theories with irrational R-charges, obtained from D-branes probing
complex cones over dP1 and dP2. | On Pure Lattice Chern-Simons Gauge Theories: We revisit the lattice formulation of the Abelian Chern-Simons model defined
on an infinite Euclidean lattice. We point out that any gauge invariant, local
and parity odd Abelian quadratic form exhibits, in addition to the zero
eigenvalue associated with the gauge invariance and to the physical zero mode
at p=0 due to traslational invariance, a set of extra zero eigenvalues inside
the Brillouin zone. For the Abelian Chern-Simons theory, which is linear in the
derivative, this proliferation of zero modes is reminiscent of the
Nielsen-Ninomiya no-go theorem for fermions. A gauge invariant, local and
parity even term such as the Maxwell action leads to the elimination of the
extra zeros by opening a gap with a mechanism similar to that leading to Wilson
fermions on the lattice. |
Cosmologies inside hyperbolic black holes: Models with closed FRW cosmologies on the worldvolume of a constant-tension
brane inside a black hole provide an interesting setup for studying cosmology
holographically. However, in more than two worldvolume dimensions, there are
limitations on such models with flat spatial slices. I show that these
limitations can be avoided by considering instead hyperbolic slices. This also
naturally makes contact with previous work on Euclidean wormholes. | On the quantisation of SU(2) magnetic monopole dynamics: We argue that there is no consistent quantisation of the two BPS SU(2)
magnetic monopole dynamical system compatible with the correspondence
principle. |
Spontaneous breaking of the rotational symmetry in dimensionally reduced
super Yang-Mills models: We investigate the spontaneous breaking of the SO(D) symmetry in matrix
models, which can be obtained by the zero-volume limit of pure SU(N) super
Yang-Mills theory in D = 6, 10 dimensions. The D = 10 case corresponds to the
IIB matrix model, which was proposed as a non-perturbative formulation of type
IIB superstring theory, and the spontaneous breaking corresponds to the
dynamical compactification of space-time suggested in that model. First we
study the D = 6 case by the Gaussian expansion method, which turns out to yield
clearer results than the previous results for the D = 10 case for certain
technical reasons. By comparing the free energy of the SO(d) symmetric vacua
for d = 2, 3, 4, 5, we conclude that the breaking SO(6) \to SO(3) actually
occurs. We find that the extent of space-time in the shrunken directions is
almost independent of d. In units of this universal scale, the extended
directions seem to have large but still finite extents depending on d. We show
that these results for the extent of space-time can be explained quantitatively
by an argument based on the low-energy effective theory. With these new
insights, we reconsider the previous results for the IIB matrix model, and find
that they are also consistent with our argument based on the low-energy
effective theory. Thus we arrive at comprehensive understanding and some
quantitative predictions concerning the nature of the spontaneous symmetry
breaking taking place in these models. The space-time picture that emerges from
the IIB matrix model and its implication on possible interpretations of the
model are also discussed. | Quantum Fusion of Domain Walls with Fluxes: We study how fluxes on the domain wall world volume modify quantum fusion of
two distant parallel domain walls into a composite wall. The elementary wall
fluxes can be separated into parallel and antiparallel components. The parallel
component affects neither the binding energy nor the process of quantum merger.
The antiparallel fluxes, instead, increase the binding energy and, against
naive expectations, suppress quantum fusion. In the small flux limit we
explicitly find the bounce solution and the fusion rate as a function of the
flux. We argue that at large (antiparallel) fluxes there exists a critical
value of the flux (versus the difference in the wall tensions), which switches
off quantum fusion altogether. This phenomenon of flux-related wall
stabilization is rather peculiar: it is unrelated to any conserved quantity.
Our consideration of the flux-related all stabilization is based on
substantiated arguments that fall short of complete proof. |
Second-Order Fermions: It has been proposed several times in the past that one can obtain an
equivalent, but in many aspects simpler description of fermions by first
reformulating their first-order (Dirac) Lagrangian in terms of two-component
spinors, and then integrating out the spinors of one chirality ($e.g.$ primed
or dotted). The resulting new Lagrangian is second-order in derivatives, and
contains two-component spinors of only one chirality. The new second-order
formulation simplifies the fermion Feynman rules of the theory considerably,
$e.g.$ the propagator becomes a multiple of an identity matrix in the field
space. The aim of this thesis is to work out the details of this formulation
for theories such as Quantum Electrodynamics, and the Standard Model of
elementary particles. After having developed the tools necessary to establish
the second-order formalism as an equivalent approach to spinor field theories,
we proceed with some important consistency checks that the new formulation is
required to pass, namely the presence or absence of anomalies in their
perturbative and non-perturbative description, and the unitarity of the
S-Matrix derived from their Lagrangian. Another aspect which is studied is
unification, where we seek novel gauge-groups that can be used to embed all of
the Standard Model content: forces and fermionic representations. Finally, we
will explore the possibility to unify gravity and the Standard Model when the
former is seen as a diffeomorphism invariant gauge-theory. | Additional fermionic fields onto parallelizable 7-spheres: The geometric Fierz identities are here employed to generate new emergent
fermionic fields on the parallelizable (curvatureless, torsionfull) 7-sphere
($S^7$). Employing recently found new classes of spinor fields on the $S^7$
spin bundle, new classes of fermionic fields are obtained from their bilinear
covariants by a generalized reconstruction theorem, on the parallelizable
$S^7$. Using a generalized non-associative product on the octonionic bundle on
the parallelizable $S^7$, these new classes of algebraic spinor fields, lifted
onto the parallelizable $S^7$, are shown to correctly transform under the
Moufang loop generators on $S^7$. |
COUPLING CHIRAL BOSONS TO GRAVITY: The chiral boson actions of Floreanini and Jackiw (FJ), and of McClain,Wu and
Yu (MWY) have been recently shown to be different representations of the same
chiral boson theory. MWY displays manifest covariance and also a (gauge)
symmetry that is hidden in the FJ side, which, on the other hand, displays the
physical spectrum in a simple manner. We make use of the covariance of the MWY
representation for the chiral boson to couple it to background gravity showing
explicitly the equivalence with the previous results for the FJ representation | Horizon symmetries and hairy black holes in AdS: We investigate whether supertranslation symmetry may appear in a scenario
that involves black holes in AdS space. The framework we consider is massive 3D
gravity, which admits a rich black hole phase space, including stationary AdS
black holes with softly decaying hair. We consider a set of asymptotic
conditions that permits such decaying near the boundary, and which, in addition
to the local conformal symmetry, is preserved by an extra local current. The
corresponding algebra of diffeomorphisms consists of two copies of Virasoro
algebra in semi-direct sum with an infinite-dimensional Abelian ideal. We then
reorient the analysis to the near horizon region, where infinite-dimensional
symmetries also appear. The supertranslation symmetry at the horizon yields an
infinite set of non-trivial charges, which we explicitly compute. The zero-mode
of these charges correctly reproduces the black hole entropy. In contrast to
Einstein gravity, in the higher-derivative theory subleading terms in the near
horizon expansion contribute to the near horizon charges. Such terms happen to
capture the higher-curvature corrections to the Bekenstein area law. |
The Action for Twisted Self-Duality: One may write the Maxwell equations in terms of two gauge potentials, one
electric and one magnetic, by demanding that their field strengths should be
dual to each other. This requirement is the condition of twisted self-duality.
It can be extended to p-forms in spacetime of D dimensions, and it survives the
introduction of a variety of couplings among forms of different rank, and also
to spinor and scalar fields, which emerge naturally from supergravity. In this
paper we provide a systematic derivation of the action principle, whose
equations of motion are the condition of twisted self-duality. The derivation
starts from the standard Maxwell action, extended to include the aforementioned
couplings, and proceeds via the Hamiltonian formalism through the resolution of
Gauss' law. In the pure Maxwell case we recover in this way an action that had
been postulated by other authors, through an ansatz based on an action given
earlier by us for untwisted self-duality. Those authors also extended their
ansatz to include Chern-Simons couplings. In that case, we find a different
result. The derivation from the standard extended Maxwell action implies of
course that the theory is Lorentz-invariant and can be locally coupled to
gravity. Nevertherless we include a direct compact Hamiltonian proof of these
properties, which is based on the surface-deformation algebra. The symmetry in
the dependence of the action on the electric and magnetic variables is
manifest, since they appear as canonical conjugates. Spacetime covariance,
although present, is not manifest. | An Index for Superconformal Quantum Mechanics: We study quantum mechanical systems with $\mathfrak{osp}(4^{*}|4)$
superconformal symmetry. We classify unitary lowest-weight representations of
this superconformal algebra and define an index which receives contributions
from short and semi-short multiplets only. We consider the example of a quantum
mechanical $\sigma$-model with hyper-K\"{a}hler target $\mathcal{M}$ equipped
with a triholomorphic homothety. The superconformal index coincides with the
Witten index of a novel form of supersymmetric quantum mechanics for a particle
moving on $\mathcal{M}$ in a background magnetic field in which an unbroken
$\mathfrak{su}(1|2)$ subalgebra of the superconformal algebra is linearly
realised as a global symmetry. |
Anyonic FRT construction: The Faddeev-Reshetikhin-Takhtajan method to construct matrix bialgebras from
non-singular solutions of the quantum Yang-Baxter equation is extended to the
anyonic or $\Z_n$-graded case. The resulting anyonic quantum matrices are
braided groups in which the braiding is given by a phase factor. | On the Schwinger Model on Riemann Surfaces: In this paper, the massless Schwinger model or two dimensional quantum
electrodynamics is exactly solved on a Riemann surface. The partition function
and the generating functional of the correlation functions involving the
fermionic currents are explicitly derived using a method of quantization valid
for any abelian gauge field theory and explained in the recent references [F.
Ferrari, {\it Class. Quantum Grav.} {\bf 10} (1993), 1065], [F. Ferrari, hep-th
9310024]. In this sense, the Schwinger model is one of the few examples of
interacting and nontopological field theories that are possible to quantize on
a Riemann surface. It is also shown here that the Schwinger model is equivalent
to a nonlocal integrable model which represents a generalization of the
Thirring model. Apart from the possible applications in string theory and
integrable models, we hope that this result can be also useful in the study of
quantum field theories in curved space-times. |
Holography and Eternal Inflation: We show that eternal inflation is compatible with holography. In particular,
we emphasize that if a region is asymptotically de Sitter in the future,
holographic arguments by themselves place no bound on the number of past
e-foldings. We also comment briefly on holographic restrictions on the
production of baby universes. | Inflation in large N limit of supersymmetric gauge theories: Within supersymmetry we provide an example where the inflaton sector is
derived from a gauge invariant polynomial of SU(N) or SO(N) gauge theory.
Inflation in our model is driven by multi-flat directions, which assist
accelerated expansion. We show that multi-flat directions can flatten the
individual non-renormalizable potentials such that inflation can occur at
sub-Planckian scales. We calculate the density perturbations and the spectral
index, we find that the spectral index is closer to scale invariance for large
N. In order to realize a successful cosmology we require large N of order,
N~600. |
String-Like BTZ on Codimension-2 Braneworlds in the Thin Brane Limit: We consider five-dimensional gravity with a Gauss-Bonnet term in the bulk and
an induced gravity term on a 2-brane of codimension-2. We show that this system
admits BTZ black holes on the 2-brane which are extended into the bulk with
regular horizons. | The Holographic Geometry of the Renormalization Group and Higher Spin
Symmetries: We consider the Wilson-Polchinski exact renormalization group applied to the
generating functional of single-trace operators at a free-fixed point in
$d=2+1$ dimensions. By exploiting the rich symmetry structure of free field
theory, we study the geometric nature of the RG equations and the associated
Ward identities. The geometry, as expected, is holographic, with $AdS$
spacetime emerging correspondent with RG fixed points. The field theory
construction gives us a particular vector bundle over the $d+1$-dimensional RG
mapping space, called a jet bundle, whose structure group arises from the
linear orthogonal bi-local transformations of the bare fields in the path
integral. The sources for quadratic operators constitute a connection on this
bundle and a section of its endomorphism bundle. Recasting the geometry in
terms of the corresponding principal bundle, we arrive at a structure
remarkably similar to the Vasiliev theory, where the horizontal part of the
connection on the principal bundle is Vasiliev's higher spin connection, while
the vertical part (the Faddeev-Popov ghost) corresponds to the $S$-field. The
Vasiliev equations are then, respectively, the RG equations and the BRST
equations, with the RG beta functions encoding bulk interactions. Finally, we
remark that a large class of interacting field theories can be studied through
integral transforms of our results, and it is natural to organize this in terms
of a large $N$ expansion. |
Multi-entropy at low Renyi index in 2d CFTs: For a static time slice of AdS$_3$ we describe a particular class of minimal
surfaces which form trivalent networks of geodesics. Through geometric
arguments we provide evidence that these surfaces describe a measure of
multipartite entanglement. By relating these surfaces to Ryu-Takayanagi
surfaces it can be shown that this multipartite contribution is related to the
angles of intersection of the bulk geodesics.
A proposed boundary dual, the multi-entropy, generalizes replica trick
calculations involving twist operators by considering monodromies with finite
group symmetry beyond the cyclic group used for the computation of entanglement
entropy. We make progress by providing explicit calculations of Renyi
multi-entropy in two dimensional CFTs and geometric descriptions of the replica
surfaces for several cases with low genus.
