anchor
stringlengths 50
3.92k
| positive
stringlengths 55
6.16k
|
|---|---|
Restricted Quantum Focusing: Quantum Focusing is a powerful conjecture, which plays a key role in the
current proofs of many well-known quantum gravity theorems, including various
consistency conditions, and causality constraints in AdS/CFT. I conjecture a
(weaker) restricted quantum focusing, which I argue is sufficient to derive all
known essential implications of quantum focusing. Subject to a technical
assumption, I prove this conjecture on brane-world semiclassical gravity
theories which are holographically dual to Einstein gravity in a higher
dimensional anti-de Sitter spacetime. | Quantum complex sine-Gordon model on a half line: The quantum complex sine-Gordon model on a half line is studied. The quantum
spectrum of boundary bound states using the the semi-classical method of
Dashen, Hasslacher and Neveu is obtained. The results are compared and found to
agree with the bootstrap programme. A particle/soliton reflection factor is
conjectured, which is consistent with unitary, crossing and our semi-classical
results. |
AdS_7/CFT_6, Gauss-Bonnet Gravity, and Viscosity Bound: We study the relation between the causality and the positivity of energy
bounds in Gauss-Bonnet gravity in AdS_7 background and find a precise
agreement. Requiring the group velocity of metastable states to be bounded by
the speed of light places a bound on the value of Gauss-Bonnet coupling. To
find the positivity of energy constraints we compute the parameters which
determine the angular distribution of the energy flux in terms of three
independent coefficients specifying the three-point function of the
stress-energy tensor. We then relate the latter to the Weyl anomaly of the
six-dimensional CFT and compute the anomaly holographically. The resulting
upper bound on the Gauss-Bonnet coupling coincides with that from causality and
results in a new bound on viscosity/entropy ratio. | Marginal Deformations and Rotating Horizons: Motivated by the near-horizon geometry of four-dimensional extremal black
holes, we study a disordered quantum mechanical system invariant under a global
$SU(2)$ symmetry. As in the Sachdev-Ye-Kitaev model, this system exhibits an
approximate $SL(2,\mathbb{R})$ symmetry at low energies, but also allows for a
continuous family of $SU(2)$ breaking marginal deformations. Beyond a certain
critical value for the marginal coupling, the model exhibits a quantum phase
transition from the gapless phase to a gapped one and we calculate the critical
exponents of this transition. We also show that charged, rotating extremal
black holes exhibit a transition when the angular velocity of the horizon is
tuned to a certain critical value. Where possible we draw parallels between the
disordered quantum mechanics and charged, rotating black holes. |
Superconformal mechanics in SU(2|1) superspace: Using the worldline SU(2|1) superfield approach, we construct N=4
superconformally invariant actions for the d=1 multiplets (1, 4, 3) and (2, 4,
2). The SU(2|1) superfield framework automatically implies the trigonometric
realization of the superconformal symmetry and the harmonic oscillator term in
the corresponding component actions. We deal with the general N=4
superconformal algebra D(2,1;$\alpha$) and its central-extended $\alpha$=0 and
$\alpha$=-1 psu(1,1|2)$\oplus$su(2) descendants. We capitalize on the
observation that D(2,1;$\alpha$) at $\alpha\neq$0 can be treated as a closure
of its two su(2|1) subalgebras, one of which defines the superisometry of the
SU(2|1) superspace, while the other is related to the first one through the
reflection of $\mu$, the parameter of contraction to the flat N=4, d=1
superspace. This closure property and its $\alpha$=0 analog suggest a simple
criterion for the SU(2|1) invariant actions to be superconformal: they should
be even functions of $\mu$. We find that the superconformal actions of the
multiplet (2, 4, 2) exist only at $\alpha$=-1, 0 and are reduced to a sum of
the free sigma-model type action and the conformal superpotential yielding,
respectively, the oscillator potential $\sim \mu^2$ and the standard conformal
inverse-square potential in the bosonic sector. The sigma-model action in this
case can be constructed only on account of non-zero central charge in the
superalgebra su(1,1|2). | Tilt and Tensor-to-Scalar Ratio in Multifield Monodromy Inflation: We study the possible range of the tilt $n_s$ and the tensor-to-scalar ratio
$r$ in multifield versions of a class of inflationary models from string
theory. We show that $r$ is the same between the single field models and
multifield models while $n_s$ is bounded above by the results of single field
models. Below its maximum value, $n_s$ depends on the specific distributions of
parameters in the model. The general trend is that the wider the distributions
are, the smaller $n_s$ is. We show that $n_s$ does not have a rigorous lower
bound. It is argued, however, that models predicting arbitrarily small $n_s$
only constitute a small portion of the possible ones and for the vast majority
of models, $n_s$ is bounded below by predictions given by models with uniformly
distributed parameters. |
Determinism and a supersymmetric classical model of quantum fields: A quantum field theory is described which is a supersymmetric classical
model. -- Supersymmetry generators of the system are used to split its
Liouville operator into two contributions, with positive and negative spectrum,
respectively. The unstable negative part is eliminated by a positivity
constraint on physical states, which is invariant under the classical
Hamiltonian flow. In this way, the classical Liouville equation becomes a
functional Schroedinger equation of a genuine quantum field theory. Thus, 't
Hooft's proposal to reconstruct quantum theory as emergent from an underlying
deterministic system, is realized here for a field theory. Quantization is
intimately related to the constraint, which selects the part of Hilbert space
where the Hamilton operator is positive. This is seen as dynamical symmetry
breaking in a suitably extended model, depending on a mass scale which
discriminates classical dynamics beneath from emergent quantum mechanical
behaviour. | A Note on the Bach Tensor in AdS/CFT: This paper has been superseded by hep-th/0303164, "The Dirichlet Obstruction
in AdS/CFT" |
Two-Loop Computation in Superstring Theory: In this paper I review some old and new works on the computation of two-loop
4-particle amplitude in superstring theory. I also present the proof by Iengo,
showing the vanishing of the term related to the two-loop correction to the
$R^4$ term. Finally I will present some recent works on two-loop computation in
hyperelliptic language following the new gauging fixing method of D'Hoker and
Phong. | Gravitational instantons and internal dimensions: We Study instanton solutions in general relativity with a scalar field. The
metric ansatz we use is composed of a particular warp product of general
Einstein metrics, such as those found in a number of cosmological settings,
including string cosmology, supergravity compactifications and general Kaluza
Klein reductions. Using the Hartle-Hawking prescription the instantons we
obtain determine whether metrics involving extra compact dimensions of this
type are favoured as initial conditions for the universe. Specifically, we find
that these product metric instantons, viewed as constrained instantons, do have
a local minima in the action. These minima are then compared with the higher
dimensional version of the Hawking-Turok instantons, and we argue that the
latter always have lower action than those associated with these product
metrics. |
Dyonic Black Holes in String Theory: An exact solution of the low-energy string theory representing static,
spherical symmetric dyonic black hole is found. The solution is labeled by
their mass, electric charge, magnetic charge and asymptotic value of the scalar
dilaton. Some interesting properties of the dyonic black holes are studied. In
particular, the Hawking temperature of dyonic black holes depends on both the
electric and magnetic charges, and the extremal ones, which have nonzero
electric and magnetic charges, have zero temperature but nonzero entropy. These
properties are quite different from those of electrically (or magnetically)
charged dilaton black holes found by Gibbons {\it et al.} and Garfinkle {\it et
al.}, but are the same as those of the dyonic black holes found by Gibbons and
Maeda. After this paper was submitted for publication, D. Wiltshire told us
that solutions, eqs.(22)-(28), are related to Gibbons-Maeda dyonic black hole
solutions by a coordinate transformation and some parameters reparametization
\cite{26}. And, we were also informed that many of our results were previously
obtained by Kallosh {\it et al.} \cite{27}. The dyonic black hole solutions,
eqs.(22)-(28), are also related to those of reference \cite{27} by another
coordinate | On "Non-Geometric" Contribution To The Entropy Of Black Hole Due To
Quantum Corrections: The quantum corrections to the entropy of charged black holes are calculated.
The Reissner-Nordstrem and dilaton black holes are considered. The appearance
of logarithmically divergent terms not proportional to the horizon area is
demonstrated. It is shown that the complete entropy which is sum of classical
Bekenstein-Hawking entropy and the quantum correction is proportional to the
area of quantum-corrected horizon. |
Nonlinear sigma models with AdS supersymmetry in three dimensions: In three-dimensional anti-de Sitter (AdS) space, there exist several
realizations of N-extended supersymmetry, which are traditionally labelled by
two non-negative integers p>=q such that p+q=N. Different choices of p and q,
with N fixed, prove to lead to different restrictions on the target space
geometry of supersymmetric nonlinear sigma-models. We classify all possible
types of hyperkahler target spaces for the cases N=3 and N=4 by making use of
two different realizations for the most general (p,q) supersymmetric
sigma-models: (i) off-shell formulations in terms of N=3 and N=4 projective
supermultiplets; and (ii) on-shell formulations in terms of covariantly chiral
scalar superfields in (2,0) AdS superspace. Depending on the type of N=3,4 AdS
supersymmetry, nonlinear sigma-models can support one of the following target
space geometries: (i) hyperkahler cones; (ii) non-compact hyperkahler manifolds
with a U(1) isometry group which acts non-trivially on the two-sphere of
complex structures; (iii) arbitrary hyperkahler manifolds including compact
ones. The option (iii) is realized only in the case of critical (4,0) AdS
supersymmetry.
As an application of the (4,0) AdS techniques developed, we also construct
the most general nonlinear sigma-model in Minkowski space with a non-centrally
extended N=4 Poincare supersymmetry. Its target space is a hyperkahler cone
(which is characteristic of N=4 superconformal sigma-models), but the
sigma-model is massive. The Lagrangian includes a positive potential
constructed in terms of the homothetic conformal Killing vector the target
space is endowed with. This mechanism of mass generation differs from the
standard one which corresponds to a sigma-model with the ordinary N=4 Poincare
supersymmetry and which makes use of a tri-holomorphic Killing vector. | Semi-simple extension of the (super)Poincaré algebra: A semi-simple tensor extension of the Poincar\'e algebra is proposed for the
arbitrary dimensions $D$. A supersymmetric also semi-simple generalization of
this extension is constructed in the D=4 dimensions. This paper is dedicated to
the memory of Anna Yakovlevna Gelyukh. |
Classical de Sitter solutions in three dimensions without tachyons?: We continue the study of compactifications of massive IIA supergravity on G2
orientifolds and demonstrate that breaking supersymmetry with anti-D2 and
anti-D6 sources leads to 3d theories for which the typical tachyons haunting
classical dS solutions can be absent. However for a concrete torus example the
meta-stable dS window disappears after a quantization of fluxes and charges. We
discuss the prospects of more general G2 compactifications and argue that they
could potentially alleviate the tachyon problem by introducing larger tadpole
numbers and warped throats. However, exactly those ingredients then seem to
push the vacuum towards the brink of perturbative brane-flux decay in the open
string sector. This is either a remarkable illustration of the no-dS swampland
conjecture or such vacua live in very difficult to control regions of parameter
space. | Low energy effective gravitational equations on a Gauss-Bonnet brane: We present effective gravitational equations at low energies in a
$Z_2$-symmetric braneworld with the Gauss-Bonnet term. Our derivation is based
on the geometrical projection approach, and we solve iteratively the bulk
geometry using the gradient expansion scheme. Although the original field
equations are quite complicated due to the presence of the Gauss-Bonnet term,
our final result clearly has the form of the Einstein equations plus correction
terms, which is simple enough to handle. As an application, we consider
homogeneous and isotropic cosmology on the brane. We also comment on the
holographic interpretation of bulk gravity in the Gauss-Bonnet braneworld. |
BPS Equations and the Stress Tensor: We exploit the relationship between the space components of the
energy-momentum tensor and the supercurrent to discuss the connection between
the BPS equations and the vanishing of the components of the stress tensor in
various supersymmetric theories with solitons.
Using the fact that certain combination of supercharges annihilate BPS
states, we show that $T_{ij}=0$ for kinks, vortices and dyons, displaying the
connection between supersymmetry and non-interacting BPS solitons. | Complete Wetting of Gluons and Gluinos: Complete wetting is a universal phenomenon associated with interfaces
separating coexisting phases. For example, in the pure gluon theory, at $T_c$
an interface separating two distinct high-temperature deconfined phases splits
into two confined-deconfined interfaces with a complete wetting layer of
confined phase between them. In supersymmetric Yang-Mills theory, distinct
confined phases may coexist with a Coulomb phase at zero temperature. In that
case, the Coulomb phase may completely wet a confined-confined interface.
Finally, at the high-temperature phase transition of gluons and gluinos,
confined-confined interfaces are completely wet by the deconfined phase, and
similarly, deconfined-deconfined interfaces are completely wet by the confined
phase. For these various cases, we determine the interface profiles and the
corresponding complete wetting critical exponents. The exponents depend on the
range of the interface interactions and agree with those of corresponding
condensed matter systems. |
Trans-Planckian censorship, inflation and excited initial states for
perturbations: The recently proposed trans-Planckian censorship conjecture (TCC) seems to
require that the energy scale of inflation is significantly lower than the
Planck scale $(H_\text{inf}<10^{-20} \Mpl)$. This, in turn, implies that the
tensor-to-scalar ratio for inflation is negligibly small, \textit{independent}
of assumptions of slow-roll or even of having a single scalar field, thus
ruling out inflation if primordial tensor modes are ever observed. After
demonstrating the robustness and generality of these bounds, we show that
having an excited initial state for cosmological perturbations seems to be a
way out of this problem for models of inflation. | Knots and entanglement: We extend the entanglement bootstrap approach to (3+1)-dimensions. We study
knotted excitations of (3+1)-dimensional liquid topological orders and exotic
fusion processes of loops. As in previous work in (2+1)-dimensions, we define a
variety of superselection sectors and fusion spaces from two axioms on the
ground state entanglement entropy. In particular, we identify fusion spaces
associated with knots. We generalize the information convex set to a new class
of regions called immersed regions, promoting various theorems to this new
context. Examples from solvable models are provided; for instance, a concrete
calculation of knot multiplicity shows that the knot complement of a trefoil
knot can store quantum information. We define spiral maps that allow us to
understand consistency relations for torus knots as well as spiral fusions of
fluxes. |
A $κ$-Symmetry Calculus for Superparticles: We develop a $\kappa$-symmetry calculus for the d=2 and d=3, N=2 massive
superparticles, which enables us to construct higher order $\kappa$-invariant
actions. The method relies on a reformulation of these models as supersymmetric
sigma models that are invariant under local worldline superconformal
transformations. We show that the $\kappa$-symmetry is embedded in the
superconformal symmetry so that a calculus for the $\kappa$-symmetry is
equivalent to a tensor calculus for the latter. We develop such a calculus
without the introduction of a worldline supergravity multiplet. | Gaussian distribution of LMOV numbers: Recent advances in knot polynomial calculus allowed us to obtain a huge
variety of LMOV integers counting degeneracy of the BPS spectrum of topological
theories on the resolved conifold and appearing in the genus expansion of the
plethystic logarithm of the Ooguri-Vafa partition functions. Already the very
first look at this data reveals that the LMOV numbers are randomly distributed
in genus (!) and are very well parameterized by just three parameters depending
on the representation, an integer and the knot. We present an accurate
formulation and evidence in support of this new puzzling observation about the
old puzzling quantities. It probably implies that the BPS states, counted by
the LMOV numbers can actually be composites made from some still more
elementary objects. |
Graviton and Massive Symmetric Rank-Two Tensor in String Theory: Spin-two particles appear in the spectra of both open and closed string
theories. We studied a graviton and massive symmetric rank-two tensor in string
theory, both of which carry spin two. A graviton is a massless spin-two
particle in closed string theory while a symmetric rank-two tensor is a massive
particle with spin two in open string theory. Using Polyakov's string path
integral formulation of string scattering amplitudes, we calculated cubic
interactions of both spin-two particles explicitly, including $\ap$-corrections
(string corrections). We observed that the cubic interactions of the massive
spin-two particle differed from those of the graviton. The massive symmetric
rank-two tensor in open string theory becomes massless in the high energy limit
where $\ap \rightarrow \infty$ and $\ap$-correction terms, containing higher
derivatives, dominate: In this limit the local cubic action of the symmetric
rank-two tensor of open string theory coincides with that of the graviton in
closed string theory. | Chaotic RG Flow in Tensor Models: We study a bi-antisymmetric tensor quantum field theory with $O(N_1)\times
O(N_2)$ symmetry. Working in $4-\epsilon$ dimensions we calculate the beta
functions up to second order in the coupling constants and analyze in detail
the Renormalization Group (RG) flow and its fixed points. We allow $N_1$ and
$N_2$ to assume general real values and treat them as bifurcation parameters.
In studying the behavior of the model in the space of $N_1$ and $N_2$ we find a
point where a zero-Hopf bifurcation occurs. In the vicinity of this point, we
provide analytical and numerical evidence for the existence of Shilnikov
homoclinic orbits, which induce chaotic behavior in the RG flow of the model.
