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Casimir Theory of the Relativistic Piecewise Uniform String: The Casimir energy for the transverse oscillations of a piecewise uniform
closed string is calculated. The string is relativistic in the sense that the
velocity of transverse waves is always equal to c. The great adaptibility of
this string model with respect to various regularization methods is pointed
out. We survey several regularization methods: the cutoff method, the complex
contour integration method, and the zeta-function method. The most powerful
method in the present case is the contour integration method. The Casimir
energy turns out to be negative, and the more so the larger is the number of
pieces in the string. The thermodynamic free energy F is calculated for a
two-piece string in the limit when the tension ratio x = T_I/T_II approaches
zero. For large values of the length ratio s = L_II/L_I, the Hagedorn
temperature becomes proportional to the square root of s.
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On quantum-mechanical equations of motion in representation dependent of
external sources: In the present paper, we consider in detail the aspects of the Heisenberg's
equations of motion, related to their transformation to the representation
dependent of external sources. We provide with a closed solution as to the
variation-derivative motion equations in the general case of a normal form
(symbol) chosen. We show that the action in the path integral does depend
actually on a particular choice of a normal symbol. We have determined both the
aspects of the latter dependence: the specific boundary conditions for virtual
trajectories, and the specific boundary terms in the action.
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A Metric for Gradient RG Flow of the Worldsheet Sigma Model Beyond First
Order: Tseytlin has recently proposed that an action functional exists whose
gradient generates to all orders in perturbation theory the Renormalization
Group (RG) flow of the target space metric in the worldsheet sigma model. The
gradient is defined with respect to a metric on the space of coupling constants
which is explicitly known only to leading order in perturbation theory, but at
that order is positive semi-definite, as follows from Perelman's work on the
Ricci flow. This gives rise to a monotonicity formula for the flow which is
expected to fail only if the beta function perturbation series fails to
converge, which can happen if curvatures or their derivatives grow large. We
test the validity of the monotonicity formula at next-to-leading order in
perturbation theory by explicitly computing the second-order terms in the
metric on the space of coupling constants. At this order, this metric is found
not to be positive semi-definite. In situations where this might spoil
monotonicity, derivatives of curvature become large enough for higher order
perturbative corrections to be significant.
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On the role of constraints and degrees of freedom in the Hamiltonian
formalism: Unfortunately, the Hamiltonian mechanics of degenerate Lagrangian systems is
usually presented as a mere recipe of Dirac, with no explanation as to how it
works. Then it comes to discussing conjectures of whether all primary
constraints correspond to gauge symmetries, and it goes all the way to
absolutely wrong claims such as the statement that electrodynamics or gravity
have only two physical components each, with others being spurious. One has to
be very careful because non-dynamical, or constrained, does not mean
unphysical. I give a pedagogical introduction to the degenerate Hamiltonian
systems, showing both very simple mechanical examples and general arguments
about how it works. For the familiar field theory models, I explain why the
gauge freedom there "hits twice" in the sense of producing twice as many
first-class constraints as gauge symmetries, and why primary, and only primary,
constraints should be put into the total Hamiltonian.
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Comment on Inflation and Alternative Cosmology: We respond to, and comment upon, a number of points raised in a recent paper
by Kofman, Linde, and Mukhanov.
|
The Grand View of Physics: Abdus Salam was known for his `grand views', grand views of science as well
as grand views of society. In this talk the grand view of theoretical physics
is put in perspective.
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Schwarzschild Fuzzball and Explicitly Unitary Hawking Radiations: We provide a fuzzball picture for Schwarzshild black holes, in which matters
and energy consisting the hole are not positioned on the central point
exclusively but oscillate around there in a serial of eigen-modes, each of
which features a special level of binding degrees and are quantum mechanically
possible to be measured outside the horizon. By listing these modes explicitly
for holes as large as $6M_\mathrm{pl}$, we find that their number increases
exponentially with the area. Basing on this picture, we present a simple but
explicitly unitary derivation of hawking radiations.