We also explore aspects of the free fermion and free scalar CFTs. For the
free fermion CFT we examine subtleties in the definition of the twist operators
used for the calculation of Renyi multi-entropy. In particular the standard
bosonization procedure used for the calculation of the usual entanglement
entropy fails and a different treatment is required. | Local SU(3) gauge invariance in Weyl 2-spinor language and quark-gluon
plasma equations of motion: In a new Weyl 2-spinor approach to Non abelian Gauge Theories, starting with
the local U(1) Gauge group of a previous work, we study now the SU(3) case
corresponding to quarks (antiquarks) interacting with color fields. The
principal difference with the conventional approach is that particle-field
interactions are not described by means of potentials but by the field strength
magnitudes. Some analytical expressions showing similarities with
electrodynamics are obtained. Classical equations that describe the behavior of
quarks under gluon fields might be in principle applied to the quark-gluon
plasma phase existing during the first instants of the Universe. |
ADDENDUM to the papers on the Weinberg Theory: The Weinberg-Tucker-Hammer equations are shown to substitute the common-used
$j=1$ massless equations. Meantime, the old equations preserve their
significance as a particular case.
Possible consequences are discussed. | New solutions for non-Abelian cosmic strings: We study the properties of classical vortex solutions in a non-Abelian gauge
theory. A system of two adjoint Higgs fields breaks the SU(2) gauge symmetry to
$Z_2$, producing 't Hooft-Polyakov monopoles trapped on cosmic strings, termed
beads; there are two charges of monopole and two degenerate string solutions.
The strings break an accidental discrete $Z_2$ symmetry of the theory,
explaining the degeneracy of the ground state. Further symmetries of the model,
not previously appreciated, emerge when the masses of the two adjoint Higgs
fields are degenerate. The breaking of the enlarged discrete symmetry gives
rise to additional string solutions and splits the monopoles into four types of
`semipole': kink solutions that interpolate between the string solutions,
classified by a complex gauge invariant magnetic flux and a $Z_4$ charge. At
special values of the Higgs self-couplings, the accidental symmetry broken by
the string is continuous, giving rise to supercurrents on the strings. The
SU(2) theory can be embedded in a wide class of Grand Unified Theories,
including SO(10). We argue that semipoles and supercurrents are generic on GUT
strings. |
Trisecting non-Lagrangian theories: We propose a way to define and compute invariants of general smooth
4-manifolds based on topological twists of non-Lagrangian 4d N=2 and N=3
theories in which the problem is reduced to a fairly standard computation in
topological A-model, albeit with rather unusual targets, such as compact and
non-compact Gepner models, asymmetric orbifolds, N=(2,2) linear dilaton
theories, "self-mirror" geometries, varieties with complex multiplication, etc. | On Large N Conformal Theories, Field Theories in Anti-De Sitter Space
and Singletons: It was proposed by Maldacena that the large $N$ limit of certain conformal
field theories can be described in terms of supergravity on anti-De Sitter
spaces (AdS). Recently, Gubser, Klebanov and Polyakov and Witten have
conjectured that the generating functional for certain correlation functions in
conformal field theory is given by the classical supergravity action on AdS. It
was shown that the spectra of states of the two theories are matched and the
two-point correlation function was studied. We discuss the interacting case and
compare the three- and four-point correlation functions computed from a
classical action on AdS with the large N limit of conformal theory. We discuss
also the large N limit for the Wilson loop and suggest that singletons which
according to Flato and Fronsdal are constituents of composite fields in
spacetime should obey the quantum Boltzmann statistics. |
Hamilton Formalism in Non-Commutative Geometry: We study the Hamilton formalism for Connes-Lott models, i.e., for Yang-Mills
theory in non-commutative geometry. The starting point is an associative
$*$-algebra $\cA$ which is of the form $\cA=C(I,\cAs)$ where $\cAs$ is itself a
associative $*$-algebra. With an appropriate choice of a k-cycle over $\cA$ it
is possible to identify the time-like part of the generalized differential
algebra constructed out of $\cA$. We define the non-commutative analogue of
integration on space-like surfaces via the Dixmier trace restricted to the
representation of the space-like part $\cAs$ of the algebra. Due to this
restriction it possible to define the Lagrange function resp. Hamilton function
also for Minkowskian space-time. We identify the phase-space and give a
definition of the Poisson bracket for Yang-Mills theory in non-commutative
geometry. This general formalism is applied to a model on a two-point space and
to a model on Minkowski space-time $\times$ two-point space. | Modes of the Sakai-Sugimoto soliton: The instanton in the Sakai-Sugimoto model corresponds to the Skyrmion on the
holographic boundary - which is asymptotically flat - and is fundamentally
different from the flat Minkowski space Yang-Mills instanton. We use the
Atiyah-Patodi-Singer index theorem and a series of transformations to show that
there are 6k zeromodes - or moduli - in the limit of infinite 't Hooft coupling
of the Sakai-Sugimoto model. The implications for the low-energy baryons - the
Skyrmions - on the holographic boundary, is a scale separation between 2k
"heavy" massive modes and 6k-9 "light" massive modes for k>1; the 9 global
transformations that correspond to translations, rotations and isorotations
remain as zeromodes. For k=1 there are 2 "heavy" modes and 6 zeromodes due to
degeneracy between rotations and isorotations. |
Supersymmetric Quantum Mechanics of Magnetic Monopoles: A Case Study: We study, in detail, the supersymmetric quantum mechanics of charge-(1,1)
monopoles in N=2 supersymmetric Yang-Mills-Higgs theory with gauge group SU(3)
spontaneously broken to U(1) x U(1). We use the moduli space approximation of
the quantised dynamics, which can be expressed in two equivalent formalisms:
either one describes quantum states by Dirac spinors on the moduli space, in
which case the Hamiltonian is the square of the Dirac operator, or one works
with anti-holomorphic forms on the moduli space, in which case the Hamiltonian
is the Laplacian acting on forms. We review the derivation of both formalisms,
explicitly exhibit their equivalence and derive general expressions for the
supercharges as differential operators in both formalisms. We propose a general
expression for the total angular momentum operator as a differential operator,
and check its commutation relations with the supercharges. Using the known
metric structure of the moduli space of charge-(1,1) monopoles we show that
there are no quantum bound states of such monopoles in the moduli space
approximation. We exhibit scattering states and compute corresponding
differential cross sections. | Symmetries in A-Type Little String Theories, Part I: We analyse the symmetries of a class of A-type little string theories that
are engineered by $N$ parallel M5-branes with M2-branes stretched between them.
This paper deals with the so-called reduced free energy, which only receives
contributions from the subset of the BPS states that carry the same charges
under all the Cartan generators of the underlying gauge algebra. We argue (and
check explicitly in a number of examples) that the former is invariant under
the paramodular group $\Sigma_N\subset Sp(4,\mathbb{Q})$, which gets extended
to a subgroup of $Sp(4,\mathbb{R})$ in the Nekrasov-Shatashvili-limit. This
extension agrees with the observation made in arXiv:1706.04425 that these BPS
states form a symmetric orbifold CFT. Furthermore, we argue that $\Sigma_N$
(along with other symmetries) places strong constraints on the BPS counting
function that governs the intersection between the M5- and M2-branes. |
A New Handle on de Sitter Compactifications: We construct a large new class of de Sitter (and anti de Sitter) vacua of
critical string theory from flux compactifications on products of Riemann
surfaces. In the construction, the leading effects stabilizing the moduli are
perturbative. We show that these effects self-consistently dominate over
standard estimates for further $\alpha^\prime$ and quantum corrections, via
tuning available from large flux and brane quantum numbers. | A Primer for Manifestly Gauge Invariant Computations in SU(N) Yang-Mills: It has recently been determined that, within the framework of the Exact
Renormalisation Group, continuum computations can be performed to any loop
order in SU(N) Yang-Mills theory without fixing the gauge or specifying the
details of the regularisation scheme. In this paper, we summarise and refine
the powerful diagrammatic techniques which facilitate this procedure and
illustrate their application in the context of a calculation of the two-loop
beta function. |
Virial Theorem for Non-relativistic Quantum Fields in D Spatial
Dimensions: The virial theorem for non-relativistic complex fields in $D$ spatial
dimensions and with arbitrary many-body potential is derived, using
path-integral methods and scaling arguments recently developed to analyze
quantum anomalies in low-dimensional systems. The potential appearance of a
Jacobian $J$ due to a change of variables in the path-integral expression for
the partition function of the system is pointed out, although in order to make
contact with the literature most of the analysis deals with the $J=1$ case. The
virial theorem is recast into a form that displays the effect of microscopic
scales on the thermodynamics of the system. From the point of view of this
paper the case usually considered, $J=1$, is not natural, and the
generalization to the case $J\neq 1$ is briefly presented. | 4d strings at strong coupling: Weakly coupled regions of 4d EFTs coupled to gravity are particularly
suitable to describe the backreaction of BPS fundamental axionic strings,
dubbed EFT strings, in a local patch of spacetime around their core. We study
the extension of these local solutions to global ones, which implies probing
regions of strong coupling and provides an estimate of the EFT string tension
therein. We conjecture that for the EFT string charge generators such a global
extension is always possible and yields a sub-Planckian tension. We
substantiate this claim by analysing global solutions of 4d strings made up
from NS5-branes wrapping Calabi-Yau threefold divisors in either type IIA or
heterotic string theory. We argue that in this case the global,
non-perturbative data of the backreaction can be simply encoded in terms of a
GLSM describing the compactification, as we demonstrate in explicit examples. |
Fermionic Operators from Bosonic Fields in 3+1 Dimensions: We present a construction of fermionic operators in 3+1 dimensions in terms
of bosonic fields in the framework of $QED_4$. The basic bosonic variables are
the electric fields $E_i$ and their conjugate momenta $A_i$. Our construction
generalizes the analogous constuction of fermionic operators in 2+1 dimensions.
Loosely speaking, a fermionic operator is represented as a product of an
operator that creates a pointlike charge and an operator that creates an
infinitesimal t'Hooft loop of half integer strength. We also show how the axial
$U(1)$ transformations are realized in this construction. | R-Charge Chemical Potential in a 2+1 Dimensional System: We study probe D5 branes in D3 brane AdS_5 and AdS_5-Schwarzschild
backgrounds as a prototype dual description of strongly coupled 2+1 dimensional
quasi-particles. We introduce a chemical potential for a weakly gauged U(1)
subgroup of the theory's global R-symmetry by spinning the D5 branes. The
resulting D5 embeddings are complicated by the existence of a region of the
space in which the local speed of light falls below the rotation speed. We find
regular embeddings through this region and show that the system does not
exhibit the spontaneous symmetry breaking that would be needed for a
superconductor. |
Discrete States in Two-Dimensional Quantum Gravity: Minor misprints corrected. | Higher-twist fermionic operators and DIS structure functions from the
AdS/CFT duality: The role of local higher-twist ($\tau > 3$) spin-1/2 fermionic operators of
the strongly coupled ${\cal {N}}=4$ supersymmetric Yang-Mills theory on the
symmetric and antisymmetric deep inelastic scattering (DIS) structure functions
is investigated. The calculations are carried out in terms of the duality
between ${\cal {N}}=4$ SYM theory and type IIB supergravity on AdS$_5 \times
S^5$. Particularly, we explicitly obtain the structure functions for
single-trace spin-1/2 fermionic operators in the 20$^*$ and 60$^*$ irreducible
representations of $SU(4)_R$, corresponding to twists 4 and 5, respectively. We
also calculate the contributions of other single-trace spin-1/2 fermionic
operators in the 4, 20 and 60 irreducible representations of $SU(4)_R$. New
important effects are found in comparison with the minimal twist ($\tau = 3$)
case, and they are studied thoroughly. |
A simple quantum system that describes a black hole: During the past decades, theorists have been studying quantum mechanical
systems that are believed to describe black holes. We review one of the
simplest examples. It involves a collection of interacting oscillators and
Majorana fermions. It is conjectured to describe a black hole in an emergent
universe governed by Einstein equations. Based on previous numerical
computations, we make an estimate of the necessary number of qubits necessary
to see some black hole features. | Dual actions for massless, partially-massless and massive gravitons in
(A)dS: We provide a unified treatment of electric-magnetic duality, at the action
level and with manifest Lorentz invariance, for massive, massless as well as
partially-massless gravitons propagating in maximally symmetric spacetimes of
any dimension n>3. For massive and massless fields, we complete previous
analyses that use parent-action techniques by giving dual descriptions that
enable direct counting of physical degrees of freedom in the flat and massless
limit. The same treatment is extended to the partially-massless case, where the
duality has been previously discussed in covariant form only at the level of
the equations of motion. The nature of the dual graviton is therefore clarified
for all values of the mass and of the cosmological constant. |
Minimum Distances in Non-Trivial String Target Spaces: The idea of minimum distance, familiar from R <-> 1/R duality when the string
target space is a circle, is analyzed for less trivial geometries. The
particular geometry studied is that of a blown-up quotient singularity within a
Calabi-Yau space and mirror symmetry is used to perform the analysis. It is
found that zero distances can appear but that in many cases this requires other
distances within the same target space to be infinite. In other cases zero
distances can occur without compensating infinite distances. | On renormalizability of the massless Thirring model: We discuss the renormalizability of the massless Thirring model in terms of
the causal fermion Green functions and correlation functions of left-right
fermion densities. We obtain the most general expressions for the causal
two-point Green function and correlation function of left-right fermion
densities with dynamical dimensions of fermion fields, parameterised by two
parameters. The region of variation of these parameters is constrained by the
positive definiteness of the norms of the wave functions of the states related
to components of the fermion vector current. We show that the dynamical
dimensions of fermion fields calculated for causal Green functions and
correlation functions of left-right fermion densities can be made equal. This
implies the renormalizability of the massless Thirring model in the sense that
the ultra-violet cut-off dependence, appearing in the causal fermion Green
functions and correlation functions of left-right fermion densities, can be
removed by renormalization of the wave function of the massless Thirring
fermion fields only. |
Classical BRST charge and observables in reducible gauge theories: We study the construction of the classical Becchi-Rouet-Stora-Tyutin (BRST)
charge and observables for arbitrary reducible gauge theory. Using a special
coordinate system in the extended phase space, we obtain an explicit expression
for the Koszul-Tate differential operator and show that the BRST charge can be
found by a simple iterative method. We also give a formula for the classical
BRST observables. | Symmetries in Two Dimensional Conformal Field Theories and Related
Integrable Models: We present part of our investigations on two dimensional N=1 and N=2
superconformal field theories. As a direct generalization we consider the SU(2)
coset models, in particular their renormalization group properties. A search
and possible implementation of additional symmetries in related integrable
models are also presented. |
Making predictions in the multiverse: I describe reasons to think we are living in an eternally inflating
multiverse where the observable "constants" of nature vary from place to place.