As a simple warm-up example for the study of chaotic RG flows, we also review
the non-hermitian Ising chain and show how for special complex values of the
coupling constant, its RG transformations are chaotic and equivalent to the
Bernoulli map. |
The Spectrum of Bogomol'nyi Solitons in Gauged Linear Sigma Models: Gauged linear sigma models with C^m-valued scalar fields and gauge group
U(1)^d, d \leq m, have soliton solutions of Bogomol'nyi type if a suitably
chosen potential for the scalar fields is also included in the Lagrangian. Here
such models are studied on (2+1)-dimensional Minkowski space. If the dynamics
of the gauge fields is governed by a Maxwell term the appropriate potential is
a sum of generalised Higgs potentials known as Fayet-Iliopoulos D-terms. Many
interesting topological solitons of Bogomol'nyi type arise in models of this
kind, including various types of vortices (e.g. Nielsen-Olesen, semilocal and
superconducting vortices) as well as, in certain limits, textures (e.g.
CP^(m-1) textures and gauged CP^(m-1) textures). This is explained and general
results about the spectrum of topological defects both for broken and partially
broken gauge symmetry are proven. When the dynamics of the gauge fields is
governed by a Chern-Simons term instead of a Maxwell term a different scalar
potential is required for the theory to be of Bogomol'nyi type. The general
form of that potential is given and a particular example is discussed. | A remark on the gauging of chiral bosons: We study the interacting chiral boson and observe that a naive gauging
procedure leaves the covariant chiral constraint incompatible with the field
equations. Consistency, therefore, rules out most gauging schemes: in a left
chiral scalar, only the coupling with the left chiral currents leads to
consistent results, in discordance with current literature. |
Broken spacetime symmetries and elastic variables: We discuss spontaneous breaking of continuum symmetries, whose generators do
explicitly depend on the spacetime coordinates. We clarify the relation between
broken symmetries and elastic variables at both zero and finite temperatures,
and/or finite densities, and show the general counting rule that is
model-independently determined by the symmetry breaking pattern. We apply it to
three intriguing examples: rotational, conformal, and gauge symmetries. | Superalgebras from $p$-brane actions: Two superalgebras associated with $p$-branes are the constraint algebra and
the Noether charge algebra. Both contain anomalous terms which modify the
standard supertranslation algebra. These anomalous terms have a natural
description in terms of double complex cohomology of generalized forms. By
retaining fermionic charges and allowing for gauge freedom in the double
complex, it is shown that the algebra of conserved charges forms a spectrum
with free parameters. The spectrum associated with the Green-Schwarz
superstring is shown to contain and generalize the known superalgebras
associated with the superstring. |
Logarithmic corrections to the entropy of non-extremal black holes in
$\mathcal{N}=1$ Einstein-Maxwell supergravity: We reviewed the field redefinition approach of Seeley-DeWitt expansion for
the determination of Seeley-DeWitt coefficients from arXiv:1505.01156. We apply
this approach to compute the first three Seeley-DeWitt coefficients for
\say{non-minimal} $\mathcal{N}=1$ Einstein-Maxwell supergravity in four
dimensions. Finally, we use the third coefficient for the computation of the
logarithmic corrections to the Bekenstein-Hawking entropy of non-extremal black
holes following arXiv:1205.0971. We determine the logarithmic corrections for
non-extremal Kerr-Newman, Kerr, Reissner-Nordstr\"{o}m and Schwarzschild black
holes in \say{non-minimal} $\mathcal{N}=1$, $d=4$ Einstein-Maxwell
supergravity. | Perturbations of brane worlds: We consider cosmological models where the universe, governed by Einstein's
equations, is a piece of a five dimensional double-sided anti-de Sitter
spacetime (that is, a "$Z_2$-symmetric bulk") with matter confined to its four
dimensional Robertson-Walker boundary or "brane". We study the perturbations of
such models. We use conformally minkowskian coordinates to disentangle the
contributions of the bulk gravitons and of the motion of the brane. We find the
restrictions put on the bulk gravitons when matter on the brane is taken to be
a scalar field and we solve in that case the brane perturbation equations. |
Transversality in the Coupling of Gravity to Gauge Theories: We consider (effective) Quantum General Relativity coupled to the Standard
Model and study its transversality. To this end, we provide all propagator and
three-valent vertex Feynman rules. Then we examine the longitudinal, identical
and transversal projection tensors for the de Donder gauge fixing and the
Lorenz gauge fixing. In particular, we recall several identities from Quantum
Yang--Mills theory and introduce their counterparts in (effective) Quantum
General Relativity: This includes decompositions of the longitudinal projection
tensors as well as expressions of the corresponding propagators in terms of
their transversal structure, together with longitudinal contraction identities
for all three-valent vertex Feynman rules. In addition, we introduce the notion
of an optimal gauge fixing as the natural choice for a given gauge theory: In
particular, we find that this is the de Donder gauge fixing in General
Relativity and the Lorenz gauge fixing in Yang--Mills theory. | Cyclic Universes from General Collisionless Braneworld Models: We investigate the full 5D dynamics of general braneworld models. Without
making any further assumptions we show that cyclic behavior can arise naturally
in a fraction of physically accepted solutions. The model does not require
brane collisions, which in the stationary case remain fixed, and cyclicity
takes place on the branes. We indicate that the cosmological constants play the
central role for the realization of cyclic solutions and we show that its
extremely small value on the observable universe makes the period of the cycles
and the maximum scale factor astronomically large. |
Secondary GWs and PBHs in string inflation: formation and detectability: We derive the spectrum and analyse the detectability prospects of secondary
gravity waves (GWs) associated to primordial black hole (PBH) production in a
class of string inflationary models called Fibre Inflation. The inflationary
potential features a near inflection point that induces a period of ultra
slow-roll responsible for an enhancement of the scalar perturbations which can
lead to PBHs with different masses and contributions to dark matter (DM) in
agreement with current observational bounds, including CMB constraints on the
scalar spectral index and the tensor-to-scalar ratio. This enhancement of the
curvature perturbations sources secondary GWs which can be detected by either
LISA, ET or BBO, depending on the GW frequency but regardless of the amount of
PBH DM since secondary GWs remain detectable even if the PBH contribution to DM
is exponentially suppressed. The possibility to see a secondary GW signal is
instead due to the presence of an ultra slow-roll epoch between CMB horizon
exit and the end of inflation. | Computing in String Field Theory Using the Moyal Star Product: Using the Moyal star product, we define open bosonic string field theory
carefully, with a cutoff, for any number of string oscillators and any
oscillator frequencies. Through detailed computations, such as Neumann
coefficients for all string vertices, we show that the Moyal star product is
all that is needed to give a precise definition of string field theory. The
formulation of the theory as well as the computation techniques are
considerably simpler in the Moyal formulation. After identifying a monoid
algebra as a fundamental mathematical structure in string field theory, we use
it as a tool to compute with ease the field configurations for wedge, sliver,
and generalized projectors, as well as all the string interaction vertices for
perturbative as well as monoid-type nonperturbative states. Finally, in the
context of VSFT we analyze the small fluctuations around any D-brane vacuum. We
show quite generally that to obtain nontrivial mass and coupling, as well as a
closed strings, there must be an associativity anomaly. We identify the
detailed source of the anomaly, but leave its study for future work. |
Natural renormalization: A careful analysis of differential renormalization shows that a distinguished
choice of renormalization constants allows for a mathematically more
fundamental interpretation of the scheme. With this set of a priori fixed
integration constants differential renormalization is most closely related to
the theory of generalized functions. The special properties of this scheme are
illustrated by application to the toy example of a free massive bosonic theory.
Then we apply the scheme to the phi^4-theory. The two-point function is
calculated up to five loops. The renormalization group is analyzed, the
beta-function and the anomalous dimension are calculated up to fourth and fifth
order, respectively. | Probable Values of the Cosmological Constant in a Holographic Theory: We point out that for a large class of universes, holography implies that the
most probable value of the cosmological constant is zero. In four spacetime
dimensions, the probability distribution takes the Baum-Hawking form,
$dP\sim\exp(cM_p^2/\Lambda)d\Lambda$. |
Rotating black holes in Randall-Sundrum II braneworlds: We find rotating black hole solutions in the Randall-Sundrum II (RSII) model,
by numerically solving a three-dimensional PDE problem using pseudospectral
collocation methods. We compute the area and equatorial inner-most stable
orbits of these solutions. For large black holes compared with the AdS length
scale, $\ell$, the black hole exhibits four-dimensional behaviour, approaching
the Kerr metric on the brane, whilst for small black holes, the solution tends
instead towards a five-dimensional Myers-Perry black hole with a single
non-zero rotation parameter aligned with the brane. This departure from exact
four-dimensional gravity may lead to different phenomenological predictions for
rotating black holes in the RSII model to those in standard four-dimensional
general relativity. This letter provides a stepping stone for studying such
modifications. | The Concept of Time in 2D Quantum Gravity: We show that the ``time'' t_s defined via spin clusters in the Ising model
coupled to 2d gravity leads to a fractal dimension d_h(s) = 6 of space-time at
the critical point, as advocated by Ishibashi and Kawai. In the unmagnetized
phase, however, this definition of Hausdorff dimension breaks down. Numerical
measurements are consistent with these results. The same definition leads to
d_h(s)=16 at the critical point when applied to flat space. The fractal
dimension d_h(s) is in disagreement with both analytical prediction and
numerical determination of the fractal dimension d_h(g), which is based on the
use of the geodesic distance t_g as ``proper time''. There seems to be no
simple relation of the kind t_s = t_g^{d_h(g)/d_h(s)}, as expected by
dimensional reasons. |
Strings on the deformed T^{1,1}: giant magnon and single spike solutions: In this paper we find giant magnon and single spike string solutions in a
sector of the gamma-deformed conifold. We examine the dispersion relations and
find a behavior analogous to the undeformed case. The transcendental functional
relations between the conserved charges are shifted by certain gamma-dependent
term. The latter is proportional to the total momentum and thus qualitatively
different from known cases. | Density of States and Tachyons in Open and Closed String Theory: In this note we reexamine the possibility of constructing stable
non-supersymmetric theories that exhibit an exponential density of states. For
weakly coupled closed strings there is a general theorem, according to which
stable theories with an exponential density of states must exhibit an almost
exact cancellation of spacetime bosons and fermions (not necessarily level by
level). We extend this result to open strings by showing that if the above
cancellation between bosons and fermions does not occur, the open strings do
not decouple from a closed string tachyon even in the NCOS scaling limit. We
conclude with a brief comment on the proposed generalization of the AdS/CFT
correspondence to non-supersymmetric theories. |
Aspects of the D=6, (2,0) Tensor Multiplet: Some aspects of the $D=6, (2,0)$ tensor multiplet are discussed. Its
formulation as an analytic superfield on a suitably defined superspace and its
superconformal properties are reviewed. Powers of the field strength superfield
define a series of superconformal fields which correspond to the KK multiplets
of D=11 supergravity on an $AdS_7\xz S^4$ background. Correlation functions of
these operators are briefly discussed. | The complex sine-Gordon model on a half line: In this paper, we examine the complex sine-Gordon model in the presence of a
boundary, and derive boundary conditions that preserve integrability. We
present soliton and breather solutions, investigate the scattering of particles
and solitons off the boundary and examine the existence of classical solutions
corresponding to boundary bound states. |
AdS/CFT prescription for angle-deficit space and winding geodesics: We present the holographic computation of the boundary two-point correlator
using the GKPW prescription for a scalar field in the AdS$_3$ space with a
conical defect. Generally speaking, a conical defect breaks conformal
invariance in the dual theory, however we calculate the classical Green
functions for a scalar field in the bulk with conical defect and use them to
compute the two-point correlator in the boundary theory. We compare the
obtained general expression with previous studies based on the geodesic
approximation. They are in good agreement for short correlators, and main
discrepancy comes in the region of long correlations. Meanwhile, in case of
$\mathbb{Z}_r$-orbifold, the GKPW result coincides with the one obtained via
geodesic images prescription and with the general result for the boundary
theory, which is conformal in this special case. | Color Confinement in QCD due to Topological Defects: We outline a derivation of area law of the Wilson loop in SU(N) Yang-Mills
theory in the maximal Abelian gauge. This is based on a new version of
non-Abelian Stokes theorem and the novel reformulation of the Yang-Mills
theory. Abelian dominance and monopole dominance of the string tension in SU(N)
QCD are immediate consequences of this derivation. |
Holographic probabilities in eternal inflation: In the global description of eternal inflation, probabilities for vacua are
notoriously ambiguous. The local point of view is preferred by holography and
naturally picks out a simple probability measure. It is insensitive to large
expansion factors or lifetimes, and so resolves a recently noted paradox. Any
cosmological measure must be complemented with the probability for observers to
emerge in a given vacuum. In lieu of anthropic criteria, I propose to estimate
this by the entropy that can be produced in a local patch. This allows for
prior-free predictions. | Some Useful Formulas in Nonlinear Sigma Models in (1+2)-Dimensions: We give in this paper some formulas which are useful in the construction of
nontrivial conserved currents for submodels of CP^1-model or QP^1-model in
(1+2) dimensions.
These are full generalization of our results in the previous paper
(hep-th/9802105). |
Geometries, Non-Geometries, and Fluxes: Using F-theory/heterotic duality, we describe a framework for analyzing
non-geometric T2-fibered heterotic compactifications to six- and
four-dimensions. Our results suggest that among T2-fibered heterotic string
vacua, the non-geometric compactifications are just as typical as the geometric
ones. We also construct four-dimensional solutions which have novel type IIB
and M-theory dual descriptions. These duals are non-geometric with three- and
four-form fluxes not of (2,1) or (2,2) Hodge type, respectively, and yet
preserve at least N=1 supersymmetry. | Product of Random States and Spatial (Half-)Wormholes: We study how coarse-graining procedure of an underlying UV-complete quantum
gravity gives rise to a connected geometry. It has been shown, quantum
entanglement plays a key role in the emergence of such a geometric structure,
namely a smooth Einstein-Rosen bridge. In this paper, we explore the
possibility of the emergence of similar geometric structure from classical
correlation, in the AdS/CFT setup. To this end, we consider a setup where we
have two decoupled CFT Hilbert spaces, then choose a random typical state in
one of the Hilbert spaces and the same state in the other. The total state in
the fine-grained picture is of course a tensor product state, but averaging
over the states sharing the same random coefficients creates a geometric
connection for simple probes. Then, the apparent spatial wormhole causes a
factorization puzzle. We argue that there is a spatial analog of
half-wormholes, which resolves the puzzle in the similar way as the spacetime
half-wormholes. |
The Superscattering Matrix for Two Dimensional Black Holes: A consistent Euclidean semi classical calculation is given for the
superscattering operator $\$ $ in the RST model for states with a constant flux
of energy. The $\$ $ operator is CPT invariant. There is no loss of quantum
coherence when the energy flux is less than a critical rate and complete loss
when the energy flux is critical. | Eikonal Approximation in Celestial CFT: We identify an eikonal regime in celestial CFT$_2$ in which massless 2-2
scattering is dominated by t-channel exchange. We derive a formula for the
celestial amplitude that resums exchanges of arbitrary integer spin to all
orders in the coupling. The resulting eikonal phase takes the same form as in
flat space with the powers of center-of-mass energy replaced by weight-shifting
operators on the celestial sphere. We independently compute the celestial
two-point function for a scalar propagating in a shockwave background and show
that to leading order in the gravitational coupling and for a suitable choice
of the source, the result agrees with the prediction from the celestial eikonal
formula for graviton exchange. We demonstrate that this two-point function can
be directly obtained from the corresponding formula in AdS$_4$ in a flat space
limit. We finally establish a general relation between scalar celestial
amplitudes in celestial CFT$_{d-1}$ and the flat space limit of scalar
AdS$_{d+1}$ Witten diagrams. |
Singularity, Sasaki-Einstein manifold, Log del Pezzo surface and
$\mathcal{N}=1$ AdS/CFT correspondence: Part I: A five dimensional Sasaki-Einstein (SE) manifold provides a AdS/CFT pair for
four dimensional $\mathcal{N}=1$ SCFT, and those pairs are very useful in
studying field theory and AdS/CFT correspondence. The space of known SE
manifolds is increased significantly in the last decade, and we initiated the
study of various field theory properties through the geometric property of
these new SE manifolds. There is an associated three dimensional log-terminal
singularity $X$ for each SE manifold $L_X$, and for quasi-regular case, there
is an associated two dimensional log Del Pezzo surface $(S,\Delta)$. The
algebraic geometrical methods are quite useful in extracting interesting
physical properties from singularity and log Del Pezzo surface. The necessary
and sufficient condition for the existence of SE metric on $L_X$ is related to
K stability of $X$. Motivated by dual field theory, we propose a conjecture on
how to reduce the check of K stability to possibly finite cases, which
hopefully would give us a guideline to find a much larger space of SE metrics. | Explicit Calculation of Multiloop Amplitudes in the Superstring Theory: Multiloop superstring amplitudes are calculated in the explicit form by the
solution of Ward identities. A naive generalization of Belavin-Knizhnik theorem
to the superstring is found to be incorrect since the period matrix turns out
to be depended on the spinor structure over the terms proportional to odd
moduli.
These terms appear because fermions mix bosons under the two-dim.
supersymmetry transformations. The closed, oriented superstring turns out to be
finite, if it possesses the ten-dimensional supersymmetry, as well as the
two-dimentional one.