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Fusion multiplicities as polytope volumes: N-point and higher-genus
su(2) fusion: We present the first polytope volume formulas for the multiplicities of
affine fusion, the fusion in Wess-Zumino-Witten conformal field theories, for
example. Thus, we characterise fusion multiplicities as discretised volumes of
certain convex polytopes, and write them explicitly as multiple sums measuring
those volumes. We focus on su(2), but discuss higher-point (N>3) and
higher-genus fusion in a general way. The method follows that of our previous
work on tensor product multiplicities, and so is based on the concepts of
generalised Berenstein-Zelevinsky diagrams, and virtual couplings. As a
by-product, we also determine necessary and sufficient conditions for
non-vanishing higher-point fusion multiplicities. In the limit of large level,
these inequalities reduce to very simple non-vanishing conditions for the
corresponding tensor product multiplicities. Finally, we find the minimum level
at which the higher-point fusion and tensor product multiplicities coincide.
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Segmented Strings in $AdS_3$: We study segmented strings in flat space and in $AdS_3$. In flat space, these
well known classical motions describe strings which at any instant of time are
piecewise linear. In $AdS_3$, the worldsheet is composed of faces each of which
is a region bounded by null geodesics in an $AdS_2$ subspace of $AdS_3$. The
time evolution can be described by specifying the null geodesic motion of kinks
in the string at which two segments are joined. The outcome of collisions of
kinks on the worldsheet can be worked out essentially using considerations of
causality. We study several examples of closed segmented strings in $AdS_3$ and
find an unexpected quasi-periodic behavior. We also work out a WKB analysis of
quantum states of yo-yo strings in $AdS_3$ and find a logarithmic term
reminiscent of the logarithmic twist of string states on the leading Regge
trajectory.
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Local BCJ numerators for ten-dimensional SYM at one loop: We obtain local numerators satisfying the BCJ color-kinematics duality at one
loop for super-Yang-Mills theory in ten dimensions. This is done explicitly for
six points via the field-theory limit of the genus-one open superstring
correlators for different color orderings, in an analogous manner to an earlier
derivation of local BCJ-satisfying numerators at tree level from disk
correlators. These results solve an outstanding puzzle from a previous analysis
where the six-point numerators did not satisfy the color-kinematics duality.
|
Asymptotic level density in heterotic string theory and rotating black
holes: We calculate the density of states with given mass and spin in string theory
and obtain asymptotic formulas. We also compute the tree-level gyromagnetic
couplings for arbitrary physical states in the heterotic string theory. These
results are then applied to study whether fundamental strings can consistently
describe the microphysics of the black hole horizon in the case of a general
classical solution characterized by mass, charge and angular momentum.
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On Some Algebraic Structures Arising in String Theory: Lian and Zuckerman proved that the homology of a topological chiral algebra
can be equipped with the structure of a BV-algebra; \ie one can introduce a
multiplication, an odd bracket, and an odd operator $\Delta$ having the same
properties as the corresponding operations in Batalin-Vilkovisky quantization
procedure. We give a simple proof of their results and discuss a generalization
of these results to the non chiral case. To simplify our proofs we use the
following theorem giving a characterization of a BV-algebra in terms of
multiplication and an operator $\Delta$: {\em If $A$ is a supercommutative,
associative algebra and $\Delta$ is an odd second order derivation on $A$
satisfying $\Delta^2=0$, one can provide $A$ with the structure of a
BV-algebra.}
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An application of Cubical Cohomology to Adinkras and Supersymmetry
Representations: An Adinkra is a class of graphs with certain signs marking its vertices and
edges, which encodes off-shell representations of the super Poincar\'e algebra.