The major obstacle to making predictions in this context is that we must
regulate the infinities of eternal inflation. I review a number of proposed
regulators, or measures. Recent work has ruled out a number of measures by
showing that they conflict with observation, and focused attention on a few
proposals. Further, several different measures have been shown to be
equivalent. I describe some of the many nontrivial tests these measures will
face as we learn more from theory, experiment, and observation. | M2-branes Theories without 3+1 Dimensional Parents via Un-Higgsing: N=2 quiver Chern-Simons theory has lately attracted attention as the world
volume theory of multiple M2 branes on a Calabi-Yau 4-fold. We study the
connection between the stringy derivation of M2 brane theories and the forward
algorithm which gives the toric Calabi-Yau 4-fold as the moduli space of the
quiver theory. Then the existence of the 3+1 dimensional parent, which is the
consistent 3+1 dimensional superconformal theory with the same quiver diagram,
is crucial for stringy derivation of M2 brane theories. We also investigate the
construction of M2 brane theories that do not have 3+1 dimensional parents. The
un-Higgsing procedure plays a key role to construct these M2 brane theories. We
find some N=2 quiver Chern-Simons theories which correspond to interesting
Calabi-Yau singularities. |
Consistency of non-minimal renormalisation schemes: Non-minimal renormalisation schemes such as the momentum subtraction scheme
(MOM) have frequently been used for physical computations. The consistency of
such a scheme relies on the existence of a coupling redefinition linking it to
MSbar. We discuss the implementation of this procedure in detail for a general
theory and show how to construct the relevant redefinition up to three-loop
order, for the case of a general theory of fermions and scalars in four
dimensions and a general scalar theory in six dimensions. | Entanglement entropy for odd spheres: It is shown, non--rigorously, that the effective action on a Z_q factored odd
spheres (lune) has a vanishing derivative at q=1. This leaves the effective
action on the ordinary odd d-sphere as (minus) the value of the entanglement
entropy associated with a (d-2)-sphere. Some numbers are given. |
Perturbative Computation of the Gluonic Effective Action via Polyaokov's
World-Line Path Integral: The Polyakov world-line path integral describing the propagation of gluon
field quanta is constructed by employing the background gauge fixing method and
is subsequently applied to analytically compute the divergent terms of the one
(gluonic) loop effective action to fourth order in perturbation theory. The
merits of the proposed approach is that, to a given order, it reduces to
performing two integrations, one over a set of Grassmann and one over a set of
Feynman-type parameters through which one manages to accomodate all Feynman
diagrams entering the computation at once. | Large N Spectrum of two Matrices in a Harmonic Potential and BMN
energies: The large N spectrum of the quantum mechanical hamiltonian of two hermitean
matrices in a harmonic potential is studied in a framework where one of the
matrices is treated exactly and the other is treated as a creation operator
impurity in the background of the first matrix. For the free case, the complete
set of invariant eigenstates and corresponding energies are obtained. When
g_{YM}^2 interactions are added, it is shown that the full string tension
corrected spectrum of BMN loops is obtained. |
Pseudoclassical Model of Spinning Particle with Anomalous Magnetic
Momentum: A generalization of the pseudoclassical action of a spinning particle in the
presence of an anomalous magnetic momentum is given. The action is written in
reparametrization and supergauge invariant form. The Dirac quantization, based
on the Hamiltonian analyses of the model, leads to the Dirac-Pauli equation for
a particle with an anomalous magnetic momentum in an external electromagnetic
field. Due to the structure of first-class constraints in that case, the Dirac
quantization demands for consistency to take into account an operators ordering
problem. | 3-Schurs from explicit representation of Yangian
$Y(\hat{\mathfrak{gl}}_1)$. Levels 1-5: We suggest an ansatz for representation of affine Yangian $Y(\hat{
\mathfrak{gl}}_1)$ by differential operators in the triangular set of
time-variables ${\bf P}_{a,i}$ with $1\leqslant i\leqslant a$, which saturates
the MacMahon formula for the number of $3d$ Young diagrams/plane partitions. In
this approach the 3-Schur polynomials are defined as the common eigenfunctions
of an infinite set of commuting "cut-and-join" generators $\psi_n$ of the
Yangian. We manage to push this tedious program through to the 3-Schur
polynomials of level 5, and this provides a rather big sample set, which can be
now investigated by other methods. |
Thermodynamics of AdS Black Holes in Einstein-Scalar Gravity: We study the thermodynamics of $n$-dimensional static asymptotically AdS
black holes in Einstein gravity coupled to a scalar field with a potential
admitting a stationary point with an AdS vacuum. Such black holes with
non-trivial scalar hair can exist provided that the mass-squared of the scalar
field is negative, and above the Breitenlohner-Freedman bound. We use the Wald
procedure to derive the first law of thermodynamics for these black holes,
showing how the scalar hair (or "charge") contributes non-trivially in the
expression. We show in general that a black hole mass can be deduced by
isolating an integrable contribution to the (non-integrable) variation of the
Hamiltonian arising in the Wald construction, and that this is consistent with
the mass calculated using the renormalised holographic stress tensor and also,
in those cases where it is defined, with the mass calculated using the
conformal method of Ashtekar, Magnon and Das. Similar arguments can also be
given for the smooth solitonic solutions in these theories. Neither the black
hole nor the soliton solutions can be constructed explicitly, and we carry out
a numerical analysis to demonstrate their existence and to provide approximate
checks on some of our thermodynamic results. | Noncommutative Gauge Theory and Gravity in Three Dimensions: The Einstein-Hilbert action in three dimensions and the transformation rules
for the dreibein and spin connection can be naturally described in terms of
gauge theory. In this spirit, we use covariant coordinates in noncommutative
gauge theory in order to describe 3D gravity in the framework of noncommutative
geometry. We consider 3D noncommutative spaces based on SU(2) and SU(1,1), as
foliations of fuzzy 2-spheres and fuzzy 2-hyperboloids respectively. Then we
construct a U(2)$\times$ U(2) and a GL(2,$\mathbb{C}$) gauge theory on them,
identifying the corresponding noncommutative vielbein and spin connection. We
determine the transformations of the fields and an action in terms of a matrix
model and discuss its relation to 3D gravity. |
New expressions for gravitational scattering amplitudes: New methods are introduced for the description and evaluation of tree-level
gravitational scattering amplitudes. An N=7 super-symmetric recursion, free
from spurious double poles, gives a more efficient method for evaluating MHV
amplitudes. The recursion is naturally associated with twistor geometry, and
thereby gives a new interpretation for the amplitudes. The recursion leads to
new expressions for the MHV amplitudes for six and seven gravitons, simplifying
their symmetry properties, and suggesting further generalization. The N=7
recursion is valid for all tree amplitudes, and we illustrate it with a
simplified expression for the six-graviton NMHV amplitude. Further new
structure emerges when MHV amplitudes are expressed in terms of momentum
twistors. | Entanglement and Correlations near Extremality: CFTs dual to
Reissner-Nordström AdS${}_5$: We use the AdS/CFT correspondence to study models of entanglement and
correlations between two $d=4$ CFTs in thermofield double states at finite
chemical potential. Our bulk spacetimes are planar Reissner-Nordstr\"om AdS
black holes. We compute both thermo-mutual information and the two-point
correlators of large-dimension scalar operators, focussing on the
small-temperature behavior -- an infrared limit with behavior similar to that
seen at large times. The interesting feature of this model is of course that
the entropy density remains finite as $T \rightarrow 0$ while the bulk geometry
develops an infinite throat. This leads to a logarithmic divergence in the
scale required for non-zero mutual information between equal-sized strips in
the two CFTs, though the mutual information between one entire CFT and a
finite-sized strip in the other can remain non-zero even at $T=0$. Furthermore,
despite the infinite throat, there can be extremally charged operators for
which the two-point correlations remain finite as $T \rightarrow 0$. This
suggests an interestingly mixed picture in which some aspects of the
entanglement remain localized on scales set by the chemical potential, while
others shift to larger and larger scales. We also comment on implications for
the localized-quasiparticle picture of entanglement. |
Cosmic evolution from phase transition of 3-dimensional flat space: Flat space cosmology spacetimes are exact time-dependent solutions of
3-dimensional gravity theories, such as Einstein gravity or topologically
massive gravity. We exhibit a novel kind of phase transition between these
cosmological spacetimes and the Minkowski vacuum. At sufficiently high
temperature (rotating) hot flat space tunnels into a universe described by flat
space cosmology. | A Toy Model of the M5-brane: Anomalies of Monopole Strings in Five
Dimensions: We study a five-dimensional field theory which contains a monopole (string)
solution with chiral fermion zero modes. This monostring solution is a close
analog of the fivebrane solution of M-theory. The cancellation of normal bundle
anomalies parallels that for the M-theory fivebrane, in particular, the
presence of a Chern-Simons term in the low-energy effective U(1) gauge theory
plays a central role. We comment on the relationship between the the
microscopic analysis of the world-volume theory and the low-energy analysis and
draw some cautionary lessons for M-theory. |
Note on antisymmetric spin-tensors: It was known for a long time that in d = 4 dimensions it is impossible to
construct the Lagrangian for antisymmetric second rank spin-tensor that will be
invariant under the gauge transformations with unconstrained spin-vector
parameter. But recently a paper arXiv:0902.1471 appeared where gauge invariant
Lagrangians for antisymmetric spin-tensors of arbitrary rank n in d > 2n were
constructed using powerful BRST approach. To clarify apparent contradiction, in
this note we carry a direct independent analysis of the most general first
order Lagrangian for the massless antisymmetric spin-tensor of second rank. Our
analysis shows that gauge invariant Lagrangian does exist but in d > 4
dimensions only, while in d = 4 this Lagrangian becomes identically zero. As a
byproduct, we obtain a very simple and convenient form of this massless
Lagrangian that makes deformation to AdS space and/or massive case a simple
task as we explicitly show here. Moreover, this simple form admits natural and
straightforward generalization on the case of massive antisymmetric
spin-tensors of rank n for d > 2n. | World Volume Action for Fractional Branes: We study the world volume action of fractional Dp-branes of type IIA string
theory compactified on the orbifold T^4/Z_2. The geometric relation between
these branes and wrapped branes is investigated using conformal techniques. In
particular we examine in detail various scattering amplitudes and find that the
leading low-energy interactions are consistent with the boundary action derived
geometrically. |
Geometries from Young Diagrams: Type IIB string theory on spacetimes that are asymptotically
AdS$_5\times$S$^5$ can be defined using four dimensional ${\cal N}=4$ super
Yang-Mills theory. Six of the dimensions of the string theory are
holographically reconstructed in the Yang-Mills theory. In this article we
study how these dimensions and local physics in these dimensions emerge. We
reorganize the dynamics of the ${1\over 2}$ BPS sector of the field theory by
rewriting it in terms of Schur polynomials. The Young diagram labeling of these
polynomials can be viewed as a book keeping device which summarizes how the
operator is constructed. We show that aspects of the geometry of the extra
holographic dimensions are captured very naturally by the Young diagram.
Gravitons which are localized at a specific position in the bulk correspond to
boxes added at a specific location on the Young diagram. | A Simple/Short Introduction to Pre-Big-Bang Physics/Cosmology: A simple, non-technical introduction to the pre-big bang scenario is given,
emphasizing physical motivations, considerations, and consequences over
formalism. |
Large N Strong Coupling Dynamics in Non-Supersymmetric Orbifold Field
Theories: We give a recipe relating holomorphic quantities in supersymmetric field
theory to their descendants in non-supersymmetric Z_2 orbifold field theories.