This problem needs a further study. |
Integrable Sigma-models and Drinfeld-Sokolov Hierarchies: Local commuting charges in sigma-models with classical Lie groups as target
manifolds are shown to be related to the conserved quantities appearing in the
Drinfeld-Sokolov (generalized mKdV) hierarchies. Conversely, the
Drinfeld-Sokolov construction can be used to deduce the existence of commuting
charges in these and in wider classes of sigma-models, including those whose
target manifolds are exceptional groups or symmetric spaces. This establishes a
direct link between commuting quantities in integrable sigma-models and in
affine Toda field theories. | Gauged Lifshitz model with Chern-Simons term: We present a gauged Lifshitz Lagrangian including second and forth order
spatial derivatives of the scalar field and a Chern-Simons term, and study
non-trivial solutions of the classical equations of motion. While the
coefficient beta of the forth order term should be positive in order to
guarantee positivity of the energy, the coefficient alpha of the quadratic one
need not be. We investigate the parameter domains finding significant
differences in the field behaviors. Apart from the usual vortex field behavior
of the ordinary relativistic Chern-Simons-Higgs model, we find in certain
parameter domains oscillatory solutions reminiscent of the modulated phases of
Lifshitz systems. |
Chiral fermions on 2D curved spacetimes: The theory of free Majorana-Weyl spinors is the prototype of conformal field
theory in two dimensions in which the gravitational anomaly and the Weyl
anomaly obstruct extending the flat spacetime results to curved backgrounds. In
this paper, we investigate a quantization scheme in which the short distance
singularity in the two-point function of chiral fermions on a two dimensional
curved spacetime is given by the Green's function corresponding to the
classical field equation. We compute the singular term in the Green's function
explicitly and observe that the short distance limit is not well-defined in
general. We identify constraints on the geometry which are necessary to resolve
this problem. On such special backgrounds the theory has locally
$c=\frac{1}{2}$ conformal symmetry. | Deconstruction of the Maldacena-Nunez Compactification: We demonstrate a classical equivalence between the large-N limit of the
Higgsed N=1* SUSY U(N) Yang-Mills theory and the Maldacena-Nunez twisted
compactification of a six dimensional gauge theory on a two-sphere. A direct
comparison of the actions and spectra of the two theories reveals them to be
identical. We also propose a gauge theory limit which should describe the
corresponding spherical compactification of Little String Theory. |
Subdivision Invariant Models in Lattice Gauge Theory: A class of lattice gauge theories is presented which exhibits novel
topological properties. The construction is in terms of compact Wilson
variables defined on a simplicial complex which models a four dimensional
manifold with boundary. The case of Z2 and Z3 gauge groups is considered in
detail, and we prove that at certain discrete values of the coupling parameter,
the partition function in these models remains invariant under subdivision of
the underlying simplicial complex. A variety of extensions is also presented. | Higgs-like (pseudo)Scalars in AdS$_4$, Marginal and Irrelevant
Deformations in CFT_3 and Instantons on S^3: With a 4-form ansatz of 11-dimensional supergravity over non-dynamical AdS$_4
\times S^7/Z_k$ background, with the internal space as a $S^1$ Hopf fibration
on CP$^3$, we get a consistent truncation. The (pseudo)scalars, in the
resulting scalar equations in Euclidean AdS_4 space, may be viewed as arising
from (anti)M-branes wrapping around internal directions in the (Wick-rotated)
skew-whiffed M2-branes background (as the resulting theory is for
anti-M2-branes) and so, realizing the modes after swapping the three
fundamental representations $8_s, 8_c, 8_v$ of SO(8). Taking the backreaction
on the external and internal spaces, we get massless and massive modes,
corresponding to exactly marginal and marginally irrelevant deformations on the
boundary CFT$_3$, and write a closed solution for the bulk equation and compute
its correction to the background action. Next, considering the Higgs-like
(breathing) mode $m^2=18$, having all supersymmetries, parity and
scale-invariance broken, by solving the associated bulk equation with
mathematical methods, especially the Adomian decomposition method, and
analyzing the behavior near the boundary of the solutions, we realize the
boundary duals in SU(4) x U(1)-singlet sectors of the ABJM model. Then,
introducing new dual deformation $\Delta_+$ = 3, 6 operators made of
bi-fundamental scalars, fermions and U(1) gauge fields, we obtain
SO(4)-invariant solutions as small instantons on a three-sphere with radius at
infinity, which actually correspond to collapsing bulk bubbles leading to
big-crunch singularities. |
The Yang-Mills vacuum in Coulomb gauge: The Yang-Mills Schr\"odinger equation is solved in Coulomb gauge for the
vacuum by the variational principle using an ansatz for the wave functional,
which is strongly peaked at the Gribov horizon. We find an infrared suppressed
gluon propagator, an infrared singular ghost propagator and an almost linearly
rising confinement potential. Using these solutions we calculate the electric
field of static color charge distributions relevant for mesons and baryons. | Even the photon propagator must break de Sitter symmetry: The propagator for the massless vector field in de Sitter space cannot
maintain de Sitter invariance in the general covaraint gauge, except in the
exactly transverse gauge limit. This is due to a previously overlooked
Ward-Takahashi identity that the propagator must satisfy. Here we construct the
propagator that satisfies all the conditions of a consistently quantized
theory. Our solution preserves cosmological symmetries and dilations, but
breaks spatial special conformal transformations. The solution amounts to
adding a homogeneous de Sitter breaking term to previously reported de Sitter
invariant solutions of the propagator equation of motion. Even though the
corrections we report pertain to the gauge sector of the linear theory, they
are relevant and have to be accounted for when interactions are included. |
Mesoscopic Fluctuations in Stochastic Spacetime: Mesoscopic effects associated with wave propagation in spacetime with metric
stochasticity are studied. We show that the scalar and spinor waves in a
stochastic spacetime behave similarly to the electrons in a disordered system.
Viewing this as the quantum transport problem, mesoscopic fluctuations in such
a spacetime are discussed. The conductance and its fluctuations are expressed
in terms of a nonlinear sigma model in the closed time path formalism. We show
that the conductance fluctuations are universal, independent of the volume of
the stochastic region and the amount of stochasticity. | Optimized Fock space in the large N limit of quartic interactions in
Matrix Models: We consider the problem of quantization of the bosonic membrane via the large
$N$ limit of its matrix regularizations $H_N$ in Fock space. We prove that
there exists a choice of the Fock space frequency such that $ H_N$ can be
written as a sum of a non-interacting Hamiltonian $H_{0,N}$ and the original
normal ordered quartic potential. Using this decomposition we obtain upper and
lower bounds for the ground state energy in the planar limit, we study a
perturbative expansion about the spectrum of $H_{0,N}$, and show that the
spectral gap remains finite at $N=\infty$ at least up to the second order. We
also apply the method to the $U(N)$-invariant anharmonic oscillator, and
demonstrate that our bounds agree with the exact result of Brezin et al. |
Supersymmetry of Black Strings in D=5 Gauged Supergravities: Supersymmetry of five dimensional string solutions is examined in the context
of gauged D=5, N=2 supergravity coupled to abelian vector multiplets. We find
magnetic black strings preserving one quarter of supersymmetry and approaching
the half-supersymmetric product space AdS_3\times H^2 near the event horizon.
The solutions thus exhibit the phenomenon of supersymmetry enhancement near the
horizon, like in the cases of ungauged supergravity theories, where the near
horizon limit is fully supersymmetric. Finally, product space compactifications
are studied in detail, and it is shown that only for negative curvature
(hyperbolic) internal spaces, some amount of supersymmetry can be preserved.
Among other solutions, we find that the extremal rotating BTZ black hole
tensored by H^2 preserves one quarter of supersymmetry. | Notes On The S-Matrix Of Bosonic And Topological Non-Critical Strings: We show that the equivalence between the c=1 non-critical bosonic string and
the N=2 topologically twisted coset SL(2)/U(1) at level one can be checked very
naturally on the level of tree-level scattering amplitudes with the use of the
Stoyanovsky-Ribault-Teschner map, which recasts $H_3^+$ correlation functions
in terms of Liouville field theory amplitudes. This observation can be applied
equally well to the topologically twisted SL(2)/U(1) coset at level n>1, which
has been argued recently to be equivalent with a c<1 non-critical bosonic
string whose matter part is defined by a time-like linear dilaton CFT. |
Positivity Bounds for Massive Spin-1 and Spin-2 Fields: We apply the recently developed positivity bounds for particles with spin,
applied away from the forward limit, to the low energy effective theories of
massive spin-1 and spin-2 theories. For spin-1 theories, we consider the
generic Proca EFT which arises at low energies from a heavy Higgs mechanism,
and the special case of a charged Galileon for which the EFT is reorganized by
the Galileon symmetry. For spin-2, we consider generic $\Lambda_5$ massive
gravity theories and the special `ghost-free' $\Lambda_3$ theories. Remarkably
we find that at the level of 2-2 scattering, the positivity bounds applied to
$\Lambda_5$ massive gravity theories impose the special tunings which generate
the $\Lambda_3$ structure. For $\Lambda_3$ massive gravity theories, the island
of positivity derived in the forward limit appears relatively stable against
further bounds. | New supersymmetric index of heterotic compactifications with torsion: We compute the new supersymmetric index of a large class of N=2 heterotic
compactifications with torsion, corresponding to principal two-torus bundles
over warped K3 surfaces with H-flux. Starting from a UV description as a (0,2)
gauged linear sigma-model with torsion, we use supersymmetric localization
techniques to provide an explicit expression of the index as a sum over the
Jeffrey-Kirwan residues of the one-loop determinant. We finally propose a
geometrical formula that gives the new supersymmetric index in terms of bundle
data, regardless of any particular choice of underlying two-dimensional theory. |
Chaotic Quantization of Classical Gauge Fields: We argue that higher dimensional classical, nonabelian gauge theory may lead
to a lower dimensional quantum field theory due to its inherent chaotic
dynamics which acts like stohastic quantization. The dimensional reduction is
based upon magnetic screening effects analagous to that in nonabelian plasmas. | Light-Ray Radon Transform for Abelianin and Nonabelian Connection in 3
and 4 Dimensional Space with Minkowsky Metric: We consider a real manifold of dimension 3 or 4 with Minkovsky metric, and
with a connection for a trivial GL(n,C) bundle over that manifold. To each
light ray on the manifold we assign the data of paralel transport along that
light ray. It turns out that these data are not enough to reconstruct the
connection, but we can add more data, which depend now not from lines but from
2-planes, and which in some sence are the data of parallel transport in the
complex light-like directions, then we can reconstruct the connection up to a
gauge transformation. There are some interesting applications of the
construction: 1) in 4 dimensions, the self-dual Yang Mills equations can be
written as the zero curvature condition for a pair of certain first order
differential operators; one of the operators in the pair is the covariant
derivative in complex light-like direction we studied. 2) there is a relation
of this Radon transform with the supersymmetry. 3)using our Radon transform, we
can get a measure on the space of 2 dimensional planes in 4 dimensional real
space. Any such measure give rise to a Crofton 2-density. The integrals of this
2-density over surfaces in R^4 give rise to the Lagrangian for maps of real
surfaces into R^4, and therefore to some string theory. 4) there are relations
with the representation theory. In particular, a closely related transform in 3
dimensions can be used to get the Plancerel formula for representations of
SL(2,R). |
N=2 Instanton Effective Action in Omega-background and D3/D(-1)-brane
System in R-R Background: We study the relation between the ADHM construction of instantons in the
Omega-background and the fractional D3/D(-1)-branes at the orbifold singularity
of C \times C^2/Z_2 in Ramond-Ramond (R-R) 3-form field strength background. We
calculate disk amplitudes of open strings connecting the D3/D(-1)-branes in
certain R-R background to obtain the D(-1)-brane effective action deformed by
the R-R background. We show that the deformed D(-1)-brane effective action
agrees with the instanton effective action in the Omega-background. | The area operator and fixed area states in conformal field theories: The fixed area states are constructed by gravitational path integrals in
previous studies.In this paper we show the dual of the fixed area states in
conformal field theories (CFTs).These CFT states are constructed by using
spectrum decomposition of reduced density matrix $\rho_A$ for a subsystem $A$.
For 2 dimensional CFTs we directly construct the bulk metric, which is
consistent with the expected geometry of the fixed area states. For arbitrary
pure geometric state $|\psi\rangle$ in any dimension we also find the
consistency by using the gravity dual of R\'enyi entropy. We also give the
relation of parameters for the bulk and boundary state. The pure geometric
state $|\psi\rangle$ can be expanded as superposition of the fixed area states.
Motivated by this, we propose an area operator $\hat A^\psi$. The fixed area
state is the eigenstate of $\hat A^\psi$, the associated eigenvalue is related
to R\'enyi entropy of subsystem $A$ in this state. The Ryu-Takayanagi formula
can be expressed as the expectation value $\langle \psi| {\hat
A}^\psi|\psi\rangle$ divided by $4G$, where $G$ is the Newton constant. We also
show the fluctuation of the area operator in the geometric state $|\psi\rangle$
is suppressed in the semiclassical limit $G\to0$. |
Chern-Simons Perturbation Theory: We study the perturbation theory for three dimensional Chern--Simons quantum
field theory on a general compact three manifold without boundary. We show that
after a simple change of variables, the action obtained by BRS gauge fixing in
the Lorentz gauge has a superspace formulation. The basic properties of the
propagator and the Feynman rules are written in a precise manner in the
language of differential forms. Using the explicit description of the
propagator singularities, we prove that the theory is finite. Finally the
anomalous metric dependence of the $2$-loop partition function on the
Riemannian metric (which was introduced to define the gauge fixing) can be
cancelled by a local counterterm as in the $1$-loop case. In fact, the
counterterm is equal to the Chern--Simons action of the metric connection,
normalized precisely as one would expect based on the framing dependence of
Witten's exact solution. | The Complex Laguerre Symplectic Ensemble of Non-Hermitian Matrices: We solve the complex extension of the chiral Gaussian Symplectic Ensemble,
defined as a Gaussian two-matrix model of chiral non-Hermitian quaternion real
matrices. This leads to the appearance of Laguerre polynomials in the complex
plane and we prove their orthogonality. Alternatively, a complex eigenvalue
representation of this ensemble is given for general weight functions. All
k-point correlation functions of complex eigenvalues are given in terms of the
corresponding skew orthogonal polynomials in the complex plane for finite-N,
where N is the matrix size or number of eigenvalues, respectively. We also
allow for an arbitrary number of complex conjugate pairs of characteristic
polynomials in the weight function, corresponding to massive quark flavours in
applications to field theory. Explicit expressions are given in the large-N
limit at both weak and strong non-Hermiticity for the weight of the Gaussian
two-matrix model. This model can be mapped to the complex Dirac operator
spectrum with non-vanishing chemical potential. It belongs to the symmetry
class of either the adjoint representation or two colours in the fundamental
representation using staggered lattice fermions. |
Magnetic Fields and Fractional Statistics in Boundary Conformal Field
Theory: We study conformal field theories describing two massless one-dimensional
fields interacting at a single spatial point. The interactions we include are
periodic functions of the bosonized fields separately plus a ``magnetic''
interaction that mixes the two fields. Such models arise in open string theory
and dissipative quantum mechanics and perhaps in edge state tunneling in the
fractional quantized Hall effect. The partition function for such theories is a
Coulomb gas with interchange phases arising from the magnetic field. These
``fractional statistics'' have a profound effect on the phase structure of the
Coulomb gas. In this paper we present new exact and approximate results for
this type of generalized Coulomb gas. | Maximal transcendental weight contribution of scattering amplitudes: Feynman integrals in quantum field theory evaluate to special functions and
numbers that are usefully described by the notion of transcendental weight. In
this paper, we propose a way of projecting a given dimensionally-regularised
Feynman integral, for example contributing to a scattering amplitudes, onto its
maximal weight part. The method uses insights into the singularity structure of
space-time loop integrands, and is complementary to usual generalised unitarity
approaches. We describe the method and give a proof-of-principle application to
the two-loop scattering amplitudes $gg \to H$ in the heavy top-quark mass
limit, which involves both planar and non-planar Feynman integrals. We also
comment on further possible applications and discuss subtleties related to
evanescent integrand terms. |
ADM reduction of IIB on $H^{p,q}$ and dS braneworld: We propose a new Kaluza-Klein reduction scheme based on ADM decomposition.