The markings on the vertices and edges of an Adinkra are cochains for cubical
cohomology. This article explores the cubical cohomology of Adinkras, treating
these markings analogously to characteristic classes on smooth manifolds.
|
Covariant Lagrange multiplier constrained higher derivative gravity with
scalar projectors: We formulate higher derivative gravity with Lagrange multiplier constraint
and scalar projectors. Its gauge-fixed formulation as well as vector fields
formulation is developed and corresponding spontaneous Lorentz symmetry
breaking is investigated. We show that the only propagating mode is higher
derivative graviton while scalar and vector modes do not propagate. Despite to
higher derivatives structure of the action, its first FRW equation is the first
order differential equation which admits the inflationary universe solution.
|
Differential Geometry on the Space of Connections via Graphs and
Projective Limits: In a quantum mechanical treatment of gauge theories (including general
relativity), one is led to consider a certain completion, $\agb$, of the space
$\ag$ of gauge equivalent connections. This space serves as the quantum
configuration space, or, as the space of all Euclidean histories over which one
must integrate in the quantum theory. $\agb$ is a very large space and serves
as a ``universal home'' for measures in theories in which the Wilson loop
observables are well-defined. In this paper, $\agb$ is considered as the
projective limit of a projective family of compact Hausdorff manifolds,
labelled by graphs (which can be regarded as ``floating lattices'' in the
physics terminology). Using this characterization, differential geometry is
developed through algebraic methods. In particular, we are able to introduce
the following notions on $\agb$: differential forms, exterior derivatives,
volume forms, vector fields and Lie brackets between them, divergence of a
vector field with respect to a volume form, Laplacians and associated heat
kernels and heat kernel measures. Thus, although $\agb$ is very large, it is
small enough to be mathematically interesting and physically useful. A key
feature of this approach is that it does not require a background metric. The
geometrical framework is therefore well-suited for diffeomorphism invariant
theories such as quantum general relativity.
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Ultraviolet Divergences and Scale-Dependent Gravitational Couplings: I review the field-theoretic renomalization group approach to quantum
gravity, built around the existence of a non-trivial ultraviolet fixed point in
four dimensions. I discuss the implications of such a fixed point, found in
three largely unrelated non-perturbative approaches, and how it relates to the
vacuum state of quantum gravity, and specifically to the running of $G$. One
distinctive feature of the new fixed point is the emergence of a second
genuinely non-perturbative scale, analogous to the scaling violation parameter
in non-abelian gauge theories. I argue that it is natural to identify such a
scale with the small observed cosmological constant, which in quantum gravity
can arise as a non-perturbative vacuum condensate.
(Plenary Talk, 12-th Marcel Grossmann Conference on Recent Developments in
General Relativity, Astrophysics and Relativistic Field Theories, UNESCO Paris,
July 12-18, 2009).
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Duality-invariant Quantum Field Theories of Charges and Monopoles: We present a manifestly Lorentz- and SO(2)-Duality-invariant local Quantum
Field Theory of electric charges, Dirac magnetic monopoles and dyons. The
manifest invariances are achieved by means of the PST-mechanism. The dynamics
for classical point particles is described by an action functional living on a
circle, if the Dirac-Schwinger quantization condition for electric and magnetic
charges holds. The inconsistent classical field theory depends on an arbitrary,
but fixed, external vector field, a generalization of the Dirac-string.
Nevertheless, the Quantum Field Theory, obtained from this classical action via
a functional integral approach, turns out to be independent of the particular
vector field chosen, and thus consistent, if the Dirac-Schwinger quantization
condition holds. We provide explicit expressions for the generating functionals
of observables, proving that they are Dirac-string independent. Since
Lorentz-invariance is manifest at each step, the quantum theory admits also a
manifestly diffeomorphism invariant coupling to external gravity. Relations
with previous formulations, and with SO(2)--non invariant theories are
clarified.
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$Λ$ Scattering Equations: The CHY representation of scattering amplitudes is based on integrals over
the moduli space of a punctured sphere. We replace the punctured sphere by a
double-cover version. The resulting scattering equations depend on a parameter
$\Lambda$ controlling the opening of a branch cut. The new representation of
scattering amplitudes possesses an enhanced redundancy which can be used to
fix, modulo branches, the location of four punctures while promoting $\Lambda$
to a variable. Via residue theorems we show how CHY formulas break up into sums
of products of smaller (off-shell) ones times a propagator. This leads to a
powerful way of evaluating CHY integrals of generic rational functions, which
we call the $\Lambda$ algorithm.