This recipe, consistent with a recent proposal of Strassler, gives exact
results for bifermion condensates, domain wall tensions and gauge coupling
constants in the planar limit of the orbifold theories. | Construction method for the Nicolai map in supersymmetric Yang-Mills
theories: Recently, a universal formula for the Nicolai map in terms of a coupling flow
functional differential operator was found. We present the full perturbative
expansion of this operator in Yang-Mills theories where supersymmetry is
realized off-shell. Given this expansion, we develop a straightforward method
to compute the explicit Nicolai map to any order in the gauge coupling. Our
work extends the previously known construction method from the Landau gauge to
arbitrary gauges and from the gauge hypersurface to the full gauge-field
configuration space. As an example, we present the map in the axial gauge to
the second order. |
Causality in AdS/CFT and Lovelock theory: We explore the constraints imposed on higher curvature corrections of the
Lovelock type due to causality restrictions in the boundary of asymptotically
AdS space-time. In the framework of AdS/CFT, this is related to positivity of
the energy constraints that arise in conformal collider physics. We present
explicit analytic results that fully address these issues for cubic Lovelock
gravity in arbitrary dimensions and give the formal analytic results that
comprehend general Lovelock theory. The computations can be performed in two
ways, both by considering a thermal setup in a black hole background and by
studying the scattering of gravitons with a shock wave in AdS. We show that
both computations coincide in Lovelock theory. The different helicities, as
expected, provide the boundaries defining the region of allowed couplings. We
generalize these results to arbitrary higher dimensions and discuss their
consequences on the shear viscosity to energy density ratio of CFT plasmas, the
possible existence of Boulware-Deser instabilities in Lovelock theory and the
extent to which the AdS/CFT correspondence might be valid for arbitrary
dimensions. | Probing renormalization group flows using entanglement entropy: In this paper we continue the study of renormalized entanglement entropy
introduced in [1]. In particular, we investigate its behavior near an IR fixed
point using holographic duality. We develop techniques which, for any static
holographic geometry, enable us to extract the large radius expansion of the
entanglement entropy for a spherical region. We show that for both a sphere and
a strip, the approach of the renormalized entanglement entropy to the IR fixed
point value contains a contribution that depends on the whole RG trajectory.
Such a contribution is dominant, when the leading irrelevant operator is
sufficiently irrelevant. For a spherical region such terms can be anticipated
from a geometric expansion, while for a strip whether these terms have
geometric origins remains to be seen. |
Maximal depth implies su(3)+su(2)+u(1): Hence it excludes proton decay and supersymmetry. The main predictions of a
gauge model based on the exceptional simple Lie superalgebra mb(3|8) (a
localized version of su(3)+su(2)+u(1)) are reviewed. | Vector Fields in Holographic Cosmology: We extend the holographic formulation of the semiclassical no-boundary wave
function (NBWF) to models with Maxwell vector fields. It is shown that the
familiar saddle points of the NBWF have a representation in which a regular,
Euclidean asymptotic AdS geometry smoothly joins onto a Lorentzian
asymptotically de Sitter universe through a complex transition region. The tree
level probabilities of Lorentzian histories are fully specified by the action
of the AdS region of the saddle points. The scalar and vector matter profiles
in this region are complex from an AdS viewpoint, with universal asymptotic
phases. The dual description of the semiclassical NBWF thus involves complex
deformations of Euclidean CFTs. |
Symplectic Gravity Models in Four, Three and Two Dimensions: A class of the $D=4$ gravity models describing a coupled system of $n$
Abelian vector fields and the symmetric $n \times n$ matrix generalizations of
the dilaton and Kalb-Ramond fields is considered. It is shown that the
Pecci-Quinn axion matrix can be entered and the resulting equations of motion
possess the $Sp(2n, R)$ symmetry in four dimensions. The stationary case is
studied. It is established that the theory allows a $\sigma$-model
representation with a target space which is invariant under the $Sp[2(n+1), R]$
group of isometry transformations. The chiral matrix of the coset $Sp[2(n+1),
R]/U(n+1)$ is constructed. A K\"ahler formalism based on the use of the Ernst
$(n+1) \times (n+1)$ complex symmetric matrix is developed. The stationary
axisymmetric case is considered. The Belinsky-Zakharov chiral matrix depending
on the original field variables is obtained. The Kramer-Neugebauer
transformation, which algebraically maps the original variables into the target
space ones, is presented. | Stability of Hairy Black Holes in Shift-Symmetric Scalar-Tensor Theories
via the Effective Field Theory Approach: Shift-symmetric Horndeski theories admit an interesting class of
Schwarzschild-de Sitter black hole solutions exhibiting time-dependent scalar
hair. The properties of these solutions may be studied via a bottom-up
effective field theory (EFT) based on the background symmetries. This is in
part possible by making use of a convenient coordinate choice --
Lema\^itre-type coordinates -- in which the profile of the Horndeski scalar
field is linear in the relevant time coordinate. We construct this EFT, and use
it to understand the stability of hairy black holes in shift-symmetric
Horndeski theories, providing a set of constraints that the otherwise-free
functions appearing in the Horndeski Lagrangian must satisfy in order to admit
stable black hole solutions. The EFT is analyzed in the decoupling limit to
understand potential sources of instability. We also perform a complete
analysis of the EFT with odd-parity linear perturbations around general
spherically symmetric space-time. |
The correlation of WGC and Hydrodynamics bound with $R^4$ correction in
the charged AdS$_{d+2}$ black brane: In this paper, we focus on the possible correlation between conjectures KSS
bound and weak gravity conjecture (WGC). The hydrodynamic values KSS bound and
weak gravity conjecture constraint the low-energy effective field theory. These
conjectures identify UV complete theories. We give four, six and eight order
derivative corrections to corresponding action and employ the hyperscaling
violating charged AdS$_{d+2}$ black brane solution. These corrections lead us
to find correlation between conjectures KSS bound and weak gravity conjecture.
We see that, with increasing perturbation correction, this correlation is more
likely to appear. We consider dynamical constant $z=1$, $d=5$ and obtain the
range of hyperscaling violation exponent $d+z-2\leq\theta\leq d+z-1$ for the
above mentioned black brane. Here, we show that higher derivative corrections
reduce the ratio of $\frac{M}{Q}$ to extremal black holes. Likewise, we also
obtain the universal relaxation bound $\tau\geq \frac{1}{\pi T}$ and KSS bound
$\frac{\eta}{s}\geq \frac{1}{4\pi}$ for our model. The results indicate that
there is a possibility of a relationship between the two conjectures. Our
studies also show the consistency of the WGC and the KSS bound conjectures for
all corrections (except curvature-cubed, $\beta_2$) in the extremal and
near-extremal condition. | Smoothed Transitions in Higher Spin AdS Gravity: We consider CFTs conjectured to be dual to higher spin theories of gravity in
AdS_3 and AdS_4. Two dimensional CFTs with W_N symmetry are considered in the
lambda=0 (k --> infinity) limit, where they are conjectured to be described by
continuous orbifolds. The torus partition function is computed, using
reasonable assumptions, and equals that of a free field theory. We find no
phase transition at temperatures of order one; the usual Hawking-Page phase
transition is removed by the highly degenerate light states associated with
conical defect states in the bulk. Three dimensional Chern-Simons-matter CFTs
with vector-like matter are considered on T^3, where the dynamics is described
by an effective theory for the eigenvalues of the holonomies. Likewise, we find
no evidence for a Hawking-Page phase transition at large level k. |
Topological Orders in (4+1)-Dimensions: We investigate the Morita equivalences of (4+1)-dimensional topological
orders. We show that any (4+1)-dimensional super (fermionic) topological order
admits a gapped boundary condition -- in other words, all (4+1)-dimensional
super topological orders are Morita trivial. As a result, there are no
inherently gapless super (3+1)-dimensional theories. On the other hand, we show
that there are infinitely many algebraically Morita-inequivalent bosonic
(4+1)-dimensional topological orders. | Integrability of the RG flows and the bulk/boundary correspondence: We suggest that RG flows in the N=2 SUSY YM theories are governed by the pair
of the integrable systems. The main dynamical ingredient amounts from the
interaction of the small size instantons with the regulator degrees of freedom.
The relation with the bulk/boundary correspondence is discussed. |
Exact Results and Holography of Wilson Loops in N=2 Superconformal
(Quiver) Gauge Theories: Using localization, matrix model and saddle-point techniques, we determine
exact behavior of circular Wilson loop in N=2 superconformal (quiver) gauge
theories. Focusing at planar and large `t Hooft couling limits, we compare its
asymptotic behavior with well-known exponential growth of Wilson loop in N=4
super Yang-Mills theory. For theory with gauge group SU(N) coupled to 2N
fundamental hypermultiplets, we find that Wilson loop exhibits non-exponential
growth -- at most, it can grow a power of `t Hooft coupling. For theory with
gauge group SU(N) x SU(N) and bifundamental hypermultiplets, there are two
Wilson loops associated with two gauge groups. We find Wilson loop in untwisted
sector grows exponentially large as in N=4 super Yang-Mills theory. We then
find Wilson loop in twisted sector exhibits non-analytic behavior with respect
to difference of two `t Hooft coupling constants. By letting one gauge coupling
constant hierarchically larger/smaller than the other, we show that Wilson
loops in the second type theory interpolate to Wilson loop in the first type
theory. We infer implications of these findings from holographic dual
description in terms of minimal surface of dual string worldsheet. We suggest
intuitive interpretation that in both type theories holographic dual background
must involve string scale geometry even at planar and large `t Hooft coupling
limit and that new results found in the gauge theory side are attributable to
worldsheet instantons and infinite resummation therein. Our interpretation also
indicate that holographic dual of these gauge theories is provided by certain
non-critical string theories. | Some Computations with Seiberg-Witten Invariant Actions: We show, with a 2-dimensional example, that the low energy effective action
which describes the physics of a single D-brane is compatible with T-duality
whenever the corresponding U(N) non-abelian action is form-invariant under the
non-commutative Seiberg-Witten transformations. |
Exact propagators in harmonic superspace: Within the background field formulation in harmonic superspace for quantum N
= 2 super Yang-Mills theories, the propagators of the matter, gauge and ghost
superfields possess a complicated dependence on the SU(2) harmonic variables
via the background vector multiplet. This dependence is shown to simplify
drastically in the case of an on-shell vector multiplet. For a covariantly
constant background vector multiplet, we exactly compute all the propagators.
In conjunction with the covariant multi-loop scheme developed in
hep-th/0302205, these results provide an efficient (manifestly N = 2
supersymmetric) technical setup for computing multi-loop quantum corrections to
effective actions in N = 2 supersymmetric gauge theories, including the N = 4
super Yang-Mills theory. | New Branches of String Compactifications and their F-Theory Duals: We study heterotic $E_8\times E_8$ models that are dual to compactifications
of F-theory and type IIA string on certain classes of elliptically fibered
Calabi-Yau manifolds. Different choices for the specific torus in the fibration
have heterotic duals that are most easily understood in terms of $E_8\times
E_8$ models with gauge backgrounds of type $H\times U(1)^{8-d}$, where $H$ is a
non-Abelian factor. The case with $d=8$ corresponds to the well known
$E_8\times E_8$ compactifications with non-Abelian instanton backgrounds
$(k_1,k_2)$ whose F-theory duals are built through compactifications on
fibrations of the torus $\IP_2^{(1,2,3)}[6]$ over $\IF_n$. The new cases with
$d < 8$ correspond to other choices for the elliptic fiber over the same base
and yield unbroken $U(1)$'s, some of which are anomalous and acquire a mass by
swallowing zero modes of the antisymmetric $B_{MN}$ field. We also study
transitions to models with no tensor multiplets in $D=6$ and find evidence of
$E_d$ instanton dynamics. We also consider the possibility of conifold
transitions among spaces with different realization of the elliptic fiber. |
Interplay between Black Holes and Ultralight Dark Matter: Analytic
Solutions: Dark matter (DM) can consist of a scalar field so light that DM particles in
the galactic halo are best described by classical waves. We investigate how
these classical solutions are influenced by the presence of a non-rotating
supermassive black hole at the center of the galaxy, using an analytical,
albeit approximate, approach.
Relying on this analytic control, we examine the consequences of imposing
causal boundary conditions at the horizon, which are typically overlooked.
First, we examine the scenario where the backreaction of dark matter can be
neglected. The scalar field decays like a power law at large distances, thus
endowing the black hole with "hair". We derive solutions for the field profile
over a wide range of parameters, including cases with rotating dark matter. As
a by-product, we extract the dynamical Love numbers for scalar perturbations.
Next, we determine the spectrum of bound states and their behaviour.