The scheme has been motivated by AdS/CFT, especially by how the worldvolume
theory should appear from the supergravity side. We apply the scheme to IIB
supergravity reduced on a 5D hyperboloidal $\cH^5$ space, and show that an
(A)dS "braneworld" is be realized after further reduction to 4D. We comment on
applications to cosmology and black hole physics. In particular, the scheme
should provide a proper paradigm for black hole physics. | Twistor and Polytope Interpretations for Subleading Color One-Loop
Amplitudes: We use the relation of the one-loop subleading-color amplitudes to the
one-loop $n$-point leading color amplitudes in ${\cal N}=4$ SYM, to derive a
polytope interpretation for the former in the $MHV$ case, and a representation
in momentum twistor space for the general $N^kMHV$ case. These techniques are
explored in detail for the 5-point and 6-point amplitudes. We briefly discuss
the implications for IR divergences. |
Gyroscopic Gravitational Memory: We study the motion of a gyroscope located far away from an isolated
gravitational source in an asymptotically flat spacetime. As seen from a local
frame tied to distant stars, the gyroscope precesses when gravitational waves
cross its path, resulting in a net "orientation memory" that carries
information on the wave profile. At leading order in the inverse distance to
the source, the memory consists of two terms: the first is linear in the metric
perturbation and coincides with the spin memory effect, while the second is
quadratic and measures the net helicity of the wave burst. Both are closely
related to symmetries of the gravitational radiative phase space at null
infinity: spin memory probes superrotation charges, while helicity is the
canonical generator of local electric-magnetic duality on the celestial sphere. | Holographic charge transport in 2+1 dimensions at finite $N$: We study holographic charge transport in (2+1) dimensions at finite $N$,
whose dual gravity background is given by perturbative black hole solution in
Einstein theory plus cubic terms of Weyl tensor. We consider the higher
derivative corrections to the standard Maxwell action, given by the interacting
terms between the Weyl tensor and the field strength. We calculate the DC
conductivity by using both the membrane paradigm and the Kubo's formula and
find precise agreement. We compute the AC conductivity and find an analog of
the crossover from `metal' to `bad metal' in the low frequency limit. Moreover,
the conductivity becomes a constant in the large frequency limit. We derive two
universal relations for the Green's functions and observe that they are exactly
the same as the infinite $N$ counterparts. |
Radiation from an oscillating dipole layer facing a conducting plane:
resonances and Dynamical Casimir Effect: We study the properties of the classical electromagnetic (EM) radiation
produced by two physically different yet closely related systems, which may be
regarded as classical analogues of the Dynamical Casimir Effect (DCE). They
correspond to two flat, infinite, parallel planes, one of them static and
imposing perfect conductor boundary conditions, while the other performs a
rigid oscillatory motion. The systems differ just in the electrical properties
of the oscillating plane: one of them is just a planar dipole layer
(representing, for instance, a small-width electret). The other, instead, has a
dipole layer on the side which faces the static plane, but behaves as a
conductor on the other side: this can be used as a representation of a
conductor endowed with patch potentials (on the side which faces the conducting
plane). We evaluate, in both cases, the dissipative flux of energy between the
system and its environment, showing that, at least for small mechanical
oscillation amplitudes, it can be written in terms of the dipole layer
autocorrelation function. We show that there are resonances as a function of
the frequency of the mechanical oscillation. | Generalized Uncertainty Principle from the Regularized Self-Energy: We use the Schr\"odinger--Newton equation to calculate the regularized
self-energy of the particle using a regular self-gravitational and
electrostatic potential derived in the string T-duality. The particle mass $M$
is no longer concentrated into a point but it is diluted and described by a
quantum-corrected smeared energy density resulting in corrections to the energy
of the particle which is interpreted as a regularized self-energy. We extend
our results and find corrections to the relativistic particles using the
Klein-Gordon, Proca, and Dirac equations. An important finding is that we
extract a form of generalized uncertainty principle (GUP) from the corrected
energy. The form of GUP is shown to depend on the nature of particles; namely,
for bosons (spin $0$ and spin $1$) we obtain a quadratic form of GUP, while for
fermions (spin $1/2$) we obtain a linear form of GUP. The correlation we found
between spin and GUP may offer insights into investigating quantum gravity. |
Domain wall seeds in CSO-gauged supergravity: Gravitational domain wall solutions in gauged supergravity are often
constructed within truncations that do not include vectors. As a consequence
the gauge group is only a global symmetry of this truncation. The consistency
of the truncation requires the restriction to solutions with vanishing Noether
charge under this global symmetry, since otherwise vector fields are sourced.
We show that this has interesting consequences for the orbit structure of the
solutions under the global symmetries. We investigate this for
$\text{CSO}(p,q,r)$-gaugings in various dimensions with scalar fields truncated
to the $\text{SL}(n,\mathbb{R})/\text{SO}(n)$ subcoset. We prove that the seed
solution $-$ which generates all other solutions using only global
transformations $-$ has a diagonal coset matrix. This means that there exists a
transformation at the boundary of the geometry that diagonalises the coset
matrix and that this same transformation also diagonalises the whole flow as a
consequence of the vanishing charge. | A Note on the Cardy-Verlinde Formula: We generalize the results of hep-th/0008140 to the case of the
(n+1)-dimensional closed FRW universe satisfying a general equation of state of
the form p=w\rho. We find that the entropy of the universe can no longer be
expressed in a form similar to the Cardy formula, when w\neq 1/n. As a result,
in general the entropy formula does not coincide with the Friedmann equation
when the conjectured bound on the Casimir energy is saturated. Furthermore, the
conjectured bound on the Casimir energy generally does not lead to the Hubble
and the Bekenstein entropy bounds. |
Boundary bound states in the SUSY sine-Gordon model with Dirichlet
boundary conditions: We analyze the ground state structure of the supersymmetric sine-Gordon model
via the lattice regularization. The nonlinear integral equations are derived
for any values of the boundary parameters by the analytic continuation and
showed three different forms depending on the boundary parameters. We discuss
the state that each set of the nonlinear integral equations characterizes in
the absence of source terms. Four different pictures of the ground state are
found by numerically studying the positions of zeros in the auxiliary
functions. We suggest the existence of two classes in the SUSY sine-Gordon
model, which cannot be mixed each other. | Bolting Multicenter Solutions: We introduce a solvable system of equations that describes non-extremal
multicenter solutions to six-dimensional ungauged supergravity coupled to
tensor multiplets. The system involves a set of functions on a
three-dimensional base metric. We obtain a family of non-extremal axisymmetric
solutions that generalize the known multicenter extremal solutions, using a
particular base metric that introduces a bolt. We analyze the conditions for
regularity, and in doing so we show that this family does not include solutions
that contain an extremal black hole and a smooth bolt. We determine the
constraints that are necessary to obtain smooth horizonless solutions involving
a bolt and an arbitrary number of Gibbons-Hawking centers. |
A metric of Yukawa potential as an exact solution to the field equations
of general relativity: It is shown that, by defining a suitable energy momentum tensor, the field
equations of general relativity admit a line element of Yukawa potential as an
exact solution. It is also shown that matter that produces strong force may be
negative, in which case there would be no Schwarzschild-like singularity | Vacuum tunneling in gravity: Topologically non-trivial vacuum structure in gravity models with Cartan
variables (vielbein and contortion) is considered. We study the possibility of
vacuum space-time tunneling in Einstein gravity assuming that the vielbein may
play a fundamental role in quantum gravitational phenomena. It has been shown
that in the case of RP3 space topology the tunneling between non-trivial
topological vacuums can be realized by means of Eguchi-Hanson gravitational
instanton. In Riemann-Cartan geometric approach to quantum gravity the vacuum
tunneling can be provided by means of contortion quantum fluctuations. We
define double self-duality condition for the contortion and give explicit
self-dual configurations which can contribute to vacuum tunneling amplitude. |
On co-dimension 2 defect anomalies in N=4 SYM and (2,0) theory via brane
probes in AdS/CFT: We consider a $\frac{1}{2}$-BPS solution for a D3 brane probe in AdS$_5
\times S^5$ that has world-volume geometry of AdS$_3 \times S^1$. It intersects
the boundary over a surface that represents a dimension 2 defect in the
boundary N=4 SYM theory. The effective action of the probe brane is
proportional to the logarithmically divergent volume of AdS$_3$ and may thus be
interpreted as computing conformal anomaly of the supersymmetric $S^2$ defect.
The classical action scales as $N$. We compute the 1-loop correction to it due
to quantum fluctuations of the D3 brane world-volume fields and compare the
result to an earlier suggested expression for the defect anomaly. We also
perform a similar analysis of a $\frac{1}{2}$-BPS M5 brane probe solution in
AdS$_7 \times S^4$ with the world-volume geometry of AdS$_5 \times S^1$ that
represents a dimension 4 defect in the boundary (2,0) 6d theory. Here the
classical M5 brane action computes the leading order $N^2$ term in $a$-anomaly
of the supersymmetric $S^4$ defect. We perform a detailed computation of the
1-loop correction to the M5 brane effective action and thus provide a
prediction for the subleading constant in the $S^4$ defect $a$-anomaly
coefficient. | T-duality, Non-geometry and Lie Algebroids in Heterotic Double Field
Theory: A number of issues in heterotic double field theory are studied. This
includes the analysis of the T-dual configurations of a flat constant gauge
flux background, which turn out to be non-geometric. Performing a field
redefinition to a non-geometric frame, these T-duals take a very simple form
reminiscent of the constant Q- and R-flux backgrounds. In addition, it is shown
how the analysis of arXiv:1304.2784 generalizes to heterotic generalized
geometry. For every field redefinition specified by an O(D,D+n) transformation,
the structure of the resulting supergravity action is governed by the
differential geometry of a corresponding Lie algebroid. |
Light-Front Quantisation as an Initial-Boundary Value Problem: In the light front quantisation scheme initial conditions are usually
provided on a single lightlike hyperplane. This, however, is insufficient to
yield a unique solution of the field equations. We investigate under which
additional conditions the problem of solving the field equations becomes well
posed. The consequences for quantisation are studied within a Hamiltonian
formulation by using the method of Faddeev and Jackiw for dealing with
first-order Lagrangians. For the prototype field theory of massive scalar
fields in 1+1 dimensions, we find that initial conditions for fixed light cone
time {\sl and} boundary conditions in the spatial variable are sufficient to
yield a consistent commutator algebra. Data on a second lightlike hyperplane
are not necessary. Hamiltonian and Euler-Lagrange equations of motion become
equivalent; the description of the dynamics remains canonical and simple. In
this way we justify the approach of discretised light cone quantisation. | Supersymmetric non-Abelian multiwaves in D=3 AdS superspace: We present a covariant, supersymmetric and kappa-symmetric action for
non-Abelian multiwave system (nAmW) in D=3 AdS superspace. Its flat superspace
limit provides a simplest counterpart of the recently proposed action for 11
dimensional system of N nearly coincident M-waves (multiple M0-branes), which
is presently known for the case of flat target superspace only. |
Conformal blocks on elliptic curves and the
Knizhnik--Zamolodchikov--Bernard equations: We give an explicit description of the vector bundle of WZW conformal blocks
on elliptic curves with marked points as subbundle of a vector bundle of Weyl
group invariant vector valued theta functions on a Cartan subalgebra. We give a
partly conjectural characterization of this subbundle in terms of certain
vanishing conditions on affine hyperplanes. In some cases, explicit calculation
are possible and confirm the conjecture. The Friedan--Shenker flat connection
is calculated, and it is shown that horizontal sections are solutions of
Bernard's generalization of the Knizhnik--Zamolodchikov equation. | Unified phantom cosmology: inflation, dark energy and dark matter under
the same standard: Phantom cosmology allows to account for dynamics and matter content of the
universe tracing back the evolution to the inflationary epoch, considering the
transition to the non-phantom standard cosmology (radiation/matter dominated
eras) and recovering the today observed dark energy epoch. We develop the
unified phantom cosmology where the same scalar plays the role of early time
(phantom) inflaton and late-time Dark Energy. The recent transition from
decelerating to accelerating phase is described too by the same scalar field.
The (dark) matter may be embedded in this scheme, giving the natural solution
of the coincidence problem. It is explained how the proposed unified phantom
cosmology can be fitted against the observations which opens the way to define
all the important parameters of the model. |
Nilpotence varieties: We consider algebraic varieties canonically associated to any Lie
superalgebra, and study them in detail for super-Poincar\'e algebras of
physical interest. They are the locus of nilpotent elements in (the
projectivized parity reversal of) the odd part of the algebra. Most of these
varieties have appeared in various guises in previous literature, but we study
them systematically here, from a new perspective: as the natural moduli spaces
parameterizing twists of a super-Poincar\'e-invariant physical theory. We
obtain a classification of all possible twists, as well as a systematic
analysis of unbroken symmetry in twisted theories. The natural stratification
of the varieties, the identification of strata with twists, and the action of
Lorentz and $R$-symmetry on the varieties are emphasized. We also include a
short and unconventional exposition of the pure-spinor superfield formalism,
from the perspective of twisting, and demonstrate that it can be applied to
construct familiar multiplets in four-dimensional minimally supersymmetric
theories; in all dimensions and with any amount of supersymmetry, this
technique produces BRST or BV complexes of supersymmetric theories from the
Koszul complex of the cone point over the coordinate ring of the nilpotence
variety, possibly tensored with a module over that coordinate ring. In
addition, we remark on a natural emergence of nilpotence varieties in the
Chevalley-Eilenberg cohomology of supertranslations, and give two applications
related to these ideas: a calculation of Chevalley-Eilenberg cohomology for the
six-dimensional $\mathcal{N}=(2,0)$ supertranslation algebra, and a BV complex
matching the field content of type IIB supergravity from the coordinate ring of
the corresponding nilpotence variety. | Exact null tachyons from RG flows: We construct exact 2d CFTs, corresponding to closed string tachyon and metric
profiles invariant under shifts in a null coordinate, which can be constructed
from any 2d renormalization group flow. These solutions satisfy first order
equations of motion in the conjugate null coordinate. The direction along which
the tachyon varies is identified precisely with the worldsheet scale, and the
tachyon equations of motion are the RG flow equations. |
One-loop string corrections for AdS Kaluza-Klein amplitudes: We discuss the string corrections to one-loop amplitudes in
AdS$_5\times$S$^5$, focussing on their expressions in Mellin space. We present
the leading $(\alpha')^3$ corrections to the family of correlators $\langle
\mathcal{O}_2 \mathcal{O}_2 \mathcal{O}_p \mathcal{O}_p \rangle$ at one loop
and begin the exploration of the form of correlators with multiple channels.
From these correlators we extract some string corrections to one-loop anomalous
dimensions of families of operators of low twist. | An introduction to universality and renormalization group techniques: These lecture notes have been written for a short introductory course on
universality and renormalization group techniques given at the VIII Modave
School in Mathematical Physics by the author, intended for PhD students and
researchers new to these topics.
First the basic ideas of dynamical systems (fixed points, stability, etc.)
are recalled, and an example of universality is discussed in this context: this
is Feigenbaum's universality of the period doubling cascade for iterated maps
on the interval. It is shown how renormalization ideas can be applied to
explain universality and compute Feigenbaum's constants.
Then, universality is presented in the scenario of quantum field theories,
and studied by means of functional renormalization group equations, which allow
for a close comparison with the case of dynamical systems. In particular,
Wetterich equation for a scalar field is derived and discussed, and then
applied to the computation of the Wilson-Fisher fixed point and critical
exponent for the Ising universality class.
References to more advanced topics and applications are provided. |
Evidence for String Substructure: We argue that the behavior of string theory at high temperature and high
longitudinal boosts, combined with the emergence of p-branes as necessary
ingredients in various string dualities, point to a possible reformulation of
strings, as well as p-branes, as composites of bits. We review the string-bit
models, and suggest generalizations to incorporate p-branes. | Three Dimensional Differential Calculus on the Quantum Group SU_q(2) and
Minimal Gauge Theory: Three-dimensional bicovariant differential calculus on the quantum group
SU_q(2) is constructed using the approach based on global covariance under the
action of the stabilizing subgroup U(1). Explicit representations of possible
q-deformed Lie algebras are obtained in terms of differential operators. The
consistent gauge covariant differential calculus on SU_q(2) is uniquely
defined. A non-standard Leibnitz rule is proposed for the exterior
differential. The minimal gauge theory with SU_q(2) quantum group symmetry is
considered. |
Extension of the N=2 Virasoro algebra by two primary fields of dimension
2 and 3: We explicitly construct the extension of the N=2 super Virasoro algebra by
two super primary fields of dimension two and three with vanishing u(1)-charge.