|
Calabi-Yau threefolds with large h^{2, 1}: We carry out a systematic analysis of Calabi-Yau threefolds that are
elliptically fibered with section ("EFS") and have a large Hodge number h^{2,
1}. EFS Calabi-Yau threefolds live in a single connected space, with regions of
moduli space associated with different topologies connected through transitions
that can be understood in terms of singular Weierstrass models. We determine
the complete set of such threefolds that have h^{2, 1} >= 350 by tuning
coefficients in Weierstrass models over Hirzebruch surfaces. The resulting set
of Hodge numbers includes those of all known Calabi-Yau threefolds with h^{2,
1} >= 350, as well as three apparently new Calabi-Yau threefolds. We speculate
that there are no other Calabi-Yau threefolds (elliptically fibered or not)
with Hodge numbers that exceed this bound. We summarize the theoretical and
practical obstacles to a complete enumeration of all possible EFS Calabi-Yau
threefolds and fourfolds, including those with small Hodge numbers, using this
approach.
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A supersymmetric Skyrme model: Construction of a supersymmetric extension of the Skyrme term was a
long-standing problem because of the auxiliary field problem; that is, the
auxiliary field may propagate and cannot be eliminated, and the problem of
having fourth-order time derivative terms. In this paper, we construct for the
first time a supersymmetric extension of the Skyrme term in four spacetime
dimensions, in the manifestly supersymmetric superfield formalism that does not
suffer from the auxiliary field problem. Chiral symmetry breaking in
supersymmetric theories results not only in Nambu-Goldstone (NG) bosons (pions)
but also in the same number of quasi-NG bosons so that the low-energy theory is
described by an SL(N,C)-valued matrix field instead of SU(N) for NG bosons. The
solution of auxiliary fields is trivial on the canonical branch of the
auxiliary field equation, in which case our model results in a fourth-order
derivative term that is not the Skyrme term. For the case of SL(2,C), we find
explicitly a nontrivial solution to the algebraic auxiliary field equations
that we call a non-canonical branch, which when substituted back into the
Lagrangian gives a Skyrme-like model. If we restrict to a submanifold, where
quasi-NG bosons are turned off, which is tantamount to restricting the Skyrme
field to SU(2), then the fourth-order derivative term reduces exactly to the
standard Skyrme term. Our model is the first example of a nontrivial auxiliary
field solution in a multi-component model.
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Observables and amplitudes for spinning particles and black holes: We develop a general formalism for computing classical observables for
relativistic scattering of spinning particles, directly from on-shell
amplitudes. We then apply this formalism to minimally coupled Einstein-gravity
amplitudes for the scattering of massive spin 1/2 and spin 1 particles with a
massive scalar, constructed using the double copy. In doing so we reproduce
recent results at first post-Minkowskian order for the scattering of spinning
black holes, through quadrupolar order in the spin-multipole expansion.
|
Superstring action in AdS_5 x S^5: kappa symmetry light cone gauge: As part of program to quantize superstrings in AdS_5 x S^5 background in
light cone approach we find the explicit form of the corresponding
Green-Schwarz action in fermionic light-cone kappa-symmetry gauge. The
resulting action is quadratic and quartic in fermions. In the flat space limit
it reduces to the standard light-cone Green-Schwarz action, and also has the
correct superparticle limit. We discuss fixing the bosonic light-cone gauge and
a reformulation of the action in terms of 2-d Dirac spinors.
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A Holographic form for Wilson's RG: An attempt is made to make precise the connection between Wilson's RG and
"Holographic RG" by writing Wilson's RG in a holographic form. A functional
formulation is given for the exact RG evolution of a scalar field in $d$ (flat)
dimensions. It is shown that a change of variables maps the action to that for
a scalar field in $AdS_{d+1}$. This provides a holographic form for Wilson's RG
that can be called "Holographic RG". This mapping can only be done for a
specific form of the cutoff function in the Exact Renormalization Group
formalism. The notion of scale and conformal invariance in the presence of a
{\em finite} UV cutoff is emphasized. The discussion is primarily about the
two-point function and the Gaussian fixed point. Some remarks are made about
nontrivial fixed points.