Finally, we incorporate the self-gravity of the scalar field, with a focus on
the situation where dark matter forms a soliton (boson star) at the center of
the galaxy. We derive an analytical expression for the soliton at every
distance from the center. With a solution that remains applicable even at
horizon scales, we can reliably compute the accretion rate of the black hole. | Abelian-Higgs Phase of SU(2) QCD and Glueball Energy: It is shown that SU(2) QCD admits an dual Abelian-Higgs phase, with a Higgs
vacuum type of type-II superconductor. This is done by using connection
decomposition for the gluon field and the random-direction approximation. Using
bag picture with soft wall, we presented a calculational procedure for glueball
energy based on the recent proof for wall-vortices [Nucl. Phys. B 741(2006)1]. |
The Hamilton-Jacobi analysis for higher order Maxwell-Chern-Simons gauge
theory: By using the Hamilton-Jacobi [$HJ$] framework the higher-order
Maxwell-Chern-Simons theory is analyzed. The complete set of $HJ$ Hamiltonians
and a generalized $HJ$ differential are reported, from which all symmetries of
the theory are identified. In addition, we complete our study by performing the
higher order Gitman-Lyakhovich-Tyutin [$GLT$] framework and compare the results
of both formalisms. | Burgers Equation vs. Large $N$ Limit in $T\bar{T}$-deformed $O(N)$
Vector Model: We study a $T\bar{T}$-deformed $O(N)$ vector model, which is classically
equivalent to the Nambu-Goto action with static gauge. The thermal free energy
density can be computed exactly by using the Burgers equation as a special
property of $T\bar{T}$-deformation. The resulting expression is valid for an
arbitrary value of $N$. One may consider a large $N$ limit while preserving
this expression. We try to derive this result in the field-theoretical approach
directly by employing the large $N$ limit. As a result, the leading
contribution coincides with the exact one. That is, the $1/N$ corrections are
cancelled out through a non-trivial mechanism. |
A Large Class of New Gravitational and Axionic Backgrounds for
Four-Dimensional Superstrings: A large class of new 4-D superstring vacua with non-trivial/singular
geometries, spacetime supersymmetry and other background fields (axion,
dilaton) are found. Killing symmetries are generic and are associated with
non-trivial dilaton and antisymmetric tensor fields. Duality symmetries
preserving N=2 superconformal invariance are employed to generate a large class
of explicit metrics for non-compact 4-D Calabi-Yau manifolds with Killing
symmetries. | Double Field Theory and Membrane Sigma-Models: We investigate geometric aspects of double field theory (DFT) and its
formulation as a doubled membrane sigma-model. Starting from the standard
Courant algebroid over the phase space of an open membrane, we determine a
splitting and a projection to a subbundle that sends the Courant algebroid
operations to the corresponding operations in DFT. This describes precisely how
the geometric structure of DFT lies in between two Courant algebroids and is
reconciled with generalized geometry. We construct the membrane sigma-model
that corresponds to DFT, and demonstrate how the standard T-duality orbit of
geometric and non-geometric flux backgrounds is captured by its action
functional in a unified way. This also clarifies the appearence of
noncommutative and nonassociative deformations of geometry in non-geometric
closed string theory. Gauge invariance of the DFT membrane sigma-model is
compatible with the flux formulation of DFT and its strong constraint, whose
geometric origin is explained. Our approach leads to a new generalization of a
Courant algebroid, that we call a DFT algebroid and relate to other known
generalizations, such as pre-Courant algebroids and symplectic nearly Lie
2-algebroids. We also describe the construction of a gauge-invariant doubled
membrane sigma-model that does not require imposing the strong constraint. |
One-loop corrections to the D3 brane action: We calculate one-loop corrections to the effective Lagrangian for the D3
brane. We perform the gauge-fixing of the kappa-symmetric Born-Infeld D3 brane
action in the flat background using Killing gauge. The linearized supersymmetry
of the gauge-fixed action coincides with that of the N=4 Yang-Mills theory. We
use the helicity amplitude and unitarity technique to calculate the one-loop
amplitudes at order alpha^4. The counterterms and the finite 1-loop corrections
are of the form (dF)^4 and their supersymmetric generalization. This is to be
contrasted with the Born-Infeld action which contains (F)^4 and other terms
which do not depend on derivatives of the vector field strength. | Bosonized Formulation of Lattice QCD: Problems in lattice gauge models with fermions are discussed. A new bosonic
Hermitean effective action for lattice QCD with dynamical quarks is presented.
In distinction of the previous version, it does not include constraints and is
better suited for Monte-Carlo simulations. |
Spacetime topology from holographic entanglement: An asymptotically AdS geometry connecting two or more boundaries is given by
a entangled state, that can be expanded in the product basis of the Hilbert
spaces of each CFT living on the boundaries. We derive a prescription to
compute this expansion for states describing spacetimes with general spatial
topology in arbitrary dimension. To large N, the expansion coincides with the
Schmidt decomposition and the coefficients are given by $n$-point correlation
functions on a particular Euclidean geometry.
We show that this applies to all spacetime that admits a Hartle-Hawking type
of wave functional, which via a standard hypothesis on the spatial topology,
can be (one to one) mapped to CFT states defined on the asymptotic boundary. It
is also observed that these states are endowed with quantum coherence
properties.
Applying this as holographic engineering, one can to construct an emergent
space geometry with certain predetermined topology by preparing an entangled
state of the dual quantum system. As an example, we apply the method to
calculate the expansion and characterize a spacetime whose initial spatial
topology is a (genus one) handlebody. | Exact Resurgent Trans-series and Multi-Bion Contributions to All Orders: The full resurgent trans-series is found exactly in near-supersymmetric
$\mathbb C P^1$ quantum mechanics. By expanding in powers of the SUSY breaking
deformation parameter, we obtain the first and second expansion coefficients of
the ground state energy. They are absolutely convergent series of
nonperturbative exponentials corresponding to multi-bions with perturbation
series on those background. We obtain all multi-bion exact solutions for finite
time interval in the complexified theory. We sum the classical multi-bion
contributions that reproduce the exact result supporting the resurgence to all
orders. This is the first result in the quantum mechanical model where the
resurgent trans-series structure is verified to all orders in nonperturbative
multi-bion contributions. |
Interpolating gauge fixing for Chern-Simons theory: Chern-Simons theory is analyzed with a gauge-fixing which allows to discuss
the Landau gauge and the light-cone gauge at the same time. | Matter fields with c > 1 coupled to 2d gravity: We solve a class of branched polymer models coupled to spin systems and show
that they have no phase transition and are either always magnetized or never
magnetized depending on the branching weights. By comparing these results with
numerical simulations of two-dimensional quantum gravity coupled to matter
fields with central charge $c$ we provide evidence that for $c$ sufficiently
large ($c\geq 12$) these models are effectively described by branched polymers.
Moreover, the numerical results indicate a remarkable universality in the
influence on the geometry of surfaces due to the interaction with matter. For
spin systems this influence only depends on the total central charge. |
Instanton Bound States in ABJM Theory: The partition function of the ABJM theory receives non-perturbative
corrections due to instanton effects. We study these non-perturbative
corrections, including bound states of worldsheet instantons and membrane
instantons, in the Fermi-gas approach. We require that the total
non-perturbative correction should be always finite for arbitrary Chern-Simons
level. This finiteness is realized quite non-trivially because each bound state
contribution naively diverges at some levels. The poles of each contribution
should be canceled out in total. We use this pole cancellation mechanism to
find unknown bound state corrections from known ones. We conjecture a general
expression of the bound state contribution. Summing up all the bound state
contributions, we find that the effect of bound states is simply incorporated
into the worldsheet instanton correction by a redefinition of the chemical
potential in the Fermi-gas system. Analytic expressions of the 3- and
4-membrane instanton corrections are also proposed. | QCD String as an Effective String: There are two cases where QCD string is described by an effective theory of
long strings: the static potential and meson scattering amplitudes in the Regge
regime. I show how the former can be solved in the mean-field approximation,
justified by the large number of space-time dimensions, and argue that it turns
out to be exact for the Nambu--Goto string. By adding extrinsic curvature I
demonstrate how the tachyonic instability of the ground-state energy can be
cured by operators less relevant in the infrared. |
Information metric, Berry connection and Berezin-Toeplitz quantization
for matrix geometry: We consider the information metric and Berry connection in the context of
noncommutative matrix geometry. We propose that these objects give a new method
of characterizing the fuzzy geometry of matrices. We first give formal
definitions of these geometric objects and then explicitly calculate them for
the well-known matrix configurations of fuzzy $S^2$ and fuzzy $S^4$. We find
that the information metrics are given by the usual round metrics for both
examples, while the Berry connections coincide with the configurations of the
Wu-Yang monopole and the Yang monopole for fuzzy $S^2$ and fuzzy $S^4$,
respectively. Then, we demonstrate that the matrix configurations of fuzzy
$S^n$ $(n=2,4)$ can be understood as images of the embedding functions
$S^n\rightarrow \textbf{R}^{n+1}$ under the Berezin-Toeplitz quantization map.
Based on this result, we also obtain a mapping rule for the Laplacian on fuzzy
$S^4$. | The stress energy tensor of neutral blackfold and dual theory: In this paper we consider charged and neutral blackfold and extract the
Brown-York stress energy tensor. Also, we show that the neutral blackfold
spacetime is Ricci- flat and the other spacetime is not. This Ricci-flat
condition gives us opportunity to calculate the AAdS spacetime. In order to
have dual theory one can consider the AAdS in Fefferman- Graham coordinates.
This frame gives correct form of stress tensor in the boundary. The
corresponding tensor with using this frame will be traceless and conserved.
Such stress tensor is same as perfect fluid and it proves the dual renormalized
theory exists for the neutral blackfold . |
$AdS_{5}$ black hole at N=2 supergravity: In this paper, we consider the charged non-extremal black hole at five
dimensional N = 2 supergravity. We study thermodynamics of AdS_{5} black hole
with three equal charges (q_{1} = q_{2} = q_{3} = q). We obtain Schrodinger
like equation and discuss the effective potential. Then, we consider the case
of the perturbed dilaton field background and find presence of odd coefficients
of the wave function. Also we find that the higher derivative corrections have
no effect on the first and second even coefficients of the wave function. | Particle physics models of inflation: Inflation models are compared with observation on the assumption that the
curvature perturbation is generated from the vacuum fluctuation of the inflaton
field. The focus is on single-field models with canonical kinetic terms,
classified as small- medium- and large-field according to the variation of the
inflaton field while cosmological scales leave the horizon. Small-field models
are constructed according to the usual paradigm for beyond Standard Model
physics |
On Functional and Holographic Renormalization Group Methods in
Stochastic Theory of Turbulence: A nonlocal quantum-field model is constructed for the system of hydrodynamic
equations for incompressible viscous fluid (the stochastic Navier--Stokes (NS)
equation and the continuity equation). This model is studied by the following
two mutually parallel methods: the Wilson--Polchinski functional
renormalization group method (FRG), which is based on the exact functional
equation for the generating functional of amputated connected Green's functions
(ACGF), and the Heemskerk--Polchinski holographic renormalization group method
(HRG), which is based on the functional Hamilton--Jacobi (HJ) equation for the
holographic boundary action. Both functional equations are equivalent to
infinite hierarchies of integro-differential equations (coupled in the FRG
case) for the corresponding families of Green's functions (GF). The RG-flow
equations can be derived explicitly for two-particle functions. Because the
HRG-flow equation is closed (contains only a two-particle GF), the explicit
analytic solutions are obtained for the two-particle GF (in terms of the
modified Bessel functions $I$ and $K$) in the framework of the minimal
holographic model and its simple generalization, and these solutions have a
remarkable property of minimal dependence on the details of the random force
correlator (the function of the energy pumping into the system). The
restrictions due to the time-gauged Galilean symmetry present in this theory,
the problem of choosing the pumping function, and some generalizations of the
standard RG-flow procedures are discussed in detail. Finally, the question of
whether the HRG-solutions can be used to solve the FRG-flow equation for the
two-particle GF (in particular, the relationship between the regulators in the
two methods) is studied. | Compactified extra dimension and entanglement island as clues to quantum
gravity: We show that the compactified extra dimension and the emergence of the island
can provide clues about quantum gravity because their combination can solve the
deepest puzzles of black hole physics. Suppose that the time dimension and the
extra dimension compactified on a circle are symmetric under \emph{double Wick
rotation}, the curvature singularity would be removed due to the end of
spacetime as a smooth bubble hidden behind the event horizon. The smooth bubble
geometries can also be interpreted as microstates leading to the
Bekenstein-Hawking entropy because the smooth bubble geometries live in the
same region of mass and charge as the black string. In addition, by applying
the quantum extremal surface prescription, we show the emergence of the island
at late times of the black string evaporation where it is located slightly
outside the event horizon. Due to the dominant contribution of the island
configuration, the entanglement entropy of the radiation grows no longer
linearly in time but it reaches a finite value that is twice the
Bekenstein-Hawking entropy at the leading order. This transition shows the
information preservation during the black string evaporation. Furthermore, we
calculate the Page time which determines the moment of the transition between
the linearly growing and constant behaviors of the entanglement entropy as well
as the scrambling time corresponding to the information recovery time of the
signal falling into the black string. |
The vacuum backreaction on a pair creating source: Solution is presented to the simplest problem about the vacuum backreaction
on a pair creating source. The backreaction effect is nonanalytic in the
coupling constant and restores completely the energy conservation law. The
vacuum changes the kinematics of motion like relativity theory does and imposes
a new upper bound on the velocity of the source. | Introduction to M(atrix) theory and noncommutative geometry: Noncommutative geometry is based on an idea that an associative algebra can
be regarded as "an algebra of functions on a noncommutative space". The major
contribution to noncommutative geometry was made by A. Connes, who, in
particular, analyzed Yang-Mills theories on noncommutative spaces, using
important notions that were introduced in his papers (connection, Chern
character, etc). It was found recently that Yang-Mills theories on
noncommutative spaces appear naturally in string/M-theory; the notions and
results of noncommutative geometry were applied very successfully to the
problems of physics.