Using a super covariant formalism we obtain two different solutions both
consistent for generic values of the central charge c. The first one can be
identified with the super W_4-algebra - the symmetry algebra of the CP(3)
Kazama-Suzuki model. With the help of unitarity arguments we predict the
self-coupling constant of the field of dimension two for all super
W_n-algebras. The second solution is special in the sense that it does not have
a finite classical limit c->infinity and generic null fields appear. In the
spirit of recent results in the N=0 case it can be understood as a unifying N=2
super W-algebra for all CP(n) coset models. It does not admit any unitary
representation. | Gauss-Bonnet Black Holes in AdS Spaces: We study thermodynamic properties and phase structures of topological black
holes in Einstein theory with a Gauss-Bonnet term and a negative cosmological
constant. The event horizon of these topological black holes can be a
hypersurface with positive, zero or negative constant curvature. When the
horizon is a zero curvature hypersurface, the thermodynamic properties of black
holes are completely the same as those of black holes without the Gauss-Bonnet
term, although the two black hole solutions are quite different. When the
horizon is a negative constant curvature hypersurface, the thermodynamic
properties of the Gauss-Bonnet black holes are qualitatively similar to those
of black holes without the Gauss-Bonnet term. When the event horizon is a
hypersurface with positive constant curvature, we find that the thermodynamic
properties and phase structures of black holes drastically depend on the
spacetime dimension $d$ and the coefficient of the Gauss-Bonnet term: when
$d\ge 6$, the properties of black hole are also qualitatively similar to the
case without the Gauss-Bonnet term, but when $d=5$, a new phase of locally
stable small black hole occurs under a critical value of the Gauss-Bonnet
coefficient, and beyond the critical value, the black holes are always
thermodynamically stable. However, the locally stable small black hole is not
globally preferred, instead a thermal anti-de Sitter space is globally
preferred. We find that there is a minimal horizon radius, below which the
Hawking-Page phase transition will not occur since for these black holes the
thermal anti de Sitter space is always globally preferred. |
Moduli Stars: We explore the possibility that (Bose-Einstein) condensation of scalar fields
from string compactifications can lead to long-lived compact objects. Depending
on the type of scalar fields we find different realisations of star-like and
solitonic objects. We illustrate in the framework of type~IIB string
compactifications that closed string moduli can lead to heavy microscopic stars
with masses of order $\mathcal{V}^\alpha M_{\rm Planck}$, $\alpha=1,3/2,5/3$
where $\mathcal{V}$ is the volume of the extra dimensions. Macroscopic compact
objects from ultra-light string axions are realised with masses of order
$e^{\mathcal{V}^{2/3}}M_{\rm Planck}.$ Q-ball configurations can be obtained
from open string moduli whereas the closed string sector gives rise to a new
class of solutions, named PQ-balls, that arise in the two-field axion-modulus
system. The stability, the potential for the formation, and the observability
of moduli stars through gravitational waves are discussed. In particular we
point out that during the early matter phase given by moduli domination,
density perturbations grow by a factor $\mathcal{V}^{\beta}$ with $\beta>2$ and
non-linear effects cannot be neglected. | Non Abelian Toda models and Constrained KP hierarchies: A general construction of affine Non Abelian Toda models in terms of gauged
two loop WZNW model is discussed. Its connection to non relativistic models
corresponding to constrained KP hierarchies is established in terms of time
evolution associated to positive and negative grading of the Lie algebra. |
Spontaneous Polarization of the $\Bbb Z _{n}$-Baxter Model: We show that correlation functions of the $\bz _n $-Baxter model in the
principal regime satisfy a system of difference equations. We obtain the
spontaneous polarization of the $\bz _n $-Baxter model as a solution of the
simplest difference equation. | Separability of Dirac equation in higher dimensional Kerr-NUT-de Sitter
spacetime: It is shown that the Dirac equations in general higher dimensional
Kerr-NUT-de Sitter spacetimes are separated into ordinary differential
equations. |
Mass And Force Relations For Einstein-Maxwell-Dilaton Black Holes: We investigate various properties of extremal dyonic static black holes in
Einstein-Maxwell-Dilaton theory. Using the fact that the long-range force
between two identical extremal black holes always vanishes, we obtain a simple
first-order ordinary differential equation for the black hole mass in terms of
its electric and magnetic charges. Although this equation appears not to be
solvable explicitly for general values of the strength a of the dilatonic
coupling to the Maxwell field, it nevertheless provides a powerful way of
characterising the black hole mass and the scalar charge. We make use of these
expressions to derive general results about the long-range force between two
non-identical extremal black holes. In particular, we argue that the force is
repulsive whenever a>1 and attractive whenever a<1 (it vanishes in the
intermediate BPS case a=1). The sign of the force is also correlated with the
sign of the binding energy between extremal black holes, as well as with the
convexity or concavity of the surface characterizing the extremal mass as a
function of the charges. Our work is motivated in part by the Repulsive Force
Conjecture and the question of whether long range forces between non-identical
states can shed new light on the Swampland. | Structure of Lorentzian algebras and Conformal Field Theory: The main properties of indefinite Kac-Moody and Borcherds algebras,
considered in a unified way as Lorentzian algebras, are reviewed. The
connection with the conformal field theory of the vertex operator construction
is discussed. By the folding procedure a class of subalgebras is obtained. |
Open string instantons and relative stable morphisms: We show how topological open string theory amplitudes can be computed by
using relative stable morphisms in the algebraic category. We achieve our goal
by explicitly working through an example which has been previously considered
by Ooguri and Vafa from the point of view of physics. By using the method of
virtual localization, we successfully reproduce their results for multiple
covers of a holomorphic disc, whose boundary lies in a Lagrangian submanifold
of a Calabi-Yau 3-fold, by Riemann surfaces with arbitrary genera and number of
boundary components. In particular we show that in the case we consider there
are no open string instantons with more than one boundary component ending on
the Lagrangian submanifold. | Hot dense magnetized spinor matter in particle and astroparticle
physics: the role of boundaries: We study the influence of boundaries on chiral effects in hot dense
relativistic spinor matter in a strong magnetic field which is orthogonal to
the boundaries. The most general set of boundary conditions ensuring the
confinement of matter within the boundaries is employed. We find that the
chiral magnetic effect disappears, whereas the chiral separation effect stays
on, becoming dependent on temperature and on a choice of boundary conditions.
As temperature increases from zero to large values, a stepped-shape behaviour
of the chiral separation effect as a function of chemical potential is changed
to a smooth one. A choice of the boundary condition can facilitate either
amplification or diminution of the chiral separation effect; in particular, the
effect can persist even at zero chemical potential, if temperature is finite.
This points at a significant role of boundaries for physical systems with hot
dense magnetized spinor matter, i.e. compact astrophysical objects (neutron
stars and magnetars), relativistic heavy-ion collisions, novel materials known
as the Dirac and Weyl semimetals. |
Breaking discrete symmetries in the effective field theory of inflation: We study the phenomenon of discrete symmetry breaking during the inflationary
epoch, using a model-independent approach based on the effective field theory
of inflation. We work in a context where both time reparameterization symmetry
and spatial diffeomorphism invariance can be broken during inflation. We
determine the leading derivative operators in the quadratic action for
fluctuations that break parity and time-reversal. Within suitable
approximations, we study their consequences for the dynamics of linearized
fluctuations. Both in the scalar and tensor sectors, we show that such
operators can lead to new direction-dependent phases for the modes involved.
They do not affect the power spectra, but can have consequences for higher
correlation functions. Moreover, a small quadrupole contribution to the sound
speed can be generated. | Topological Corrections and Conformal Backreaction in the Einstein
Gauss-Bonnet/Weyl Theories of Gravity at D=4: We investigate the gravitational backreaction, generated by coupling a
general conformal sector to external, classical gravity, as described by a
conformal anomaly effective action. We address the issues raised by the
regularization of the topological Gauss-Bonnet and Weyl terms in these actions
and the use of dimensional regularization (DR). We discuss both their local and
nonlocal expressions, as possible IR and UV descriptions of conformal theories,
below and above the conformal breaking scale. Our discussion overlaps with
several recent studies of dilaton gravities - obtained via a certain singular
limit of the Einstein-Gauss-Bonnet (EGB) theory - originally introduced as a
way to bypass Lovelock's theorem. We show that nonlocal, purely gravitational
realizations of such EGB theories, quadratic in the dilaton field, beside their
local quartic forms, are possible by a finite renormalization of the Euler
density. Such nonlocal versions, which are deprived of any scale, can be
expanded, at least around flat space, in terms of the combination $R \Box^{-1}$
times multiple variations of the anomaly functional, as pointed out in recent
studies at $d=4$. Similar conclusions can be drawn for the proposed nonlocal
EGB theory. The expansion emerges from previous investigations of the anomalous
conformal Ward identities that constrain such theories around the flat
spacetime limit in momentum space. |
Dynamical construction of Horava-Lifshitz geometry: We derive the projectable version of Horava - Lifshitz gravity from the
localisation of the Galilean symmetry. Specifically we provide a dynamical
construction of the metric, from first principles, that reproduces the
transformations of the physical variables - lapse, shift and spatial component
of the metric. Also, the measure defining the action is reproduced. The
geometrical basis of the Horava-Lifshitz gravity is thereby revealed which also
elucidates its difference from the Newton-Cartan geometry - the spacetime of
Newtonian gravity. The connection of Newton's gravity with Horava-Lifshitz
gravity is elucidated. | Comment on "Density perturbations in the ekpyrotic scenario": In the paper ``Density perturbations in the ekpyrotic scenario'', it is
argued that the expected spectrum of primordial perturbations should be scale
invariant in this scenario. Here we show that, contrary to what is claimed in
that paper, the expected spectrum depends on an arbitrary choice of matching
variable. As no underlying (microphysical) principle exists at the present time
that could lift the arbitrariness, we conclude that the ekpyrotic scenario is
not yet a predictive model. |
The Ten-dimensional Effective Action of Strongly Coupled Heterotic
String Theory: We derive the ten-dimensional effective action of the strongly coupled
heterotic string as the low energy limit of M-theory on S^1/Z_2. In contrast to
a conventional dimensional reduction, it is necessary to integrate out
nontrivial heavy modes which arise from the sources located on the orbifold
fixed hyperplanes. This procedure, characteristic of theories with dynamical
boundaries, is illustrated by a simple example. Using this method, we determine
a complete set of R^4, F^2R^2, and F^4 terms and the corresponding Chern-Simons
and Green-Schwarz terms in ten dimensions. As required by anomaly cancelation
and supersymmetry, these terms are found to exactly coincide with their weakly
coupled one-loop counterparts. | Quantum BTZ black hole: We study a holographic construction of quantum rotating BTZ black holes that
incorporates the exact backreaction from strongly coupled quantum conformal
fields. It is based on an exact four-dimensional solution for a black hole
localized on a brane in AdS$_4$, first discussed some years ago but never fully
investigated in this manner. Besides quantum CFT effects and their
backreaction, we also investigate the role of higher-curvature corrections in
the effective three-dimensional theory. We obtain the quantum-corrected
geometry and the renormalized stress tensor. We show that the quantum black
hole entropy, which includes the entanglement of the fields outside the
horizon, satisfies the first law of thermodynamics exactly, even in the
presence of backreaction and with higher-curvature corrections, while the
Bekenstein-Hawking-Wald entropy does not. This result, which involves a rather
non-trivial bulk calculation, shows the consistency of the holographic
interpretation of braneworlds. We compare our renormalized stress tensor to
results derived for free conformal fields, and for a previous holographic
construction without backreaction effects, which is shown to be a limit of the
solutions in this article. |
Is it possible to construct exactly solvable models?: We develop a constructive method to derive exactly solvable quantum
mechanical models of rational (Calogero) and trigonometric (Sutherland) type.
This method starts from a linear algebra problem: finding eigenvectors of
triangular finite matrices. These eigenvectors are transcribed into
eigenfunctions of a selfadjoint Schr\"odinger operator. We prove the
feasibility of our method by constructing a new "$AG_3$ model" of trigonometric
type (the rational case was known before from Wolfes 1975). Applying a Coxeter
group analysis we prove its equivalence with the $B_3$ model. In order to
better understand features of our construction we exhibit the $F_4$ rational
model with our method. | Duality Origami: Emergent Ensemble Symmetries in Holography and
Swampland: We discuss interrelations between several ideas in quantum gravity. One is
the Swampland program, which states that a low-energy effective field theory
should satisfy non-trivial constraints to have an ultraviolet (UV) completion
in quantum gravity. Another is the concept of ensemble averaging in holography,
where a coarse-grained description is obtained by an integral over a moduli
space. To examine the relation between the two, we study ensemble averages of
generalized Narain-type theories associated with a general even quadratic form
and their holographic duals. We establish the emergence of global symmetries
and discuss their consistency with the Swampland conjecture forbidding exact
global symmetries. Out of all the zero-form symmetries, the quantum symmetries
in the bulk are truly emergent, while classical symmetries are identified as
vestiges of T-duality of the Narain-type theories. The latter mechanism can be
formulated very generally as a ``folding'' of T-duality orbits via the
Siegel-Weil Theorem. We also discuss the interrelations between the Swampland
distance conjecture, on one hand, and ensemble averaging and spectral
decompositions, on the other. The spectral decomposition also illustrates how
ensemble averaging sits within the low-energy limit of certain string
compactifications. Our analysis suggests fascinating links between the
Swampland, the Landscape, and ensemble averaging. |
The N=4 string is the same as the N=2 string: We redo the quantization of the N=4 string, taking into account the
reducibility of the constraints. The result is equivalent to the N=2 string,
with critical dimension D=4 and signature (++--). The N=4 formulation has
several advantages: the sigma-model field equations are implied classically,
rather than by quantum/beta-function calculations; self-duality/chirality is
one of the super-Virasoro constraints; SO(2,2) covariance is manifest. This
reveals that the theory includes fermions, and is apparently spacetime
supersymmetric. | Graded Chern-Simons field theory and graded topological D-branes: We discuss graded D-brane systems of the topological A model on a Calabi-Yau
threefold, by means of their string field theory. We give a detailed analysis
of the extended string field action, showing that it satisfies the classical
master equation, and construct the associated BV system. The analysis is
entirely general and it applies to any collection of D-branes (of distinct
grades) wrapping the same special Lagrangian cycle, being valid in arbitrary
topology. Our discussion employs a $\Z$-graded version of the covariant BV
formalism, whose formulation involves the concept of {\em graded
supermanifolds}. We discuss this formalism in detail and explain why
$\Z$-graded supermanifolds are necessary for a correct geometric understanding
of BV systems. For the particular case of graded D-brane pairs, we also give a
direct construction of the master action, finding complete agreement with the
abstract formalism. We analyze formation of acyclic composites and show that,
under certain topological assumptions,all states resulting from the
condensation process of a pair of branes with grades differing by one unit are
BRST trivial and thus the composite can be viewed as a closed string vacuum. We
prove that there are {\em six} types of pairs which must be viewed as generally
inequivalent. This contradicts the assumption that `brane-antibrane' systems
exhaust the nontrivial dynamics of topological A-branes with the same geometric
support. |
Spontaneous symmetry breaking in cosmos: The hybrid symmetron as a dark
energy switching device: We consider symmetron model in a generalized background with a hope to make
it compatible with dark energy. We observe a "no go" theorem at least in case
of a conformal coupling. Being convinced of symmetron incapability to be dark
energy, we try to retain its role for spontaneous symmetry breaking and assign
the role of dark energy either to standard quintessence or $F(R)$ theory which
are switched on by symmetron field in the symmetry broken phase. The scenario
reduces to standard Einstein gravity in the high density region. After the
phase transition generated by symmetron field, either the $F(R)$ gravity or the
standard quintessence are induced in the low density region. we demonstrate
that local gravity constraints and other requirements are satisfied although
the model could generate the late-time acceleration of Universe. | Anisotropic plasma at finite $U(1)$ chemical potential: We present a type IIB supergravity solution dual to a spatially anisotropic
$\mathcal{N}=4$ super Yang-Mills plasma at finite $U(1)$ chemical potential and
finite temperature. The effective five-dimensional gravitational theory is a
consistent Einstein-Maxwell-dilaton-Axion truncation of the gauged
supergravity. We obtain the solutions both numerically and analytically. We
study the phase structure and thermodynamic instabilities of the solution, and
find new instabilities independent of the renormalization scheme. |
Comments on the beta-deformed N=4 SYM Theory: Several calculations of 2- and 3-point correlation functions in the deformed
theory are presented. The central charge in the Lunin-Maldacena gravity dual is
shown to be independent of the deformation parameter. Calculations show that 2-
and 3-point functions of chiral primary operators have no radiative corrections
to lowest order in the interactions. Correlators of the operator tr(Z_1Z_2),
which has not previously been identified as chiral primary, also have vanishing
lowest order corrections. | Duality Cascade and Oblique Phases in Non-Commutative Open String Theory: We investigate the complete phase diagram of the decoupled world-sheet theory
of (P,Q) strings. These theories include 1+1 dimensional super Yang-Mills
theory and non-commutative open string theory. We find that the system exhibits
a rich fractal phase structure, including a cascade of alternating
supergravity, gauge theory, and matrix string theory phases. The cascade
proceeds via a series of SL(2,Z) S-duality transformations, and depends
sensitively on P and Q. In particular, we find that the system may undergo
multiple Hagedorn-type transitions as the temperature is varied. |
Feynman's proper time approach to QED: The genesis of Feynman's original approach to QED is reviewed. The main ideas
of his original presentation at the Pocono Conference are discussed and
compared with the ones involved in his action-at-distance formulation of
classical electrodynamics. The role of the de Sitter group in Feynman's
visualization of space-time processes is pointed out. | Stability of magnetic condensation and mass generation for confinement
in SU(2) Yang-Mills theory: In the framework of the functional renormalization group, we reexamine the
stability of the Yang-Mills vacuum with a chromomagnetic condensation. We show
that the Nielsen-Olesen instability of the Savvidy vacuum with a homogeneous
chromomagnetic condensation disappears in the $SU(2)$ Yang-Mills theory. As a
physical mechanism for maintaining the stability even for the small infrared
cutoff, we argue that dynamical gluon mass generation occurs due to a
BRST-invariant vacuum condensate of mass dimension-two, which is related to
two-gluon bound states identified with glueballs. These results support the
dual superconductor picture for quark confinement. |
Local Equilibrium Spin Distribution From Detailed Balance: As the core ingredient for spin polarization, the local equilibrium spin
distribution function is derived from the detailed balance principle. The
kinetic theory for interacting fermionic systems is applied to the
Nambu--Jona-Lasinio model at quark level. Under the semi-classical expansion
with respect to $\hbar$ and non-perturbative expansion with respect to $N_c$,
the kinetic equations for the vector and axial-vector distribution functions
are derived with collision terms. It is found that, for an initially
unpolarized system, non-zero spin polarization can be generated at the order of
$\hbar$ from the coupling between the vector and axial-vector charges. The
local equilibrium spin polarization is derived from the requirement of detailed
balance. It arises from the thermal vorticity and is orthogonal to the particle
momentum. | Instability of Near-Extremal Black Holes in N=2, d=4 Supergravity: As a precursor to studying the bound states of multiple non-extremal black
holes in $\mathcal{N}=2$, $d=4$ supergravity, we investigate the stability of a
near-extremal D0-D4 black hole in the probe limit, when the parameters of the
black hole solution lie within a certain regime. We determine whether it is
possible to form bound states of this "core" non-extremal black hole with BPS
probe particles, and whether it is possible for the "core" black hole to decay
by the emission of such BPS probes either to a local minimum of the probe
potential, or spatial infinity. We first carry out a qualitative analysis of
the probe potential to determine when quantum tunneling of probes from the
black hole is possible. We then find the wavefunction of the scattered probe by
using the WKB approximation to solve the Dirac equation in the black hole
background, and use this solution to compute the tunneling amplitude. |
The hypermultiplet low-energy effective action, N=2 supersymmetry
breaking and confinement: Some exact solutions to the hypermultiplet low-energy effective action in N=2
supersymmetric four-dimensional gauge field theories with massive `quark'
hypermultiplets are discussed. The need for a spontaneous N=2 supersymmetry
breaking is emphasized, because of its possible relevance in the search for an
ultimate theoretical solution to the confinement problem. | Coarse Graining Holographic Black Holes: We expand our recent work on the outer entropy, a holographic coarse-grained
entropy defined by maximizing the boundary entropy while fixing the classical
bulk data outside some surface. When the surface is marginally trapped and
satisfies certain "minimar" conditions, we prove that the outer entropy is
exactly equal to a quarter the area (while for other classes of surfaces, the
area gives an upper or lower bound). We explicitly construct the
entropy-maximizing interior of a minimar surface, and show that it satisfies
the appropriate junction conditions. This provides a statistical explanation
for the area-increase law for spacelike holographic screens foliated by minimar
surfaces. Our construction also provides an interpretation of the area for a
class of non-minimal extremal surfaces.