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RS1, Higher Derivatives and Stability: We demonstrate the classical stability of the weak/Planck hierarchy within
the Randall-Sundrum scenario, incorporating the Goldberger-Wise mechanism and
higher-derivative interactions in a systematic perturbative expansion. Such
higher-derivative interactions are expected if the RS model is the low-energy
description of some more fundamental theory. Generically, higher derivatives
lead to ill-defined singularities in the vicinity of effective field theory
branes. These are carefully treated by the methods of classical
renormalization.
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Solving CFTs with Weakly Broken Higher Spin Symmetry: The method of large spin perturbation theory allows to analyse conformal
field theories (CFT) by turning the crossing equations into an algebraic
problem. We apply this method to a generic CFT with weakly broken higher spin
(HS) symmetry, to the first non-trivial order in the breaking parameter. We
show that the spectrum of broken currents, for any value of the spin, follows
from crossing symmetry. After discussing a generic model of a single scalar
field, we focus on vector models with $O(N)$ global symmetry. We rediscover the
spectrum of several models, including the $O(N)$ Wilson-Fisher model around
four dimensions, the large $O(N)$ model in $2<d<4$ and cubic models around six
dimensions, not necessarily unitary. We also discuss models where the
fundamental field is not part of the spectrum. Examples of this are weakly
coupled gauge theories and our method gives an on-shell gauge invariant way to
study them. At first order in the coupling constant we show that again the
spectrum follows from crossing symmetry, to all values of the spin. Our method
provides an alternative to usual perturbation theory without any reference to a
Lagrangian.
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Logarithmic correction to the entropy of extremal black holes in
$\mathcal{N}=1$ Einstein-Maxwell supergravity: We study one-loop covariant effective action of \say{non-minimally coupled}
$\mathcal{N}=1$, $d=4$ Einstein-Maxwell supergravity theory by heat kernel
tool. By fluctuating the fields around the classical background, we study the
functional determinant of Laplacian differential operator following
Seeley-DeWitt technique of heat kernel expansion in proper time. We then
compute the Seeley-DeWitt coefficients obtained through the expansion. A
particular Seeley-DeWitt coefficient is used for determining the logarithmic
correction to Bekenstein-Hawking entropy of extremal black holes using quantum
entropy function formalism. We thus determine the logarithmic correction to the
entropy of Kerr-Newman, Kerr and Reissner-Nordstr\"{o}m black holes in
{\say{non-minimally coupled}} $\mathcal{N}=1$, $d=4$ Einstein-Maxwell
supergravity theory.
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Why the Cosmological Constant Problem is Hard: We consider a recent proposal to solve the cosmological constant problem
within the context of brane world scenarios with infinite volume extra
dimensions. In such theories bulk can be supersymmetric even if brane
supersymmetry is completely broken. The bulk cosmological constant can
therefore naturally be zero. Since the volume of the extra dimensions is
infinite, it might appear that at large distances one would measure the bulk
cosmological constant which vanishes. We point out a caveat in this argument.
In particular, we use a concrete model, which is a generalization of the
Dvali-Gabadadze-Porrati model, to argue that in the presence of non-zero brane
cosmological constant at large distances such a theory might become effectively
four dimensional. This is due to a mass gap in the spectrum of bulk graviton
modes. In fact, the corresponding distance scale is set precisely by the brane
cosmological constant. This phenomenon appears to be responsible for the fact
that bulk supersymmetry does not actually protect the brane cosmological
constant.
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New Insight into the Relation between Torsion and Electromagnetism: In several unified field theories the torsion trace is set equal to the
electromagnetic potential. Using fibre bundle techniques we show that this is
no leading principle but a formal consequence of another geometric relation
between space-time and electromagentism.
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Low-Energy Dynamics of String Solitons: The dynamics of a class of fivebrane string solitons is considered in the
moduli space approximation. The metric on moduli space is found to be flat.
This implies that at low energies the solitons do not interact, and their
scattering is trivial. The range of validity of the approximation is also
briefly discussed.