In this paper we give a mostly self-contained review of some aspects of
M(atrix) theory, of Connes' noncommutative geometry and of applications of
noncommutative geometry to M(atrix) theory. The topics include introduction to
BFSS and IKKT matrix models, compactifications on noncommutative tori, a review
of basic notions of noncommutative geometry with a detailed discussion of
noncommutative tori, Morita equivalence and $SO(d,d|{\mathbb Z})$-duality, an
elementary discussion of instantons and noncommutative orbifolds. The review is
primarily intended for physicists who would like to learn some basic techniques
of noncommutative geometry and how they can be applied in string theory and to
mathematicians who would like to learn about some new problems arising in
theoretical physics. |
Four-dimensional Traversable Wormholes and Bouncing Cosmologies in
Vacuum: In this letter we point out the existence of solutions to General Relativity
with a negative cosmological constant in four dimensions, which contain
solitons as well as traversable wormholes. The latter connect two
asymptotically locally AdS$_{4}$ spacetimes. At every constant value of the
radial coordinate the spacetime is a spacelike warped AdS$_{3}$. We compute the
dual energy momentum tensor at each boundary showing that it yields different
results. We also show that these vacuum wormholes can have more than one throat
and that they are indeed traversable by computing the time it takes for a light
signal to go from one boundary to the other, as seen by a geodesic observer. We
generalize the wormholes to include rotation and charge. When the cosmological
constant is positive we find a cosmology that is everywhere regular, has either
one or two bounces and that for late and early times matches the
Friedmann-Lema\^{\i}tre-Robertson-Walker metric with spherical topology. | Effect of quantum deformed black hole on BH shadow in two-dimensional
Dilaton gravity: In recent years, the study of quantum effects near the event horizon of black
hole (BH) has attracted extensive attention. It has become one of the important
methods to explore BH quantum properties by using the related properties of the
quantum deformed black hole. In this work, we study the effect of quantum
deformed black hole on BH shadow in two-dimensional Dilaton gravity. In this
model, quantum effects are reflected on the quantum correction parameter m. By
calculation, we find that: (1) the shape of the shadow boundary of a rotating
black hole is determined by the BH spin $a$, the quantum correction parameter
$m$ and the BH type parameter $n$; (2) when the spin $a=0$, the shape of the BH
shadow is a perfect circle; when $a\neq 0$, the shape is distorted; if the
quantum correction parameter $m=0$, their shapes reduce to the cases of
Schwarzschild BH and Kerr BH respectively; (3) the degree of distortion of the
BH shadow is different for various quantum correction parameters $m$; with the
increase of the values of $m$, the shadow will become more and more obvious;
(4) the results of different BH type parameter $n$ differ greatly. Since the
value of $m$ in actual physics should be very small, the current observations
of EHT cannot distinguish quantum effect from BH shadow, and can only constrain
the upper limit of $m$. In future BH shadow measurements, it will be possible
to distinguish quantum deformed black holes, which will help to better
understand the quantum effects of BHs. |
A near-NHEK/CFT correspondence: We consider excitations around the recently introduced near-NHEK metric
describing the near-horizon geometry of the near-extremal four-dimensional Kerr
black hole. This geometry has a U(1)_L x U(1)_R isometry group which can be
enhanced to a pair of commuting Virasoro algebras. We present boundary
conditions for which the conserved charges of the corresponding asymptotic
symmetries are well defined and non-vanishing and find the central charges
c_L=12J/hbar and c_R=0 where J is the angular momentum of the black hole.
Applying the Cardy formula reproduces the Bekenstein-Hawking entropy of the
black hole. This suggests that the near-extremal Kerr black hole is
holographically dual to a non-chiral two-dimensional conformal field theory. | Flux-vacua in Two Dimensional String Theory: We analyze the two dimensional type 0 theory with background RR-fluxes. Both
the 0A and the 0B theory have two distinct fluxes $q$ and $\tilde q$. We study
these two theories at finite temperature (compactified on a Euclidean circle of
radius $R$) as a function of the fluxes, the tachyon condensate $\mu$ and the
radius $R$. Surprisingly, the dependence on $q$, $\tilde q$ and $\mu$ is rather
simple. The partition function is the absolute value square of a holomorphic
function of $y=|q|+|\tilde q| + i \sqrt{2\alpha'} \mu$ (up to a simple but
interesting correction). As expected, the 0A and the 0B answers are related by
T-duality. Our answers are derived using the exact matrix models description of
these systems and are interpreted in the low energy spacetime Lagrangian. |
D-Branes on the Null-Brane: We study D-branes in the null-brane background. Using the covariant formalism
of the worldsheet theory, we construct the boundary states describing D-branes
on the null-brane. From the cylinder amplitudes, we find that the D-branes with
codimension zero or two have time-dependent effective tensions. | Weighted power counting and Lorentz violating gauge theories. II:
Classification: We classify the local, polynomial, unitary gauge theories that violate
Lorentz symmetry explicitly at high energies and are renormalizable by weighted
power counting. We study the structure of such theories and prove that
renormalization does not generate higher time derivatives. We work out the
conditions to renormalize vertices that are usually non-renormalizable, such as
the two scalar-two fermion interactions and the four fermion interactions. A
number of four dimensional examples are presented. |
Exotic Branes in Exceptional Field Theory: $E_{7(7)}$ and Beyond: In recent years, it has been widely argued that the duality transformations
of string and M-theory naturally imply the existence of so-called `exotic
branes'---low codimension objects with highly non-perturbative tensions,
scaling as $g_s^{\alpha}$ for $\alpha \leq -3$. We argue that their intimate
link with these duality transformations make them an ideal object of study
using the general framework of Double Field Theory (DFT) and Exceptional Field
Theory (EFT)---collectively referred to as ExFT. Parallel to the theme of
dualities, we also stress that these theories unify known solutions in string-
and M-theory into a single solution under ExFT. We argue that not only is there
a natural unifying description of the lowest codimension objects, many of these
exotic states require this formalism as a consistent supergravity description
does not exist. | Future Foam: We study pocket universes which have zero cosmological constant and
non-trivial boundary topology. These arise from bubble collisions in eternal
inflation. Using a simplified dust model of collisions we find that boundaries
of any genus can occur. Using a radiation shell model we perform analytic
studies in the thin wall limit to show the existence of geometries with a
single toroidal boundary. We give plausibility arguments that higher genus
boundaries can also occur. In geometries with one boundary of any genus a
timelike observer can see the entire boundary. Geometries with multiple
disconnected boundaries can also occur. In the spherical case with two
boundaries the boundaries are separated by a horizon. Our results suggest that
the holographic dual description for eternal inflation, proposed by Freivogel,
Sekino, Susskind and Yeh, should include summation over the genus of the base
space of the dual conformal field theory. We point out peculiarities of this
genus expansion compared to the string perturbation series. |
Einstein-Born-Infeld-dilaton black holes in non-asymptotically flat
spacetimes: We derive exact magnetically charged, static and spherically symmetric black
hole solutions of the four-dimensional Einstein-Born-Infeld-dilaton gravity.
These solutions are neither asymptotically flat nor (anti)-de Sitter. The
properties of the solutions are discussed. It is shown that the black holes are
stable against linear radial perturbations. | Reentrant phase transitions of quantum black holes: We show backreaction of quantum fields on black hole geometries can trigger
new thermal phase transitions. Specifically, we study the phase behavior of the
three-dimensional quantum-corrected static BTZ black hole, an exact solution to
specific semi-classical gravitational equations due to quantum conformal
matter, discovered through braneworld holography. Focusing on the canonical
ensemble, for large backreaction, we find novel reentrant phase transitions as
the temperature monotonically increases, namely, from thermal anti-de Sitter
space to the black hole and back to thermal anti-de Sitter. The former phase
transition is first-order, a quantum analog of the classical Hawking-Page phase
transition, while the latter is zeroth-order and has no classical counterpart. |
Quintessence from higher curvature supergravity: In this contribution we revisit higher curvature N=1 supergravity and discuss
the quintessence phase that can appear due to the $R^4$ terms. In particular we
focus on the bosonic supersymmetric completion within the old-minimal and the
new-minimal formulations. | Non-extremal, $α'$-corrected black holes in 5-dimensional Heterotic
Superstring Theory: We compute the first-order $\alpha'$ corrections of the non-extremal
Strominger-Vafa black hole and its non-supersymmetric counterparts in the
framework of the Bergshoeff-de Roo formulation of the heterotic superstring
effective action. The solution passes several tests: its extremal limit is the
one found in an earlier publication and the effect of a T duality
transformation on it is another solution of the same form with T dual charges.
We compute the Hawking temperature and Wald entropy showing that they are
related by the first law and Smarr formula. On the other hand, these two
contain additional terms in which the dimensionful parameter $\alpha'$ plays
the role of thermodynamical variable. |
Gauge fields and quantum entanglement: The purpose of this letter is to explore the relation between gauge fields,
which are at the base of our understanding of fundamental interactions, and the
quantum entanglement. To this end, we investigate the case of ${\rm SU}(2)$
gauge fields. It is first argued that holonomies of the ${\rm SU}(2)$ gauge
fields are naturally associated with maximally entangled two-particle states.
Then, we provide some evidence that the notion of such gauge fields can be
deduced from the transformation properties of maximally entangled two-particle
states. This new insight unveils a possible relation between gauge fields and
spin systems, as well as contributes to understanding of the relation between
tensor networks (such as MERA) and spin network states considered in loop
quantum gravity. In consequence, our results turn out to be relevant in the
context of the emerging Entanglement/Gravity duality. | Gyros as geometry of the standard model: We investigate the (noncommutative) geometry defined by the standard model,
which turns out to be of Kaluza-Klein type. We find that spacetime points are
replaced by extended two-dimensional objects which resemble the surface of a
gyro. Their size is of the order of the inverse top quark mass. |
Boundary Stress-Energy Tensor and Newton-Cartan Geometry in Lifshitz
Holography: For a specific action supporting z=2 Lifshitz geometries we identify the
Lifshitz UV completion by solving for the most general solution near the
Lifshitz boundary. We identify all the sources as leading components of bulk
fields which requires a vielbein formalism. This includes two linear
combinations of the bulk gauge field and timelike vielbein where one asymptotes
to the boundary timelike vielbein and the other to the boundary gauge field.
The geometry induced from the bulk onto the boundary is a novel extension of
Newton-Cartan geometry that we call torsional Newton-Cartan (TNC) geometry.
There is a constraint on the sources but its pairing with a Ward identity
allows one to reduce the variation of the on-shell action to unconstrained
sources. We compute all the vevs along with their Ward identities and derive
conditions for the boundary theory to admit conserved currents obtained by
contracting the boundary stress-energy tensor with a TNC analogue of a
conformal Killing vector. We also obtain the anisotropic Weyl anomaly that
takes the form of a Horava-Lifshitz action defined on a TNC geometry. The
Fefferman-Graham expansion contains a free function that does not appear in the
variation of the on-shell action. We show that this is related to an irrelevant
deformation that selects between two different UV completions. | One-loop analysis with nonlocal boundary conditions: In the eighties, Schroder studied a quantum mechanical model where the
stationary states of Schrodinger's equation obey nonlocal boundary conditions
on a circle in the plane. For such a problem, we perform a detailed one-loop
calculation for three choices of the kernel characterizing the nonlocal
boundary conditions. In such cases, the zeta(0) value is found to coincide with
the one resulting from Robin boundary conditions. The detailed technique here
developed may be useful for studying one-loop properties of quantum field
theory and quantum gravity if nonlocal boundary conditions are imposed. |
Non-Abelian Aharonov-Bohm Scattering of Spin 1/2 Particles: We study the low energy regime of the scattering of two fermionic particles
carrying isospin 1/2 and interacting through a non-Abelian Chern-Simons field.
We calculate the one-loop scattering amplitude for both the nonrelativistic and
also for the relativistic theory. In the relativistic case we introduce an
intermediate cutoff, separating the regions with low and high loop momenta
integration. In this procedure purely relativistic field theory effects as the
vacuum polarization and anomalous magnetic moment corrections are automatically
incorporated. | Perturbative Construction of Stationary Randall-Sundrum II Black Holes
on a 5-Brane: We numerically construct large Randall-Sundrum II brane black holes in 4 and
5 dimensions from associated AdS/CFT spacetimes. Our solutions are leading
order perturbations of a representative of the boundary conformal structure of
the AdS spacetime sourced by the dual CFT stress tensor. The 4-dimensional
solutions are static perturbations of the Euclidean Schwarzschild metric, while
the 5-dimensional solutions are perturbations of the Myers-Perry metric with
equal angular momenta. We compare the former with previous numerical results
for Randall-Sundrum bulk black holes and find good agreement down to a horizon
radius of about rH ~30l. The latter are the first numerical results pertaining
to rotating Randall-Sundrum black holes. They have the same entropy, but a
larger horizon area than Myers-Perry black holes of the same mass and angular
momentum. |
Massive strings from a haunted field theory: In this work we present the $\alpha'$-exact background equations of motion of
the bosonic chiral string (also known as Hohm-Siegel-Zwiebach model), with the
spin two ghost fields integrated out. This is the first instance of a
worldsheet model in which all corrections are fully determined in a generic
curved spacetime. As a concrete cross-check, we find complete agreement between
all three-point and a sample of four-point tree level scattering amplitudes
computed using field theory methods and the chiral string prescription. These
equations of motion provide a field theoretical shortcut to compute worldsheet
correlators in conventional bosonic strings (with arbitrary number of massless
and mass level one states), and outline a new perspective on massive resonances
in string theory. | Finite Temperature Systems of Brane-Antibrane Pairs and Non-BPS D-branes: We investigate the thermodynamic properties of D-brane-anti-D-brane pairs and
non-BPS D-branes on the basis of boundary string field theory. We calculate the
finite temperature effective potential of N D-brane-anti-D-brane pairs in a
non-compact background and in a toroidal background. In the non-compact
background case, a phase transition occurs slightly below the Hagedorn
temperature, and the D9-anti-D9 pairs become stable. Moreover, the total energy
at the critical temperature is a decreasing function of N as long as the 't
Hooft coupling is very small. This leads to the conclusion that a large number
N of D9-anti-D9 pairs are created simultaneously near the Hagedorn temperature.