On the boundary side, we define an increasing simple entropy by maximizing
the entropy subject to a set of "simple experiments" performed after some time.
We show (to all orders in perturbation theory around equilibrium) that the
simple entropy is the boundary dual to our bulk construction. |
Observational Consequences of Quantum Cosmology: Our universe is born of a tunnelling from nothing in quantum cosmology.
Nothing here can be interpreted as a state with zero entropy. As a reliable
modification of the Hartle-Hawking wave function of the universe, the improved
Hartle-Hawking wave function proposed by Firouzjahi, Sarangi and Tye gives many
interesting observational consequences which we explore in this paper. Fruitful
observations are obtained for chaotic inflation, including a detectable spatial
curvature and a negligible tunnelling probability for eternal chaotic
inflation. And we find that the tensor-scalar ratio and the spatial curvature
for brane inflation type models should be neglected. | Non-Supersymmetric Attractors in String Theory: We find examples of non-supersymmetric attractors in Type II string theory
compactified on a Calabi Yau three-fold. For a non-supersymmetric attractor the
fixed values to which the moduli are drawn at the horizon must minimise an
effective potential. For Type IIA at large volume, we consider a configuration
carrying D0, D2, D4 and D6 brane charge. When the D6 brane charge is zero, we
find for some range of the other charges, that a non-supersymmetric attractor
solution exists. When the D6 brane charge is non-zero, we find for some range
of charges, a supersymmetry breaking extremum of the effective potential.
Closer examination reveals though that it is not a minimum of the effective
potential and hence the corresponding black hole solution is not an attractor.
Away from large volume, we consider the specific case of the quintic in CP^4.
Working in the mirror IIB description we find non-supersymmetric attractors
near the Gepner point. |
The M5-Brane Elliptic Genus: Modularity and BPS States: The modified elliptic genus for an M5-brane wrapped on a four-cycle of a
Calabi-Yau threefold encodes the degeneracies of an infinite set of BPS states
in four dimensions. By holomorphy and modular invariance, it can be determined
completely from the knowledge of a finite set of such BPS states. We show the
feasibility of such a computation and determine the exact modified elliptic
genus for an M5-brane wrapping a hyperplane section of the quintic threefold. | Quantum Gravity Corrections and Entropy at the Planck time: We investigate the effects of Quantum Gravity on the Planck era of the
universe. In particular, using different versions of the Generalized
Uncertainty Principle and under specific conditions we find that the main
Planck quantities such as the Planck time, length, mass and energy become
larger by a factor of order 10-10^{4} compared to those quantities which result
from the Heisenberg Uncertainty Principle. However, we prove that the
dimensionless entropy enclosed in the cosmological horizon at the Planck time
remains unchanged. These results, though preliminary, indicate that we should
anticipate modifications in the set-up of cosmology since changes in the Planck
era will be inherited even to the late universe through the framework of
Quantum Gravity (or Quantum Field Theory) which utilizes the Planck scale as a
fundamental one. More importantly, these corrections will not affect the
entropic content of the universe at the Planck time which is a crucial element
for one of the basic principles of Quantum Gravity named Holographic Principle. |
On deformation theory of quantum vertex algebras: We study an algebraic deformation problem which captures the data of the
general deformation problem for a quantum vertex algebra. We derive a system of
coupled equations which is the counterpart of the Maurer-Cartan equation on the
usual Hochschild complex of an assocative algebra. We show that this system of
equations results from an action principle. This might be the starting point
for a perturbative treatment of the deformation problem of quantum vertex
algebras. Our action generalizes the action of the Kodaira-Spencer theory of
gravity and might therefore also be of relevance for applications in string
theory. | Dynamics of holographic thermalization: Dynamical evolution of thin shells composed by different kinds of degrees of
freedom collapsing within asymptotically AdS spaces is explored with the aim of
investigating models of holographic thermalization of strongly coupled systems.
From the quantum field theory point of view this corresponds to considering
different thermal quenches. We carry out a general study of the thermalization
time scale using different parameters and space-time dimensions, by calculating
renormalized space-like geodesic lengths and rectangular minimal area surfaces
as extended probes of thermalization, which are dual to two-point functions and
rectangular Wilson loops. Different kinds of degrees of freedom in the shell
are described by their corresponding equations of state. We consider a scalar
field, as well as relativistic matter, a pressureless massive fluid and
conformal matter, which can be compared with the collapse of an AdS-Vaidya thin
shell. Remarkably, for conformal matter, the thermalization time scale becomes
much larger than the others. Furthermore, in each case we also investigate
models where the cosmological constants of the inner and outer regions
separated by the shell are different. We found that in this case only a scalar
field shell collapses, and that the thermalization time scale is also much
larger than the AdS-Vaidya case. |
Selection Rules for Black-Hole Quantum Transitions: We suggest that quantum transitions of black holes comply with selection
rules, analogous to those of atomic spectroscopy. In order to identify such
rules, we apply Bohr's correspondence principle to the quasinormal ringing
frequencies of black holes. In this context, classical ringing frequencies with
an asymptotically vanishing real part \omega_R correspond to virtual quanta,
and may thus be interpreted as forbidden quantum transitions. With this
motivation, we calculate the quasinormal spectrum of neutrino fields in
spherically symmetric black-hole spacetimes. It is shown that \omega_R->0 for
these resonances, suggesting that the corresponding fermionic transitions are
quantum mechanically forbidden. | Unitarity relation and unitarity bounds for scalars with different sound
speeds: Motivated by scalar-tensor gravities, we consider a theory which contains
massless scalar fields with different sound speeds. We derive unitarity
relations for partial wave amplitudes of $2 \to 2$ scattering, with explicit
formulas for contributions of two-particle intermediate states. Making use of
these relations, we obtain unitarity bounds both in the most general case and
in the case considered in literature for unit sound speed. These bounds can be
used for estimating the strong coupling scale of a pertinent EFT. We illustrate
our unitarity relations by explicit calculation to the first non-trivial order
in couplings in a simple model of two scalar fields with different sound
speeds. |
On the R-Matrix Formulation of Deformed Algebras and Generalized
Jordan-Wigner Transformations: The deformed algebra $\cal{A(R)}$, depending upon a Yang-Baxter R- matrix, is
considered. The conditions under which the algebra is associative are discussed
for a general number of oscillators. Four types of solutions satisfying these
conditions are constructed and two of them can be represented by generalized
Jordan-Wigner transformations.Our analysis is in some sense an extension of the
boson realization of fermions from single-mode to multimode oscillators. | Dynamical Structure of the Fields in the Light Cone Coordinates: It is well-known that additional constraints emerge in light cone
coordinates. We enumerate the number of physical modes in light cone
coordinates and compare it with conventional coordinates. We show that the
number of Schrodinger modes is divided by two in light cone coordinates. We
study the effect of this reduction in the number ladder operators acting on
physical states of a system. We analyse the scaler, spinor and vector field
theories carefully to see the effect of changes in the dynamical structure of
these theories from the view point of the reduction of Schrodinger modes in
light-cone coordinates. |
An orientifold of adS_5xT^11 with D7-branes, the associated alpha'^2-
corrections and their role in the dual N=1 Sp(2N+2M)xSp(2N) gauge theory: We study the N=1 Sp(2N+2M)xSp(2N) gauge theory on a stack of N physical and M
fractional D3-branes in the background of an orientifolded conifold. The
gravity dual is a type IIB orientifold of adS_5xT^11 (with certain background
fluxes turned on) containing an O7-plane and 8 D7-branes. In the conformal case
(M=0), we argue that the alpha'^2-corrections localized on the 8 D7-branes and
the O7-plane should give vanishing contributions to the supergravity equations
of motion for the bulk fields. In the cascading case (M not equal to 0), we
argue that the alpha'^2-terms give rise to corrections which in the dual
Sp(2N+2M)xSp(2N) gauge theory can be interpreted as corrections to the
anomalous dimensions of the matter fields. | Yang-Mills Fields and Riemannian Geometry: It is possible to define new, gauge invariant variables in the Hilbert space
of Yang-Mills theories which manifestly implement Gauss' law on physical
states. These variables have furthermore a geometrical meaning, and allow one
to uncover further constraints physical states must satisfy. For gauge group
$SU(2)$, the underlying geometry is Riemannian and based on the group $GL(3)$.
The formalism allows also for the inclusion of static color sources and the
extension to gauge groups $SU(N>2)$, both of which are discussed here. |
Near-BPS baby Skyrmions: We consider the baby-Skyrme model in the regime close to the so-called
restricted baby-Skyrme model, which is a BPS model with area-preserving
diffeomorphism invariance. The perturbation takes the form of the standard
kinetic Dirichlet term with a small coefficient $\epsilon$. Classical solutions
of this model, to leading order in $\epsilon$, are called restricted harmonic
maps. In the BPS limit ($\epsilon\to 0$) of the model with the potential being
the standard pion-mass term, the solution with unit topological charge is a
compacton. Using analytical and numerical arguments we obtain solutions to the
problem for topological sectors greater than one. We develop a perturbative
scheme in $\epsilon$ with which we can calculate the corrections to the BPS
mass. The leading order ($\mathcal{O}(\epsilon^1)$) corrections show that the
baby Skyrmion with topological charge two is energetically preferred. The
binding energy requires us to go to the third order in $\epsilon$ to capture
the relevant terms in perturbation theory, however, the binding energy
contributes to the total energy at order $\epsilon^2$. We find that the baby
Skyrmions - in the near-BPS regime - are compactons of topological charge two,
that touch each other on their periphery at a single point and with
orientations in the attractive channel. | A Large-$N$ Phase Transition in a Finite Lattice Gauge Theory: We consider gauge theories of non-Abelian $finite$ groups, and discuss the
1+1 dimensional lattice gauge theory of the permutation group $S_N$ as an
illustrative example. The partition function at finite $N$ can be written
explicitly in a compact form using properties of $S_N$ conjugacy classes. A
natural large-$N$ limit exists with a new 't Hooft coupling, $\lambda=g^2 \log
N$. We identify a Gross-Witten-Wadia-like phase transition at infinite $N$, at
$\lambda=2$. It is first order. An analogue of the string tension can be
computed from the Wilson loop expectation value, and it jumps from zero to a
finite value. We view this as a type of large-$N$ (de-)confinement transition.
Our holographic motivations for considering such theories are briefly
discussed. |
Two-Loop SL(2) Form Factors and Maximal Transcendentality: Form factors of composite operators in the SL(2) sector of N=4 SYM theory are
studied up to two loops via the on-shell unitarity method. The non-compactness
of this subsector implies the novel feature and technical challenge of an
unlimited number of loop momenta in the integrand's numerator. At one loop, we
derive the full minimal form factor to all orders in the dimensional
regularisation parameter. At two loops, we construct the complete integrand for
composite operators with an arbitrary number of covariant derivatives, and we
obtain the remainder functions as well as the dilatation operator for composite
operators with up to three covariant derivatives. The remainder functions
reveal curious patterns suggesting a hidden maximal uniform transcendentality
for the full form factor. Finally, we speculate about an extension of these
patterns to QCD. | Quantum state of the black hole interior: If a black hole (BH) is initially in an approximately pure state and it
evaporates by a unitary process, then the emitted radiation will be in a highly
quantum state. As the purifier of this radiation, the state of the BH interior
must also be in some highly quantum state. So that, within the interior region,
the mean-field approximation cannot be valid and the state of the BH cannot be
described by some semiclassical metric. On this basis, we model the state of
the BH interior as a collection of a large number of excitations that are
packed into closely spaced but single-occupancy energy levels; a sort-of "Fermi
sea" of all light-enough particles. This highly quantum state is surrounded by
a semiclassical region that lies close to the horizon and has a non-vanishing
energy density. It is shown that such a state looks like a BH from the outside
and decays via gravitational pair production in the near-horizon region at a
rate that agrees with the Hawking rate. We also consider the fate of a
classical object that has passed through to the BH interior and show that, once
it has crossed over the near-horizon threshold, the object meets its demise
extremely fast. This result cannot be attributed to a "firewall", as the trauma
to the in-falling object only begins after it has passed through the
near-horizon region and enters a region where semiclassical spacetime ends but
the energy density is still parametrically smaller than Planckian. |
On Lorentz Invariance, Spin-Charge Separation And SU(2) Yang-Mills
Theory: Previously it has been shown that in spin-charge separated SU(2) Yang-Mills
theory Lorentz invariance can become broken by a one-cocycle that appears in
the Lorentz boosts. Here we study in detail the structure of this one-cocycle.
In particular we show that its non-triviality relates to the presence of a
(Dirac) magnetic monopole bundle. We also explicitely present the finite
version of the cocycle. | Holograms In Our World: In AdS/CFT, the entanglement wedge EW$(B)$ is the portion of the bulk
geometry that can be reconstructed from a boundary region $B$; in other words,
EW$(B)$ is the hologram of $B$. We extend this notion to arbitrary spacetimes.
Given any gravitating region $a$, we define a max- and a min-entanglement
wedge, $e_{\rm max}(a)$ and $e_{\rm min}(a)$, such that $e_{\rm min}(a)\supset
e_{\rm max}(a)\supset a$.
Unlike their analogues in AdS/CFT, these two spacetime regions can differ
already at the classical level, when the generalized entropy is approximated by
the area. All information outside $a$ in $e_{\rm max}(a)$ can flow inwards
towards $a$, through quantum channels whose capacity is controlled by the areas
of intermediate homology surfaces. In contrast, all information outside $e_{\rm
min}(a)$ can flow outwards.
The generalized entropies of appropriate entanglement wedges obey strong
subadditivity, suggesting that they represent the von Neumann entropies of
ordinary quantum systems. The entanglement wedges of suitably independent
regions satisfy a no-cloning relation. This suggests that it may be possible
for an observer in $a$ to summon information from spacelike related points in
$e_{\rm max}(a)$, using resources that transcend the semiclassical description
of $a$. |
Matrix Models and Black Holes: We show that an integral transform of the fluctuations of the collective
field of the $d=1$ matrix model satisfy the same linearized equation as that of
the massless "tachyon" in the black hole background of the two dimensional
critical string. This suggests that the $d=1$ matrix model may provide a
non-perturbative description of black holes in two dimensional string theory. | Mini-BFSS in Silico: We study a mass-deformed $\mathcal{N}=4$ version of the BFSS matrix model
with three matrices and gauge group $SU(2)$. This model has zero Witten index.
Despite this, we give numerical evidence for the existence of four
supersymmetric ground states, two bosonic and two fermionic, in the limit where
the mass deformation is tuned to zero. |
Tree-level S-matrix of Pohlmeyer reduced form of AdS_5 x S^5 superstring
theory: With a motivation to find a 2-d Lorentz-invariant solution of the AdS_5 x S^5
superstring we continue the study of the Pohlmeyer-reduced form of this theory.