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IR Dynamics on Branes and Space-Time Geometry: We consider the type I theory compactified on $T^3$. When the D5-brane wraps
the $T^3$ it yields a D2-brane in seven dimensions. In the leading
approximation the moduli space of vacua of the three dimensional field theory
on the brane is $T^4/\ZZ_2$. The dual M theory description of this theory is a
compactification on K3 and our 2-brane is the eleven dimensional 2-brane at a
point in K3. We use this fact to conclude that strong coupling IR effects in
the three dimensional theory on the brane turn its moduli space into a K3. This
interpretation allows us to solve various strongly coupled gauge theories in
three dimensions by identifying their Coulomb branch with a piece of a
(sometime singular) K3.
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Summing one- and two-dimensional series related to the Euler series: We present results for some infinite series appearing in Feynman diagram
calculations, many of which are similar to the Euler series. These include both
one-dimensional and two-dimensional series. Most of these series can be
expressed in terms of zeta(2), zeta(3), the Catalan constant G and Cl{2}(pi/3)
where Cl{2}(theta) is Clausen's function.
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A comment on a fine-grained description of evaporating black holes with
baby universes: We study a partially fine-grained description of an evaporating black hole by
introducing an open baby universe with a boundary. Since the Page's calculation
of the entropy of Hawking radiation involves an ensemble average over a class
of states, one can formally obtain a fine-grained state by purifying this
setup. For AdS black holes with a holographic dual, this purification amounts
to introducing an additional boundary (i.e., baby universe) and then connecting
it to the original black hole through an Einstein-Rosen bridge. We uncover
several details of this setup. As applications, we briefly discuss how this
baby universe modifies the semi-classical gravitational Gauss law as well as
the gravitational dressing of operators behind the horizon.
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A Quantum Gravitational Relaxation of The Cosmological Constant: Similar to QCD, general relativity has a $\Theta$ sector due to large
diffeomorphisms. We make explicit, for the first time, that the gravitational
CP violating $\Theta$ parameter is non-perturbatively related to the
cosmological constant. A gravitational pseudoscalar coupling to massive
fermions gives rise to general relativity from a topological $B\wedge F$ theory
through a chiral symmetry breaking mechanism. We show that a gravitational
Peccei-Quinn like mechanism can dynamically relax the cosmological constant.
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Open String Fields as Matrices: We show that the action expanded around Erler-Maccaferri's N D-brane solution
describes the N+1 D-brane system where one D-brane disappears due to tachyon
condensation. String fields on multi-branes can be regarded as block matrices
of a string field on a single D-brane in the same way as matrix theories.
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Branes, AdS gravitons and Virasoro symmetry: We consider travelling waves propagating on the anti-de Sitter (AdS)
background. It is pointed out that for any dimension d, this space of solutions
has a Virasoro symmetry with a non-zero central charge. This result is a
natural generalization to higher dimensions of the three-dimensional
Brown-Henneaux symmetry.
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On the Spectrum of Superspheres: Sigma models on coset superspaces, such as odd dimensional superspheres, play
an important role in physics and in particular the AdS/CFT correspondence. In
this work we apply recent general results on the spectrum of coset space models
and on supergroup WZNW models to study the conformal sigma model with target
space S^{3|2}. We construct its vertex operators and provide explicit formulas
for their anomalous dimensions, at least to leading order in the sigma model
coupling. The results are used to revisit a non-perturbative duality between
the supersphere and the OSP(4|2) Gross-Neveu model that was conjectured by
Candu and Saleur. With the help of powerful all-loop results for 1/2 BPS
operators in the Gross-Neveu model we are able to recover the entire zero mode
spectrum of the sigma model at a certain finite value of the Gross-Neveu
coupling. In addition, we argue that the sigma model constraints and equations
of motion are implemented correctly in the dual Gross-Neveu description. On the
other hand, high(er) gradient operators of the sigma model are not all
accounted for. It is possible that this discrepancy is related to an
instability from high gradient operators that has previously been observed in
the context of Anderson localization.