In the toroidal background case (M_{1,9-D} * T_{D}), a phase transition occurs
only if the Dp-anti-Dp pair is extended in all the non-compact directions, as
long as the 't Hooft coupling is very small. The total energy at the critical
temperature also decreases as N increases. We also calculate the finite
temperature effective potential of non-BPS D-branes, and we obtain similar
results. Then, we consider the thermodynamic balance between open strings on
these branes and closed strings in the bulk in the ideal gas approximation, and
conclude that the total energy is dominated by the open strings. |
Liouville's Imaginary Shadow: N=1 super Liouville field theory is one of the simplest non-rational
conformal field theories. It possesses various important extensions and
interesting applications, e.g. to the AGT relation with 4D gauge theory or the
construction of the OSP(1|2) WZW model. In both setups, the N=1 Liouville field
is accompanied by an additional free fermion. Recently, Belavin et al.
suggested a bosonization of the product theory in terms of two bosonic
Liouville fields. While one of these Liouville fields is standard, the second
turns out to be imaginary (or time-like). We extend the proposal to the R
sector and perform extensive checks based on detailed comparison of 3-point
functions involving several super-conformal primaries and descendants. On the
basis of such strong evidence we sketch a number of interesting potential
applications of this intriguing bosonization. | One conjecture and two observations on de Sitter space: We propose that the state represented by the Nariai black hole inside de
Sitter space is the ground state of the de Sitter gravity, while the pure de
Sitter space is the maximal energy state. With this point of view, we
investigate thermodynamics of de Sitter space, we find that if there is a dual
field theory, this theory can not be a CFT in a fixed dimension. Near the
Nariai limit, we conjecture that the dual theory is effectively an 1+1 CFT
living on the radial segment connecting the cosmic horizon and the black hole
horizon. If we go beyond the de Sitter limit, the "imaginary" high temperature
phase can be described by a CFT with one dimension lower than the spacetime
dimension. Below the de Sitter limit, we are approaching a phase similar to the
Hagedorn phase in 2+1 dimensions, the latter is also a maximal energy phase if
we hold the volume fixed. |
Power corrections to symmetric point vertices in Gribov-Zwanziger theory: The 3-point vertices of QCD are examined at the symmetric subtraction point
at one loop in the Landau gauge in the presence of the Gribov mass, gamma. They
are expanded in powers of gamma^2 up to dimension four in order to determine
the order of the leading correction. As well as analysing the pure
Gribov-Zwanziger Lagrangian, its extensions to include localizing ghost masses
are also examined. For comparison a pure gluon mass term is also considered. | A Minimal Length from the Cutoff Modes in Asymptotically Safe Quantum
Gravity: Within asymptotically safe Quantum Einstein Gravity (QEG), the quantum
4-sphere is discussed as a specific example of a fractal spacetime manifold.
The relation between the infrared cutoff built into the effective average
action and the corresponding coarse graining scale is investigated. Analyzing
the properties of the pertinent cutoff modes, the possibility that QEG
generates a minimal length scale dynamically is explored. While there exists no
minimal proper length, the QEG sphere appears to be "fuzzy" in the sense that
there is a minimal angular separation below which two points cannot be resolved
by the cutoff modes. |
A Capped Black Hole in Five Dimensions: We present the first non-BPS exact solution of an asymptotically flat,
stationary spherical black hole having domain of outer communication with
nontrivial topology in five-dimensional minimal supergravity. It describes a
charged rotating black hole capped by a disc-shaped bubble. The existence of
the ``capped black hole'' shows the non-uniqueness of spherical black holes. | On-shell actions with lightlike boundary data: We argue that finite-region observables in quantum gravity are best
approached in terms of boundary data on null hypersurfaces. This has
far-reaching effects on the basic notions of classical and quantum mechanics,
such as Hamiltonians and canonical conjugates. Such radical properties are not
unexpected in finite-region quantum gravity. We are thus motivated to
reformulate field theory in terms of null boundary data. As a starting point,
we consider the on-shell action functional for classical field theory in finite
null-bounded regions. Closed-form results are obtained for free scalars and for
Maxwell fields. The action of classical gravity is also discussed, to the
extent possible without solving the field equations. These action functionals
exhibit non-locality and, in special cases, a "holographic" reduction of the
degrees of freedom. Also, they cannot be used to define global charges. Whereas
for ordinary field theory these are just artifacts of a restrictive formalism,
in quantum gravity they are expected to be genuine features. This further
supports a connection between quantum gravity and null-boundary observables. In
our treatment of the GR action, we identify a universal imaginary term that
reproduces the Bekenstein entropy formula. |
One-loop mass shift formula for kinks and self-dual vortices: A formula is derived that allows us to compute one-loop mass shifts for kinks
and self-dual Abrikosov-Nielsen-Olesen vortices. The procedure is based in
canonical quantization and heat kernel/zeta function regularization methods. | Evidence of fractal structures in hadrons: This study focuses on the presence of (multi)fractal structures in confined
hadronic matter through the momentum distributions of mesons produced in
proton-proton collisions between 23 GeV and 63 GeV. The analysis demonstrates
that the $q$-exponential behaviour of the particle momentum distributions is
consistent with fractal characteristics, exhibiting fractal structures in
confined hadronic matter with features similar to those observed in the
deconfined quark-gluon plasma (QGP) regime. Furthermore, the systematic
analysis of meson production in hadronic collisions at energies below 1 TeV
suggests that specific fractal parameters are universal, independently of
confinement or deconfinement, while others may be influenced by the quark
content of the produced meson. These results pave the way for further research
exploring the implications of fractal structures on various physical
distributions and offer insights into the nature of the phase transition
between confined and deconfined regimes. |
Quantum Hall Droplets on Disc and Effective Wess-Zumino-Witten Action
for Edge States: We algebraically analysis the quantum Hall effect of a system of particles
living on the disc ${\bf B}^1$ in the presence of an uniform magnetic field
$B$. For this, we identify the non-compact disc with the coset space
$SU(1,1)/U(1)$. This allows us to use the geometric quantization in order to
get the wavefunctions as the Wigner ${\cal D}$-functions satisfying a suitable
constraint. We show that the corresponding Hamiltonian coincides with the Maass
Laplacian. Restricting to the lowest Landau level, we introduce the
noncommutative geometry through the star product. Also we discuss the state
density behavior as well as the excitation potential of the quantum Hall
droplet. We show that the edge excitations are described by an effective
Wess-Zumino-Witten action for a strong magnetic field and discuss their nature.
We finally show that
LLL wavefunctions are intelligent states. | Consistent, covariant and multiplicative anomalies: It is shown that the multiplicative anomaly in the vector-axial-vector model,
which apparently has nothing to do with the breaking of classical current
symmetries, nevertheless is strictly related to the well known consistent and
covariant anomalies. |
Scalar two-point functions at the late-time boundary of de Sitter: We calculate two-point functions of scalar fields of mass $m$ and their
conjugate momenta at the late-time boundary of de Sitter with Bunch-Davies
boundary conditions, in general $d+1$ spacetime dimensions. We perform the
calculation using the wavefunction picture and using canonical quantization.
With the latter one clearly sees how the late-time field and conjugate momentum
operators are linear combinations of the normalized late-time operators
$\alphaN$ and $\betaN$ that correspond to unitary irreducible representations
of the de Sitter group with well-defined inner products. The two-point
functions resulting from these two different methods are equal and we find that
both the autocorrelations of $\alphaN$ and $\betaN$ and their cross
correlations contribute to the late-time field and conjugate momentum two-point
functions. This happens both for light scalars ($m<\frac{d}{2}H$),
corresponding to complementary series representations, and heavy scalars
($m>\frac{d}{2}H$), corresponding to principal series representations of the de
Sitter group, where $H$ is the Hubble scale of de Sitter. In the special case
$m=0$, only the $\betaN$ autocorrelation contributes to the conjugate momentum
two-point function in any dimensions and we gather hints that suggest $\alphaN$
to correspond to discrete series representations for this case at $d=3$. | Higher-spin realization of a dS static patch/cut-off CFT correspondence: We derive a holographic relation for the dS static patch with the dual field
theory defined on the observer horizon. The starting point is the duality of
higher-spin theory on AdS_4 and the O(N) vector model. We build on a similar
analytic continuation as used recently to obtain a realization of dS/CFT, and
adapt it to the static patch. The resulting duality relates higher-spin theory
on the dS_4 static patch to a cut-off CFT on the cylinder RxS^2. The
construction permits a derivation of the finite thermodynamic entropy
associated to the horizon of the static patch from the dual field theory. As a
further brick we recover the spectrum of quasinormal frequencies from the
correlation functions of the boundary theory. In the last part we incorporate
the dS/dS correspondence as an independent proposal for holography on dS and
show that a concrete realization can be obtained by similar reasoning. |
Systematics of string loop threshold corrections in orbifold models: String theory one-loop threshold corrections are studied in a background
field approach due to Kiritsis and Kounnas which uses space-time curvature as
an infrared regulator. We review the conformal field theory aspects using the
semiwormhole space-time solution. The comparison of string and effective field
theories vacuum functionals is made for the low derivative order, as well as
for certain higher-derivative, gauge and gravitational interactions. We study
the dependence on the infrared cut-off. Numerical applications are considered
for a sample of four-dimensional abelian orbifold models. The implications on
the perturbative string theory unification are examined. We present numerical
results for the gauge interactions coupling constants as well as for the
quadratic order gravitational ($R^2$) and the quartic order gauge ($F^4$)
interactions. | Deep Inelastic Scattering on an Extremal RN-AdS Black Hole: We consider deep inelastic scattering (DIS) on a large nucleus described as
an extremal RN-AdS black hole using the holographic principle. Using the
R-current correlators we determine the structure functions as a function
Bjorken-x, and map it on a finite but large nucleus with fixed atomic number.
The R-ratio of the nuclear structure functions exhibit strong shadowing at
low-x. |
Tackling Feynman integrals with quantum minimization algorithms: One of the most severe bottlenecks to reach high-precision predictions in QFT
is the calculation of multiloop multileg Feynman integrals. Several new
strategies have been proposed in the last years, allowing impressive results
with deep implications in particle physics. Still, the efficiency of such
techniques starts to drastically decrease when including many loops and legs.
In this talk, we explore the implementation of quantum algorithms to optimize
the integrands of scattering amplitudes. We rely on the manifestly causal
loop-tree duality, which translates the loop into phase-space integrals and
avoids the spurious singularities due to non-causal effects. Then, we built a
Hamiltonian codifying causal-compatible contributions and minimize it using a
Variational Quantum Eigensolver. Our very promising results point towards a
potential speed-up for achieving a more numerically-stable representation of
Feynman integrals by using quantum computers. | Interacting Wess-Zumino-Novikov-Witten Models: We study the system of two WZNW models coupled to each other via the
current-current interaction. The system is proven to possess the strong/weak
coupling duality symmetry. The strong coupling phase of this theory is
discussed in detail. It is shown that in this phase the interacting WZNW models
approach non-trivial conformal points along the renormalization group flow. The
relation between the principal chiral model and interacting WZNW models is
investigated. |
Predictive Landscapes and New Physics at a TeV: We propose that the Standard Model is coupled to a sector with an enormous
landscape of vacua, where only the dimensionful parameters--the vacuum energy
and Higgs masses--are finely "scanned" from one vacuum to another, while
dimensionless couplings are effectively fixed. This allows us to preserve
achievements of the usual unique-vacuum approach in relating dimensionless
couplings while also accounting for the success of the anthropic approach to
the cosmological constant problem. It can also explain the proximity of the
weak scale to the geometric mean of the Planck and vacuum energy scales. We
realize this idea with field theory landscapes consisting of $N$ fields and
$2^N$ vacua, where the fractional variation of couplings is smaller than
$1/\sqrt{N}$. These lead to a variety of low-energy theories including the
Standard Model, the MSSM, and Split SUSY. This picture suggests sharp new rules
for model-building, providing the first framework in which to simultaneously
address the cosmological constant problem together with the big and little
hierarchy problems. Requiring the existence of atoms can fix ratio of the QCD
scale to the weak scale, thereby providing a possible solution to the hierarchy
problem as well as related puzzles such as the $\mu$ and doublet-triplet
splitting problems. We also present new approaches to the hierarchy problem,
where the fine-tuning of the Higgs mass to exponentially small scales is
understood by even more basic environmental requirements such as vacuum
stability and the existence of baryons. These theories predict new physics at
the TeV scale, including a dark matter candidate. The simplest theory has
weak-scale "Higgsinos" as the only new particles charged under the Standard
Model, with gauge coupling unification near $10^{14}$ GeV. | Baxter's Q-operators for supersymmetric spin chains: We develop Yang-Baxter integrability structures connected with the quantum
affine superalgebra Uq(\hat sl(2|1)). Baxter's Q-operators are explicitly
constructed as supertraces of certain monodromy matrices associated with
(q-deformed) bosonic and fermionic oscillator algebras. There are six different
Q-operators in this case, obeying a few fundamental fusion relations, which
imply all functional relations between various commuting transfer matrices. The
results are universal in the sense that they do not depend on the quantum space
of states and apply both to lattice models and to continuous quantum field
theory models as well. |
Pistons modeled by potentials: In this article we consider a piston modelled by a potential in the presence
of extra dimensions. We analyze the functional determinant and the Casimir
effect for this configuration. In order to compute the determinant and Casimir
force we employ the zeta function scheme. Essentially, the computation reduces
to the analysis of the zeta function associated with a scalar field living on
an interval $[0,L]$ in a background potential. Although, as a model for a
piston, it seems reasonable to assume a potential having compact support within
$[0,L]$, we provide a formalism that can be applied to any sufficiently smooth
potential. | Higgs Mechanism and Symmetry Breaking without Redundant Variables: The Higgs mechanism is reconsidered in the canonical Weyl gauge formulation
of quantized gauge theories, using an approach in which redundant degrees of
freedom are eliminated. As a consequence, its symmetry aspects appear in a
different light. All the established physics consequences of the Higgs
mechanism are recovered without invoking gauge symmetry breaking. The occurence
of massless vector bosons in non-abelian Higgs models is interpreted as signal
of spontaneous breakdown of certain global symmetries. Characteristic
differences between the relevant ``displacement symmetries'' of QED and the
Georgi Glashow model are exhibited. Implications for the symmetry aspects of
the electroweak sector of the standard model and the interpretation of the
physical photon as Goldstone boson are pointed out. |
NJL and QCD from String Theory: We study a configuration of D-branes in string theory that is described at
low energies by a four-dimensional field theory with a dynamically broken
chiral symmetry. In a certain region of the parameter space of the brane
configuration the low-energy theory is a non-local generalization of the
Nambu-Jona-Lasinio (NJL) model. This vector model is exactly solvable at large
N_c and dynamically breaks chiral symmetry at arbitrarily weak 't Hooft
coupling. At strong coupling the dynamics is determined by the low-energy
theory on D-branes living in the near-horizon geometry of other branes. In a
different region of parameter space the brane construction gives rise to large
N_c QCD. Thus the D-brane system interpolates between NJL and QCD. | Fermion evaporation of a black hole off a tense brane: Using the WKBJ approximation we obtain numerical plots of the power emission
spectrum for the evaporation of massless bulk Dirac fermions from six
dimensional black holes off a tense 3-brane with codimension two. We also
present the multiplicity factors for eigenvalues of the deficit four sphere and
show that these reduce to the usual case in the tenseless limit. |
A Generalization of Gravity: I consider theories of gravity built not just from the metric and affine
connection, but also other (possibly higher rank) symmetric tensor(s). The
Lagrangian densities are scalars built from them, and the volume forms are
related to Cayley's hyperdeterminants. The resulting diff-invariant actions
give rise to geometric theories that go beyond the metric paradigm (even
metric-less theories are possible), and contain Einstein gravity as a special
case. Examples contain theories with generalizeations of Riemannian geometry.