The reduced theory is constructed from currents of the superstring sigma model
and is classically equivalent to it. Its action is that of
G/H=Sp(2,2)xSp(4)/SU(2)^4 gauged WZW model deformed by an integrable potential
and coupled to fermions. This theory is UV finite and is conjectured to be
related to the superstring theory also at the quantum level. Expanded near the
trivial vacuum it has the same elementary excitations (8+8 massive bosonic and
fermionic 2-d degrees of freedom) as the AdS_5 x S^5 superstring in the
light-cone gauge or near plane-wave expansion. In contrast to the superstring
case, the interaction terms in the reduced action are manifestly 2-d Lorentz
invariant. Since the theory is integrable, its S-matrix should be effectively
determined by the two-particle scattering. Here we explicitly compute the
tree-level two-particle S-matrix for the elementary excitations of the reduced
theory. We find that this S-matrix has the same index structure and group
factorization properties as the superstring S-matrix computed in hep-th/0611169
but has simpler coefficients, depending only on the difference of two
rapidities. While the gauge-fixed form of the reduced action has only the
bosonic SU(2)^4 part of the PSU(2|2) x PSU(2|2) symmetry of the light-cone
superstring spectrum as its manifest symmetry we conjecture that it should also
have a hidden fermionic symmetry that effectively interchanges bosons and
fermions and which should guide us towards understanding the relation between
the two S-matrices. | Spinning Particle as a Non-trivial Rotating Super Black Hole with Broken
N=2 Supersymmetry: Non-trivial supergeneralization of the Kerr-Newman solution is considered as
representing a combined model of the Kerr-Newman spinning particle and
superparticle.
We show that the old problem of obtaining non-trivial super black hole
solutions can be resolved in supergravity broken by Goldstone fermion.
Non-linear realization of broken N=2 supersymmetry specific for the Kerr
geometry is considered and some examples of the super-Kerr geometries generated
by Goldstone fermion are analyzed. The resulting geometries acquire torsion,
Rarita-Schwinger field and extra wave contributions to metric and
electromagnetic field caused by Grassmann variables.
One family of the self-consistent super-Kerr-Newman solutions to broken N=2
supergravity is selected, and peculiarities of these solutions are discussed.
In particular, the appearance of extra `axial' singular line and traveling
waves concentrated near `axial' and ring-like singularities. |
On Special Relativity with Cosmological Constant: Based on the principle of relativity and the postulate of invariant speed and
length, we propose the theory of special relativity with cosmological constant
${\cal SR}_{c,R}$ if the invariant length whose square is the inverse of the
one-third cosmological constant of the universe. It is on the Beltrami-de
Sitter spacetime ${\cal B}_R$ with de Sitter invariance. We define the
observables of free particles and generalize famous Einstein's formula. We also
define two kinds of simultaneity. The first is for local experiments and
inertial motions. The second is for cosmological observations. Thus there is a
relation between the relativity principle and the cosmological principle. We
predict that the 3-d cosmic space is then of positive spatial curvature of
order cosmological constant. The relation between ${\cal SR}_{c,R}$ and the
doubly special relativity is briefly disucssed. | From quantum curves to topological string partition functions: This paper describes the reconstruction of the topological string partition
function for certain local Calabi-Yau (CY) manifolds from the quantum curve, an
ordinary differential equation obtained by quantising their defining equations.
Quantum curves are characterised as solutions to a Riemann-Hilbert problem. The
isomonodromic tau-functions associated to these Riemann-Hilbert problems admit
a family of natural normalisations labelled by the chambers in the extended
K\"ahler moduli space of the local CY under consideration. The corresponding
isomonodromic tau-functions admit a series expansion of generalised theta
series type from which one can extract the topological string partition
functions for each chamber. |
Broken Scale Invariance in the Standard Model: We introduce Weyl's scale invariance as an additional local symmetry in the
standard model of electroweak interactions. An inevitable consequence is the
introduction of general relativity coupled to scalar fields a la Dirac and an
additional vector particle we call the Weylon. We show that once Weyl's scale
invariance is broken, the phenomenon (a) generates Newton's gravitational
constant G_N and (b) triggers spontaneous symmetry breaking in the normal
manner resulting in masses for the conventional fermions and bosons. The scale
at which Weyl's scale symmetry breaks is of order Planck mass. If right-handed
neutrinos are also introduced, their absence at present energy scales is
attributed to their mass which is tied to the scale where scale invariance
breaks. | Quantization of Spinning Particle with Anomalous Magnetic Momentum: A generalization of the pseudoclassical action of a spinning particle in the
presence of an anomalous magnetic moment is given. The leading considerations,
to write the action, are gotten from the path integral representation for the
causal Green's function of the generalized (by Pauli) Dirac equation for the
particle with anomalous magnetic momentum in an external electromagnetic field.
The action can be written in reparametrization and supergauge invariant form.
Both operator (Dirac) and path-integral (BFV) quantization are discussed. The
first one leads to the Dirac-Pauli equation, whereas the second one gives the
corresponding propagator. One of the nontrivial points in this case is that
both quantizations schemes demand for consistency to take into account an
operators ordering problem. |
The rigid limit of N=2 supergravity: In this paper we review the rigid limit of N=2 supergravity coupled to vector
and hypermultiplets. In particular we show how the respective scalar field
spaces reduce to their global counterparts. In the hypermultiplet sector we
focus on the relation between the local and rigid c-map. | Why is quantum gravity so difficult (compared to QCD)?: Gravity is difficult to quantize. This is a well-known fact but its reason is
given simply by non-renormalizability of the Newton constant and little is
discussed why among many quantum gauge theories, gravity is special. In this
essay we try to treat the gravity as one of many gauge theories, and discuss
how it is special and why it is difficult to quantize. |
Unstable Hadrons in Hot Hadron Gas in Laboratory and in the Early
Universe: We study kinetic master equations for chemical reactions involving the
formation and the natural decay of unstable particles in a thermal bath. We
consider the decay channel of one into two particles, and the inverse process,
fusion of two thermal particles into one. We present the master equations the
evolution of the density of the unstable particles in the early Universe. We
obtain the thermal invariant reaction rate using as an input the free space
(vacuum) decay time and show the medium quantum effects on $\pi+\pi
\leftrightarrow \rho$ reaction relaxation time. As another laboratory example
we describe the $K+K \leftrightarrow \phi$ process in thermal hadronic gas in
heavy-ion collisions. A particularly interesting application of our formalism
is the $\pi^{0}\leftrightarrow \gamma +\gamma$ process in the early Universe.
We also explore the physics of $\pi^{\pm}$ and $\mu^{\pm}$ freeze-out in the
Universe. | A classification of near-horizon geometries of extremal vacuum black
holes: We consider the near-horizon geometries of extremal, rotating black hole
solutions of the vacuum Einstein equations, including a negative cosmological
constant, in four and five dimensions. We assume the existence of one
rotational symmetry in 4d, two commuting rotational symmetries in 5d and in
both cases non-toroidal horizon topology. In 4d we determine the most general
near-horizon geometry of such a black hole, and prove it is the same as the
near-horizon limit of the extremal Kerr-AdS(4) black hole. In 5d, without a
cosmological constant, we determine all possible near-horizon geometries of
such black holes. We prove that the only possibilities are one family with a
topologically S^1 X S^2 horizon and two distinct families with topologically
S^3 horizons. The S^1 X S^2 family contains the near-horizon limit of the
boosted extremal Kerr string and the extremal vacuum black ring. The first
topologically spherical case is identical to the near-horizon limit of two
different black hole solutions: the extremal Myers-Perry black hole and the
slowly rotating extremal Kaluza-Klein (KK) black hole. The second topologically
spherical case contains the near-horizon limit of the fast rotating extremal KK
black hole. Finally, in 5d with a negative cosmological constant, we reduce the
problem to solving a sixth-order non-linear ODE of one function. This allows us
to recover the near-horizon limit of the known, topologically S^3, extremal
rotating AdS(5) black hole. Further, we construct an approximate solution
corresponding to the near-horizon geometry of a small, extremal AdS(5) black
ring. |
Cornering the unphysical vertex: In the classical pure spinor worldsheet theory of AdS5xS5 there are some
vertex operators which do not correspond to any physical excitations. We study
their flat space limit. We find that the BRST operator of the worldsheet theory
in flat space-time can be nontrivially deformed without deforming the
worldsheet action. Some of these deformations describe the linear dilaton
background. But the deformation corresponding to the nonphysical vertex differs
from the linear dilaton in not being worldsheet parity even. The nonphysically
deformed worldsheet theory has nonzero beta-function at one loop. This means
that the classical Type IIB SUGRA backgrounds are not completely characterized
by requiring the BRST symmetry of the classical worldsheet theory; it is also
necessary to require the vanishing of the one-loop beta-function. | Leading singularities in Baikov representation and Feynman integrals
with uniform transcendental weight: We provide a leading singularity analysis protocol in Baikov representation,
for the searching of Feynman integrals with uniform transcendental (UT) weight.
This approach is powered by the recent developments in rationalizing square
roots and syzygy computations, and is particularly suitable for finding UT
integrals with multiple mass scales. We demonstrate the power of our approach
by determining the UT basis for a two-loop diagram with three external mass
scales. |
Generalised conservation laws in non-local field theories: We propose a geometrical treatment of symmetries in non-local field theories,
where the non-locality is due to a lack of identification of field arguments in
the action. We show that the existence of a symmetry of the action leads to a
generalised conservation law, in which the usual conserved current acquires an
additional non-local correction term, obtaining a generalisation of the
standard Noether theorem. We illustrate the general formalism by discussing the
specific physical example of complex scalar field theory of the type describing
the hydrodynamic approximation of Bose-Einstein condensates. We expect our
analysis and results to be of particular interest for the group field theory
formulation of quantum gravity. | Thermodynamics of Black Holes in Schroedinger Space: A black hole and a black hyperboloid solutions in the space with the
Schroedinger isometries are presented and their thermodynamics is examined. The
on-shell action is obtained by the difference between the extremal and
non-extremal ones with the unusual matching of the boundary metrics. This
regularization method is first applied to the black brane solution in the space
of the Schroedinger symmetry and shown to correctly reproduce the known
thermodynamics. The actions of the black solutions all turn out to be the same
as the AdS counterparts. The phase diagram of the black hole system is obtained
in the parameter space of the temperature and chemical potential and the
diagram contains the Hawking-Page phase transition and instability lines. |
Quasiclassical asymptotics of solutions to the KZ equations: The quasiclassical asymptotics of the Knizhnik-Zamolodchikov system is
studied. Solutions to this system in this limit are related naturally to Bethe
vectors in the Gaudin model of spin chains. | Evolution of cosmological perturbations and the production of
non-Gaussianities through a nonsingular bounce: Indications for a no-go
theorem in single field matter bounce cosmologies: Assuming that curvature perturbations and gravitational waves originally
arise from vacuum fluctuations in a matter-dominated phase of contraction, we
study the dynamics of the cosmological perturbations evolving through a
nonsingular bouncing phase described by a generic single scalar field
Lagrangian minimally coupled to Einstein gravity. In order for such a model to
be consistent with the current upper limits on the tensor-to-scalar ratio,
there must be an enhancement of the curvature fluctuations during the bounce
phase. We show that, while it remains possible to enlarge the amplitude of
curvature perturbations due to the nontrivial background evolution, this growth
is very limited because of the conservation of curvature perturbations on
super-Hubble scales. We further perform a general analysis of the evolution of
primordial non-Gaussianities through the bounce phase. By studying the general
form of the bispectrum we show that the non-Gaussianity parameter
$f_{\mathrm{NL}}$ (which is of order unity before the bounce phase) is enhanced
during the bounce phase if the curvature fluctuations grow. Hence, in such
nonsingular bounce models with matter given by a single scalar field, there
appears to be a tension between obtaining a small enough tensor-to-scalar ratio
and not obtaining a value of $f_{\mathrm{NL}}$ in excess of the current upper
bounds. This conclusion may be considered as a "no-go" theorem that rules out
any single field matter bounce cosmology starting with vacuum initial
conditions for the fluctuations. |
Pure type I supergravity and DE(10): We establish a dynamical equivalence between the bosonic part of pure type I
supergravity in D=10 and a D=1 non-linear sigma-model on the Kac-Moody coset
space DE(10)/K(DE(10)) if both theories are suitably truncated. To this end we
make use of a decomposition of DE(10) under its regular SO(9,9) subgroup. Our
analysis also deals partly with the fermionic fields of the supergravity theory
and we define corresponding representations of the generalized spatial Lorentz
group K(DE(10)). | N=4 gauged supergravity and a IIB orientifold with fluxes: We analyze the properties of a spontaneously broken D=4, N=4 supergravity
without cosmological constant, obtained by gauging translational isometries of
its classical scalar manifold. This theory offers a suitable low energy
description of the super-Higgs phases of certain Type-IIB orientifold
compactifications with 3-form fluxes turned on. We study its N=3,2,1,0 phases
and their classical moduli spaces and we show that this theory is an example of
no-scale extended supergravity. |
Thermal order in large N conformal gauge theories: In this work we explore the possibility of spontaneous breaking of global
symmetries at all nonzero temperatures for conformal field theories (CFTs) in
$D = 4$ space-time dimensions. We show that such a symmetry-breaking indeed
occurs in certain families of non-supersymmetric large $N$ gauge theories at a
planar limit. We also show that this phenomenon is accompanied by the system
remaining in a persistent Brout-Englert-Higgs (BEH) phase at any temperature.
These analyses are motivated by the work done in arXiv:2005.03676 where
symmetry-breaking was observed in all thermal states for certain CFTs in
fractional dimensions.
In our case, the theories demonstrating the above features have gauge groups
which are specific products of $SO(N)$ in one family and $SU(N)$ in the other.
Working in a perturbative regime at the $N\rightarrow\infty$ limit, we show
that the beta functions in these theories yield circles of fixed points in the
space of couplings. We explicitly check this structure up to two loops and then
present a proof of its survival under all loop corrections. We show that under
certain conditions, an interval on this circle of fixed points demonstrates
both the spontaneous breaking of a global symmetry as well as a persistent BEH
phase at all nonzero temperatures. The broken global symmetry is $\mathbb{Z}_2$
in one family of theories and $U(1)$ in the other. The corresponding order
parameters are expectation values of the determinants of bifundamental scalar
fields in these theories. We characterize these symmetries as baryon-like
symmetries in the respective models. | On the kinematics of the last Wigner particle: Wigner's particle classification provides for "continuous spin"
representations of the Poincar\'e group, corresponding to a class of (as yet
unobserved) massless particles. Rather than building their induced realizations
by use of "Wigner rotations" in the textbooks' way, here we exhibit a
scalar-like first-quantized form of those (bosonic) Wigner particles directly,
by combining wave equations proposed by Wigner long ago with a recent
prequantized treatment employing Poisson structures. |
Parafermionic excitations and critical exponents of random cluster and
O(n) models: We introduce the notion of parafermionic fields as the chiral fields which
describe particle excitations in two-dimensional conformal field theory, and
argue that the parafermionic conformal dimensions can be determined using scale
invariant scattering theory. Together with operator product arguments this may
provide new information, in particular for non-rational conformal theories. We
obtain in this way the field theoretical derivation of the critical exponents
of the random cluster and O(n) models, which in the limit of vanishing central
charge yield percolation and self-avoiding walks. A simple derivation of the
relation between S-matrix and Lagrangian couplings of sine-Gordon model is also
given. | Background field method and the cohomology of renormalization: Using the background field method and the Batalin-Vilkovisky formalism, we
prove a key theorem on the cohomology of perturbatively local functionals of
arbitrary ghost numbers, in renormalizable and nonrenormalizable quantum field
theories whose gauge symmetries are general covariance, local Lorentz symmetry,
non-Abelian Yang-Mills symmetries and Abelian gauge symmetries. Interpolating
between the background field approach and the usual, nonbackground approach by
means of a canonical transformation, we take advantage of the properties of
both approaches and prove that a closed functional is the sum of an exact
functional plus a functional that depends only on the physical fields and
possibly the ghosts. The assumptions of the theorem are the mathematical
versions of general properties that characterize the counterterms and the local
contributions to the potential anomalies. This makes the outcome a theorem on
the cohomology of renormalization, rather than the whole local cohomology. The
result supersedes numerous involved arguments that are available in the
literature. |
Non-thermal signature of the Unruh effect in field mixing: Mixing transformations for a uniformly accelerated observer (Rindler
observer) are analyzed within the quantum field theory framework as a basis for
investigating gravitational effects on flavor oscillations. In particular, the
case of two charged boson fields with different masses is discussed. In spite
of such a minimal setting, the standard Unruh radiation is found to loose its
characteristic thermal interpretation due to the interplay between the
Bogolubov transformation hiding in field mixing and the one arising from the
Rindler spacetime structure. The modified spectrum detected by the Rindler
observer is explicitly calculated in the limit of small mass difference. | UV And IR Effects On Hawking Radiation: We study the time-dependence of Hawking radiation for a black hole in the
Unruh vacuum, and find that it is not robust against certain UV and IR effects.