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q-Electroweak, q-Gravity, and Knotted Solitons: If the Lie group of a non-Abelian theory is replaced by the corresponding
q-group, one is led to replace the Lie algebra by two dual algebras. The first
of these lies close to the Lie algebra that it is replacing while the second
introduces new degrees of freedom. We interpret the theory based on the first
algebra as a modification of standard field theory while we propose that the
new degrees of freedom introduced by the second algebra describe solitonic
rather than point particle sources. We have earlier found that the modified
q-electroweak theory differs very little from the standard theory. Here we find
a similar result for q-gravity. Both of the modified theories are incomplete,
however, and must be completed by the solitonic sector. We propsoe that the
solitonic sector of both q-electroweak and q-gravity have the symmetry of knots
associated with SU_q(2). Since the Lorentz group is here deformed, there is no
longer the standard classification of particles described by mass and spin.
There is instead a classification of irreducible structures determined by
SU_q(2).
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Non-universal corrections to the tension ratios in softly broken N=2
SU(N) gauge theory: Calculation by Douglas and Shenker of the tension ratios for vortices of
different N-alities in the softly broken N=2 supersymmetric SU(N) Yang-Mills
theory, is carried to the second order in the adjoint multiplet mass m.
Corrections to the ratios violating the well-known sine formula are found,
showing that it is not a universal quantity.
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Holography, Hydrodynamization and Heavy-Ion Collisions: In the course of the past several years holography has emerged as an ab
initio tool in exploring strongly-time-dependent phenomena in gauge theories.
These lecture notes overview recent developments in this area driven by
phenomenological questions concerning applicability of hydrodynamics
(hydrodynamization) under extreme conditions occurring in ultrarelativistic
heavy-ion collisions at RHIC and LHC. The topics include hydrodynamization time
scale, holographic collisions, as well as hydrodynamization from the point of
view of the asymptotic character of the hydrodynamic gradient expansion. The
emphasis is put on concepts rather than calculational techniques and a
particular attention is devoted to present these developments in the context of
the most recent advances and some of the open problems.
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Massive graviton from diffeomorphism invariance: We describe a mechanism in which the graviton acquires a mass from the
functional measure without violating the diffeomorphism symmetry nor including
St\"uckelberg fields. Since gauge invariance is not violated, the number of
degrees of freedom goes as in general relativity. For the same reason,
Boulware-Deser ghosts and the vDVZ disconinuity do not show up. The graviton
thus becomes massive at the quantum level while avoiding the usual issues of
massive gravity.
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Presymplectic minimal models of local gauge theories: We elaborate on the recently proposed notion of a weak presymplectic gauge
PDE. It is a $\mathbb{Z}$-graded bundle over the space-time manifold, equipped
with a degree $1$ vector field and a compatible graded presymplectic structure.
This geometrical data naturally defines a Lagrangian gauge field theory.
Moreover, it encodes not only the Lagrangian of the theory but also its
full-scale Batalin-Vilkovisky (BV) formulation. In particular, the respective
field-antifield space arises as a symplectic quotient of the super-jet bundle
of the initial fiber bundle. A remarkable property of this approach is that
among the variety of presymplectic gauge PDEs encoding a given gauge theory we
can pick a minimal one that usually turns out to be finite-dimensional, and
unique in a certain sense. The approach can be considered as an extension of
the familiar AKSZ construction to not necessarily topological and
diffeomorphism-invariant theories. We present a variety of examples including
$p$-forms, chiral Yang-Mills theory, Holst gravity, and conformal gravity. We
also explain the explicit relation to the non-BV-BRST version of the formalism,
which happens to be closely related to the covariant phase space and the
multisymplectic approaches.
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Magnetic Photon Splitting: the S-Matrix Formulation in the Landau
Representation: Calculations of reaction rates for the third-order QED process of photon
splitting in strong magnetic fields traditionally have employed either the
effective Lagrangian method or variants of Schwinger's proper-time technique.