The 0-tensor case is related to dilaton gravity. These theories can give rise
to new types of spontaneous Lorentz breaking and might be relevant for "dark"
sector cosmology. | D-particle bound states and the D-instanton measure: A connection is made between the Witten index of relevance to threshold bound
states of D-particles in the type IIA superstring theory and the measure that
enters D-instanton sums for processes dominated by single multiply-charged
D-instantons in the type IIB theory. |
Dual photons and gravitons: We review the status of electric/magnetic duality for free gauge field
theories in four space-time dimensions with emphasis on Maxwell theory and
linearized Einstein gravity. Using the theory of vector and tensor spherical
harmonics, we provide explicit construction of dual photons and gravitons by
decomposing the fields into axial and polar configurations with opposite parity
and interchanging the two sectors. When the theories are defined on AdS(4)
space-time there are boundary manifestations of the duality, which for the case
of gravity account for the energy-momentum/Cotton tensor duality (also known as
dual graviton correspondence). For AdS(4) black-hole backgrounds there is no
direct analogue of gravitational duality on the bulk, but there is still a
boundary duality for quasi-normal modes satisfying a selected set of boundary
conditions. Possible extensions of this framework and some open questions are
also briefly discussed. | Proof that Casimir force does not originate from vacuum energy: We present a simple general proof that Casimir force cannot originate from
the vacuum energy of electromagnetic (EM) field. The full QED Hamiltonian
consists of 3 terms: the pure electromagnetic term $H_{\rm em}$, the pure
matter term $H_{\rm matt}$ and the interaction term $H_{\rm int}$. The $H_{\rm
em}$-term commutes with all matter fields because it does not have any explicit
dependence on matter fields. As a consequence, $H_{\rm em}$ cannot generate any
forces on matter. Since it is precisely this term that generates the vacuum
energy of EM field, it follows that the vacuum energy does not generate the
forces. The misleading statements in the literature that vacuum energy
generates Casimir force can be boiled down to the fact that $H_{\rm em}$
attains an implicit dependence on matter fields by the use of the equations of
motion and the illegitimate treatment of the implicit dependence as if it was
explicit. The true origin of the Casimir force is van der Waals force generated
by $H_{\rm int}$. |
Covariant anomalies and Hawking radiation from charged rotating black
strings in anti-de Sitter spacetimes: Motivated by the success of the recently proposed method of anomaly
cancellation to derive Hawking fluxes from black hole horizons of spacetimes in
various dimensions, we have further extended the covariant anomaly cancellation
method shortly simplified by Banerjee and Kulkarni to explore the Hawking
radiation of the (3+1)-dimensional charged rotating black strings and their
higher dimensional extensions in anti-de Sitter spacetimes, whose horizons are
not spherical but can be toroidal, cylindrical or planar, according to their
global identifications. It should be emphasized that our analysis presented
here is very general in the sense that the determinant of the reduced
(1+1)-dimensional effective metric from these black strings need not be equal
to one $(\sqrt{-g} \neq 1)$. Our results indicate that the gauge and energy
momentum fluxes needed to cancel the (1+1)-dimensional covariant gauge and
gravitational anomalies are compatible with the Hawking fluxes. Besides,
thermodynamics of these black strings are studied in the case of a variable
cosmological constant. | M theory, Joyce Orbifolds and Super Yang-Mills: We geometrically engineer d=4 N=1 supersymmetric Yang-Mills theories by
considering M theory on various Joyce orbifolds. We argue that the
superpotential of these models is generated by fractional membrane instantons.
The relation of this superpotential to membrane anomalies is also discussed. |
Scalar field scattering by a Lifshitz black hole under a non-minimal
coupling: We study the behavior of a scalar field under a z = 3 Lifshitz black hole
background, in a way that is non-minimally coupled to the gravitational field.
A general analytical solution is obtained along with two sets of quasinormal
modes associated to different boundary conditions that can be imposed on the
scalar field, non-minimal coupling parameter appears explicitly on these
solutions. Stability of quasinormal modes can be studied and ensured for both
cases. Also, the reflection and absorption coefficients are calculated, as well
as the absorption cross section which features an interesting behavior because
of being attenuated by terms strongly dependant on the non-minimal coupling. By
a suitable change of variables a soliton solution can also be obtained and the
stability of the quasinormal modes are studied and ensured. | Does Geometric Coupling Generates Resonances?: Geometrical coupling in a co-dimensional one Randall-Sundrum scenario (RS) is
used to study resonances of $p-$form fields. The resonances are calculated
using the transfer matrix method. The model studied consider the standard RS
with delta-like branes, and branes generated by kinks and domain-wall as well.
The parameters are changed to control the thickness of the smooth brane. With
this a very interesting pattern is found for the resonances. The geometrical
coupling does not generate resonances for the reduced $p-$form in all cases
considered. |
Massive higher spin fields in curved spacetime and necessity of
non-minimal couplings: Free massive higher spin fields in weak background gravitational fields are
discussed. Contrary to the spin one case, higher spin fields should have
nontrivial non-minimal couplings to the curvature. A precise analysis is given
for the spin 2 case, and it is shown that two conditions should be satisfied
among five non-minimal coupling constants, which we derive both in the
Hamiltonian and Lagrangian formalisms. It is checked that the linearized limit
of the massive gravity theory indeed has the non-minimal couplings that satisfy
the conditions. We also discuss the form of the non-minimal couplings for the
spin 3 case. | Quantum Codes, CFTs, and Defects: We give a general construction relating Narain rational conformal field
theories (RCFTs) and associated 3d Chern-Simons (CS) theories to quantum
stabilizer codes. Starting from an abelian CS theory with a fusion group
consisting of $n$ even-order factors, we map a boundary RCFT to an $n$-qubit
quantum code. When the relevant 't Hooft anomalies vanish, we can orbifold our
RCFTs and describe this gauging at the level of the code. Along the way, we
give CFT interpretations of the code subspace and the Hilbert space of qubits
while mapping error operations to CFT defect fields. |
On the Measure in Simplicial Gravity: Functional measures for lattice quantum gravity should agree with their
continuum counterparts in the weak field, low momentum limit. After showing
that the standard simplicial measure satisfies the above requirement, we prove
that a class of recently proposed non-local measures for lattice gravity do not
satisfy such a criterion, already to lowest order in the weak field expansion.
We argue therefore that the latter cannot represent acceptable discrete
functional measures for simplicial geometries. | Worldvolume Superalgebra Of BLG Theory With Nambu-Poisson Structure: Recently it was proposed that the Bagger-Lambert-Gustavsson theory with
Nambu-Poisson structure describes an M5-brane in a three-form flux background.
In this paper we investigate the superalgebra associated with this theory. We
derive the central charges corresponding to M5-brane solitons in 3-form
backgrounds. We also show that double dimensional reduction of the superalgebra
gives rise to the Poisson bracket terms of a non-commutative D4-brane
superalgebra. We provide interpretations of the D4-brane charges in terms of
spacetime intersections. |
Spontaneous Breakdown of the Lorentz Invariance: We re-examine three-dimensional gauge theory with a Chern-Simons term in
which the Lorentz invariance is spontaneously broken by dynamical generation of
a magnetic field. A non-vanishing magnetic field leads, through the
Nambu-Goldstone theorem, to the decrease of zero-point energies of photons,
which accounts for a major part of the mechanism. The asymmetric spectral flow
plays an important role. The instability in pure Chern-Simons theory is also
noted. | Thermodynamic properties of black holes in de Sitter space: We study the thermodynamic properties of Schwarzschild-de Sitter (SdS) black
hole and Reissner-Nordstr\"{o}m-de Sitter (RNdS) black hole in the view of
global and effective thermodynamic quantities. Making use of the effective
first law of thermodynamics, we can derive the effective thermodynamic
quantities of de Sitter black holes. It is found that these effective
thermodynamic quantities also satisfy Smarr-like formula. Especially, the
effective temperatures are nonzero in the Nariai limit, which is consistent
with the idea of Bousso and Hawking. By calculating heat capacity and Gibbs
free energy, we find SdS black hole is always thermodynamically stable and RNdS
black hole may undergoes phase transition at some points. |
Mirror dualities with four supercharges: We consider 3d N=2 non-abelian Hanany-Witten brane setups with chiral flavor
symmetry. We propose that the associated field theories are quivers with
improved bifundamentals, instead of standard bifundamentals. The improved
bifundamental is a strongly coupled SCFT that carries one more U(1) global
symmetry than the standard bifundamental. As a consequence, our proposal
overcomes the long standing challenge of associating to each N=2 brane setup a
gauge theory with the full rank global symmetry, allowing the study of all the
usual supersymmetric observables, such as superconformal index, sphere
partition function, chiral ring and moduli space. The construction passes many
non-trivial tests, for instance we algorithmically prove that any two improved
quivers associated to S-dual brane setups are infrared dual. The 3d N=2 mirror
dualities can be uplifted to 4d dualities with 4d improved bifundamentals
connecting USp(2N) nodes. | Deformed N=2 theories, generalized recursion relations and S-duality: We study the non-perturbative properties of N=2 super conformal field
theories in four dimensions using localization techniques. In particular we
consider SU(2) gauge theories, deformed by a generic epsilon-background, with
four fundamental flavors or with one adjoint hypermultiplet. In both cases we
explicitly compute the first few instanton corrections to the partition
function and the prepotential using Nekrasov's approach. These results allow to
reconstruct exact expressions involving quasi-modular functions of the bare
gauge coupling constant and to show that the prepotential terms satisfy a
modular anomaly equation that takes the form of a recursion relation with an
explicitly epsilon-dependent term. We then investigate the implications of this
recursion relation on the modular properties of the effective theory and find
that with a suitable redefinition of the prepotential and of the effective
coupling it is possible, at least up to the third order in the deformation
parameters, to cast the S-duality relations in the same form as they appear in
the Seiberg-Witten solution of the undeformed theory. |
Review of AdS/CFT Integrability, Chapter IV.4: Integrability in QCD and
N<4 SYM: There is a growing amount of evidence that QCD (and four-dimensional gauge
theories in general) possess a hidden symmetry which does not exhibit itself as
a symmetry of classical Lagrangians but is only revealed on the quantum level.
In this review we consider the scale dependence of local gauge invariant
operators and high-energy (Regge) behavior of scattering amplitudes to explain
that the effective QCD dynamics in both cases is described by completely
integrable systems that prove to be related to the celebrated Heisenberg spin
chain and its generalizations. | Production of Topological Defects at the End of Inflation: Cosmological inflation and topological defects have been considered for a
long time, either in disagreement or in competition. On the one hand an
inflationary era is required to solve the shortcomings of the hot big bang
model, while on the other hand cosmic strings and string-like objects are
predicted to be formed in the early universe. Thus, one has to find ways so
that both can coexist. I discuss how to reconcile cosmological inflation with
cosmic strings. |
Uplifting Maximal Gauged Supergravities: Which theories have a higher dimensional origin in String/M-theory is a non
trivial question and it is still far from being understood in the constrained
scenario of maximal supergravities. After 35 years of progress in this
direction we have found supporting evidence in favor of the idea that every
electric maximal supergravity in 4 dimensions can be uplifted to M-theory. We
will review the current understanding of this problem with special emphasis in
the uplifting of non compact supergravities and their relation with Exceptional
Generalised Geometry. | On Mathieu moonshine and Gromov-Witten invariants: We show that a large number of $CY_3$ manifolds are involved in an intricate
way in Mathieu moonshine viz. their Gromov--Witten invariants are related to
the expansion coefficients of the twined/ twisted--twined elliptic genera of
$K3$. We use the string duality between CHL orbifolds of heterotic string
theory on $K3 \times T^2$ and type IIA string theory on $CY_3$ manifolds to
explicitly show this connection. We then work out two concrete examples where
we exactly match the expansion coefficients on both sides of the duality. |
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