If there is a UV cutoff at the Planck scale, Hawking radiation is turned off
after the scrambling time. In the absence of a UV cutoff, Hawking radiation is
sensitive to the IR cutoff through a UV/IR connection due to higher-derivative
interactions in the effective theory. Furthermore, higher-derivative
interactions with the background contribute to a large amplitude of particle
creation that changes Hawking radiation. This unexpected large effect is
related to a peculiar feature of the Hawking particle wave packets. |
Fusion Rings Related to Affine Weyl Groups: The construction of the fusion ring of a quasi-rational CFT based on
$\hat{sl}(3)_k$ at generic level $k\not \in {\Bbb Q}$ is reviewed. It is a
commutative ring generated by formal characters, elements in the group ring
${\Bbb Z}[\tilde{W}]$ of the extended affine Weyl group $\tilde{W}$ of
$\hat{sl}(3)_k$. Some partial results towards the $\hat{sl}(4)_k$
generalisation of this character ring are presented. | Yangian Symmetry in D=4 Superconformal Yang-Mills Theory: We will discuss an integrable structure for weakly coupled superconformal
Yang-Mills theories, describe certain equivalences for the Yangian algebra, and
fill a technical gap in our previous study of this subject. |
The Axion-Instanton Weak Gravity Conjecture and Scalar Fields: We study the Weak Gravity Conjecture in the presence of scalar fields. The
Weak Gravity Conjecture is a consistency condition for a theory of quantum
gravity asserting that for a U(1) gauge field, there is a particle charged
under this field whose mass is bounded by its charge. It was extended to a
statement about any canonical pair of (p - 1)-dimensional object and p-form
coupling to it, in particular to axion-instanton pairs. The gauge-scalar Weak
Gravity Conjecture is a modification of this bound that includes scalar
interactions. We propose a similar extension to cases where scalar fields are
present for the axion-instanton Weak Gravity Conjecture and provide evidence
from Type IIA supergravity. | Revisiting N=4 superconformal blocks: We study four-point correlation functions of four generic half-BPS
supermultiplets of N=4 SCFT in four dimensions. We use the two-particle Casimir
of four-dimensional superconformal algebra to derive superconformal blocks
which contribute to the partial wave expansion of such correlators. The derived
blocks are defined on analytic superspace and allow us in principle to find any
component of the four-point correlator. The lowest component of the result
agrees with the superconformal blocks found by Dolan and Osborn. |
Compact Chern-Simons vortices: We introduce and investigate new models of the Chern-Simons type in the
three-dimensional spacetime, focusing on the existence of compact vortices. The
models are controlled by potentials driven by a single real parameter that can
be used to change the profile of the vortex solutions as they approach their
boundary values. One of the models unveils an interesting new behavior, the
tendency to make the vortex compact, as the parameter increases to larger and
larger values. We also investigate the behavior of the energy density and
calculate the total energy numerically. | Higher T-duality of super M-branes: We establish a higher generalization of super L-infinity-algebraic T-duality
of super WZW-terms for super p-branes. In particular, we demonstrate spherical
T-duality of super M5-branes propagating on exceptional-geometric 11d super
spacetime. |
Vacuum polarization by fermionic fields in higher dimensional cosmic
string space-time: In this paper we investigate vacuum polarization effects associated with
charged massive quantum fermionic fields in a six-dimensional cosmic string
space-times considering the presence of a magnetic flux running along its core.
We have shown that for specific values of the parameters which codify the
presence of the cosmic string, and the fractional part of the ratio of the
magnetic flux by the quantum one, a closed expression for the respective Green
function is obtained. Adopting this result, we explicitly calculate the
renormalized vacuum expectation value of the energy-momentum tensors,
$<T^A_B>_{Ren}$, and analyse this result in some limitting cases. | Tri-linear Couplings in an Heterotic Minimal Supersymmetric Standard
Model: We calculate, at the classical level, the superpotential tri-linear couplings
of the only known globally consistent heterotic minimal supersymmetric Standard
Model [ hep-th/0512149 ]. This recently constructed model is based on a
compactification of the E_8 x E_8 heterotic string theory on a Calabi-Yau
threefold with Z_2 fundamental group, coupled with a slope-stable holomorphic
SU(5) vector bundle. In the observable sector the massless particle content is
that of the three-family supersymmetric Standard Model with n=0,1,2 massless
Higgs pairs, depending on the location in the vector bundle moduli space, and
no exotic particles. We obtain non-zero Yukawa couplings for the three
up-sector quarks, and vanishing R-parity violating terms. In particular, the
proton is stable. Another interesting feature is the existence of tri-linear
couplings, on the loci with massless Higgs pairs, generating \mu-mass
parameters for the Higgs pairs and neutrino mass terms, with specific vector
bundle moduli playing the role of right-handed neutrinos. |
The double copy: gravity from gluons: Three of the four fundamental forces in nature are described by so-called
gauge theories, which include the effects of both relativity and quantum
mechanics. Gravity, on the other hand, is described by General Relativity, and
the lack of a well-behaved quantum theory - believed to be relevant at the
centre of black holes, and at the Big Bang itself - remains a notorious
unsolved problem. Recently a new correspondence, the double copy, has been
discovered between scattering amplitudes (quantities related to the probability
for particles to interact) in gravity, and their gauge theory counterparts.
This has subsequently been extended to other quantities, providing gauge theory
analogues of e.g. black holes. We here review current research on the double
copy, and describe some possible applications. | Isolated Skyrmions in the $CP^2$ nonlinear $σ$-model with a
Dzyaloshinskii-Moriya type interaction: We study two dimensional soliton solutions in the $CP^2$ nonlinear
$\sigma$-model with a Dzyaloshinskii-Moriya type interaction. First, we derive
such a model as a continuous limit of the $SU(3)$ tilted ferromagnetic
Heisenberg model on a square lattice. Then, introducing an additional potential
term to the derived Hamiltonian, we obtain exact soliton solutions for
particular sets of parameters of the model. The vacuum of the exact solution
can be interpreted as a spin nematic state. For a wider range of coupling
constants, we construct numerical solutions, which possess the same type of
asymptotic decay as the exact analytical solution, both decaying into a spin
nematic state. |
Type IIB supergravity on squashed Sasaki-Einstein manifolds: We provide a consistent N=4 Kaluza-Klein truncation of type IIB supergravity
on general 5-dimensional squashed Sasaki-Einstein manifolds. Our reduction
ansatz keeps all and only the supergravity modes dual to the universal gauge
sector of the associated conformal theories, via the gauge/gravity
correspondence. The reduced 5-dimensional model displays remarkable features:
it includes both zero-modes as well as massive iterations of the Kaluza-Klein
operators on the internal manifold; it contains tensor fields dual to vectors
charged under a non-abelian gauge group; it has a scalar potential with a
non-supersymmetric AdS vacuum in addition to the supersymmetric one. | Holographic free energy and thermodynamic geometry: We analytically obtain the free energy and thermodynamic geometry of
holographic superconductors in $2+1$-dimensions. The gravitational theory in
the bulk dual to this $2+1$-dimensional strongly coupled theory lives in the
$3+1$-dimensions and is that of a charged $AdS$ black hole together with a
massive charged scalar field. The matching method is applied to obtain the
nature of the fields near the horizon using which the holographic free energy
is computed through the gauge/gravity duality. The critical temperature is
obtained for a set of values of the matching point of the near horizon and the
boundary behaviour of the fields. The thermodynamic geometry is then computed
from the free energy of the boundary theory. From the divergence of the
thermodynamic scalar curvature, the critical temperature is obtained once
again. We then compare this result for the critical temperature with that
obtained from the matching method. |
Stability Constraints on Classical de Sitter Vacua: We present further no-go theorems for classical de Sitter vacua in Type II
string theory, i.e., de Sitter constructions that do not invoke
non-perturbative effects or explicit supersymmetry breaking localized sources.
By analyzing the stability of the 4D potential arising from compactification on
manfiolds with curvature, fluxes, and orientifold planes, we found that
additional ingredients, beyond the minimal ones presented so far, are necessary
to avoid the presence of unstable modes. We enumerate the minimal setups for
(meta)stable de Sitter vacua to arise in this context. | Generic approach to dimensional reduction and selection principle for
low-energy limit of M theory: We propose the approach to deriving lower-dimensional limit of modern
high-energy theory which does not make explicit use of the Kaluza-Klein scheme
and predefined compactification manifolds. The approach is based on the
selection principle in which a crucial role is played by p-brane solutions and
their preservation, in a certain sense, under dimensional reduction. Then we
engage a previously developed method of reconstruction of a theory from a given
solution which eventually leads to some model acting in the space of field
couplings. Thus, our approach focuses on those general features of effective 4D
theories which are independent of how the decomposition of spacetime dimensions
into ``observable'' and ``unobservable'' ones could be done. As an example, we
exactly derive the simplified abelian sector of the effective low-energy
M-theory together with its fundamental 0-brane solution describing the family
of charged black holes with scalar hair in asymptotically flat, de Sitter or
anti-de Sitter spacetime. |
Adelic Harmonic Oscillator: Using the Weyl quantization we formulate one-dimensional adelic quantum
mechanics, which unifies and treats ordinary and $p$-adic quantum mechanics on
an equal footing. As an illustration the corresponding harmonic oscillator is
considered. It is a simple, exact and instructive adelic model. Eigenstates are
Schwartz-Bruhat functions. The Mellin transform of a simplest vacuum state
leads to the well known functional relation for the Riemann zeta function. Some
expectation values are calculated. The existence of adelic matter at very high
energies is suggested. | $T\bar{T}$-deformation and Liouville gravity: We consider a gravitational perturbation of the Jackiw-Teitelboim (JT)
gravity with an arbitrary dilaton potential and study the condition under which
the quadratic action can be seen as a $T\bar{T}$-deformation of the matter
action. As a special case, the flat-space JT gravity discussed by Dubovsky et
al[arXiv:1706.06604 ] is included. Another interesting example is a hyperbolic
dilaton potential. This case is equivalent to a classical Liouville gravity
with a negative cosmological constant and then a finite $T\bar{T}$-deformation
of the matter action is realized as a gravitational perturbation on AdS$_2$. |
Deformed Intersecting D6-Brane GUTS and N=1 SUSY: We analyze the construction of non-supersymmetric three generation six-stack
Pati-Salam (PS) $SU(4)_C \times SU(2)_L \times SU(2)_R$ GUT classes of models,
by localizing D6-branes intersecting at angles in four dimensional
orientifolded toroidal compactifications of type IIA. Special role in the
models is played by the presence of extra branes needed to satisfy the RR
tadpole cancellation conditions. The models contain at low energy {\em exactly
the Standard model} with no extra matter and/or extra gauge group factors. They
are build such that they represent deformations around the quark and lepton
basic intersection number structure. The models possess the same
phenomenological characteristics of some recently discussed examples (PS-A,
PS-I; PS-II GUT classes; hep-th/0203187, hep-th/0209202; hep-th/0210004) of
four and five stack PS GUTS respectively. Namely, there are no colour triplet
couplings to mediate proton decay and proton is stable as baryon number is a
gauged symmetry.
The mass relation $m_e = m_d$ at the GUT scale is recovered. Even though more
complicated, than in lower stack GUTS, the conditions of the non-anomalous
U(1)'s to survive massless the generalized Green-Schwarz mechanism are solved
consistently by the angle conditions coming from the presence of N=1
supersymmetric sectors involving the presence of {\em extra} branes and also
required for the existence of a Majorana mass term for the right handed
neutrinos. | Amplitudes for massive vector and scalar bosons in spontaneously-broken
gauge theory from the CHY representation: In the formulation of Cachazo, He, and Yuan, tree-level amplitudes for
massless particles in gauge theory and gravity can be expressed as rational
functions of the Lorentz invariants $k_a \cdot k_b$, $\epsilon_a \cdot k_b$,
and $\epsilon_a \cdot \epsilon_b$, valid in any number of spacetime dimensions.
We use dimensional reduction of higher-dimensional amplitudes of particles with
internal momentum $\kappa$ to obtain amplitudes for massive particles in lower
dimensions. In the case of gauge theory, we argue that these massive amplitudes
belong to a theory in which the gauge symmetry is spontaneously broken by an
adjoint Higgs field. Consequently, we show that tree-level $n$-point amplitudes
containing massive vector and scalar bosons in this theory can be obtained by
simply replacing $k_a \cdot k_b$ with $k_a \cdot k_b - \kappa_a \kappa_b $ in
the corresponding massless amplitudes, where the masses of the particles are
given by $|\kappa_a|$. |
Poincaré-like extension Mixing Higgs and Gauge Fields in a U(1)
symmetric model: We continue the program by investigating symmetric structures underlying
features of the Standard Model. We then expand the symmetry to encompass
translations before contraction. A field theory model emerges with the goal of
replicating a coupling to gravity before contraction. Then we obtain an
expanded second-order gravity model after contraction that incorporates the
abelian internal symmetry. | Study on Noncommutative Representations of Galilean Generators: The representations of Galilean generators are constructed on a space where
both position and momentum coordinates are noncommutating operators. A
dynamical model invariant under noncommutative phase space transformations is
constructed. The Dirac brackets of this model reproduce the original
noncommutative algebra. Also, the generators in terms of noncommutative phase
space variables are abstracted from this model in a consistent manner. Finally,
the role of Jacobi identities is emphasised to produce the noncommuting
structure that occurs when an electron is subjected to a constant magnetic
field and Berry curvature. |
Intersecting branes and Supersymmetry: We consider intersecting M-brane solutions of supergravity in eleven
dimensions. Supersymmetry turns out to be a powerful tool in obtaining such
solutions and their generalizations. | Stability of QED: It is shown for a class of random, time-independent, square-integrable,
three-dimensional magnetic fields that the one-loop effective fermion action of
four-dimensional QED increases faster than a quadratic in B in the strong
coupling limit. The limit is universal. The result relies on the paramagnetism
of charged spin - 1/2 fermions and the diamagnetism of charged scalar bosons. |
Rational Theories of 2D Gravity from the Two-Matrix Model: The correspondence claimed by M. Douglas, between the multicritical regimes
of the two-matrix model and 2D gravity coupled to (p,q) rational matter field,
is worked out explicitly. We found the minimal (p,q) multicritical potentials
U(X) and V(Y) which are polynomials of degree p and q, correspondingly. The
loop averages W(X) and \tilde W(Y) are shown to satisfy the Heisenberg
relations {W,X} =1 and {\tilde W,Y}=1 and essentially coincide with the
canonical momenta P and Q. The operators X and Y create the two kinds of
boundaries in the (p,q) model related by the duality (p,q) - (q,p). Finally, we
present a closed expression for the two two-loop correlators and interpret its
scaling limit. | C-deformation of Supergravity: A four-dimensional supergravity toy model in an arbitrary self-dual
gravi-photon background is constructed in Euclidean space, by freezing out the
gravi-photon field strength in the standard N=(1,1) extended supergravity with
two non-chiral gravitini. Our model has local N=(1/2,0) supersymmetry.
Consistency of the model requires the background gravi-photon field strength to
be equal to the self-dual (bilinear) anti-chiral gravitino condensate. |
Radiation reaction reexamined: bound momentum and Schott term: We review and compare two different approaches to radiation reaction in
classical electrodynamics of point charges: a local calculation of the
self-force using the charge equation of motion and a global calculation
consisting in integration of the electromagnetic energy-momentum flux through a
hypersurface encircling the world-line. Both approaches are complementary and,
being combined together, give rise to an identity relating the locally and
globally computed forces. From this identity it follows that the Schott terms
in the Abraham force should arise from the bound field momentum and can not be
introduced by hand as an additional term in the mechanical momentum of an
accelerated charge. This is in perfect agreement with the results of Dirac and
Teitelboim, but disagrees with the recent calculation of the bound momentum in
the retarded coordinates. We perform an independent calculation of the bound
electromagnetic momentum and verify explicitly that the Schott term is the
derivative of the finite part of the bound momentum indeed. The failure to
obtain the same result using the method of retarded coordinates tentatively
lies in an inappropriate choice of the integration surface. We also discuss the
definition of the delta-function on the semi-axis involved in the local
calculation of the radiation reaction force and demonstrate inconsistency of
one recent proposal. | Gravitational Cheshire effect: Nonminimally coupled scalar fields may
not curve spacetime: It is shown that flat spacetime can be dressed with a real scalar field that
satisfies the nonlinear Klein-Gordon equation without curving spacetime.
Surprisingly, this possibility arises from the nonminimal coupling of the
scalar field with the curvature, since a footprint of the coupling remains in
the energy-momentum tensor even when gravity is switched off.
Requiring the existence of solutions with vanishing energy-momentum tensor
fixes the self-interaction potential as a local function of the scalar field
depending on two coupling constants. The solutions describe shock waves and, in
the Euclidean continuation, instanton configurations in any dimension. As a
consequence of this effect, the tachyonic solutions of the free massive
Klein-Gordon equation become part of the vacuum. |
Holographic Gauge Theory with Maxwell Magnetic Field: We first apply the transformation of mixing azimuthal with wrapped coordinate
to the 11D M-theory with a stack N M5-branes to find the spacetime of a stack
of N D4-branes with magnetic field in 10D IIA string theory, after the
Kaluza-Klein reduction. In the near-horizon limit the background becomes the
Melvin magnetic field deformed $AdS_6 \times S^4$. Although the solution
represents the D-branes under the Melvin RR one-form we use a simple
observation to see that it also describes the solution of D-branes under the
Maxwell magnetic field. As the magnetic field we consider is the part of the
background itself we have presented an alternative to previous literature,
because our method does not require the assumption of negligible back reaction.
Next, we use the found solution to investigate the meson property through D4/D8
system (Sakai-Sugimoto model) and compare it with those studied by other
authors. Finally, we present a detailed analysis about the Wilson loop therein
and results show that the external Maxwell magnetic field will enhance the
quark-antiquark potential. | Adinkra Isomorphisms and `Seeing' Shapes with Eigenvalues: We create an algorithm to determine whether any two graphical representations
(adinkras) of equations possessing the property of supersymmetry in one or two
dimensions are isomorphic in shape. The algorithm is based on the determinant
of `permutation matrices' that are defined in this work and derivable for any
adinkra. |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.