Recently, Mentzel, Berg and Wunner (1994) presented an alternative derivation
via an S-matrix formulation in the Landau representation. Advantages of such a
formulation include the ability to compute rates near pair resonances above
pair threshold. This paper presents new developments of the Landau
representation formalism as applied to photon splitting, providing significant
advances beyond the work of Mentzel et al. by summing over the spin quantum
numbers of the electron propagators, and analytically integrating over the
component of momentum of the intermediate states that is parallel to field. The
ensuing tractable expressions for the scattering amplitudes are satisfyingly
compact, and of an appearance familiar to S-matrix theory applications. Such
developments can facilitate numerical computations of splitting considerably
both below and above pair threshold. Specializations to two regimes of interest
are obtained, namely the limit of highly supercritical fields and the domain
where photon energies are far inferior to that for the threshold of
single-photon pair creation. In particular, for the first time the
low-frequency amplitudes are simply expressed in terms of the Gamma function,
its integral and its derivatives. In addition, the equivalence of the
asymptotic forms in these two domains to extant results from effective
Lagrangian/proper-time formulations is demonstrated.
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Holography and the Page curve of an evaporating black hole: We consider a radiating black hole with a holographic dual such that its
entanglement entropy does not exceed the Bekenstein-Hawking entropy, to obtain
a Page curve. We make use of some mathematical identities that should be held
for the entanglement entropy to be well-defined. This work is not going to give
a resolution to the information paradox. Rather it shows that the general shape
of the Page curve is a consequence of holography, independent of the details of
gravitation theory.
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New Formulations of D=10 Supersymmetry and D8-O8 Domain Walls: We discuss a generalized form of IIA/IIB supergravity depending on all R-R
potentials C^(p) (p=0,1,...,9) as the effective field theory of Type IIA/IIB
superstring theory. For the IIA case we explicitly break this R-R democracy to
either p<=3 or p>=5 which allows us to write a new bulk action that can be
coupled to N=1 supersymmetric brane actions.
The case of 8-branes is studied in detail using the new bulk & brane action.
The supersymmetric negative tension branes without matter excitations can be
viewed as orientifolds in the effective action. These D8-branes and O8-planes
are fundamental in Type I' string theory. A BPS 8-brane solution is given which
satisfies the jump conditions on the wall. It implies a quantization of the
mass parameter in string units. Also we find a maximal distance between the two
walls, depending on the string coupling and the mass parameter. We derive the
same results via supersymmetric flow equations.
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The Interface of Cosmology with String and M(ILLENNIUM) Theory: The purpose of this review is to discuss recent developments occurring at the
interface of cosmology with string and M-theory. We begin with a short review
of 1980s string cosmology and the Brandenberger-Vafa mechanism for explaining
spacetime dimensionality. It is shown how this scenario has been modified to
include the effects of p-brane gases in the early universe. We then introduce
the Pre-Big-Bang scenario (PBB), Ho\v{r}ava-Witten heterotic M-theory and the
work of Lukas, Ovrut and Waldram, and end with a discussion of large extra
dimensions, the Randall-Sundrum model and Brane World cosmologies.
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Nonextensive entropies impact onto thermodynamics and phase structure of
Kerr-Newman black holes: Taking the nonextensive Tsallis and R\'enyi entropies into account, we
explore thermodynamic properties and phase transitions of the Kerr-Newman black
holes (KNBH) in the microcanonical and canonical ensembles. We also compare our
results with those obtained by attributing the Bekenstein-Hawking entropy bound
to the mentioned black holes. Our analysis indicates that, similarly to the
standard Boltzmann picture, isolated KNBH in the microcanonical approach are
stable against axisymmetric perturbations in both Tsallis and R\'enyi models.
On the other hand, in considering the case when the black holes are enveloped
by a bath of thermal radiation in the canonical treatment, the KNBH based on
the Tsallis and R\'enyi entropies can be stable for some values of the entropy
parameters, in contrast to the traditional Boltzmann framework. For the case of
R\'enyi entropy, we find that a Hawking-Page transition and a first order small
black hole/large black hole transition can occur in a similar fashion as in
rotating black holes in an anti-de Sitter space. Finally, we employ the
Ruppeneir geometrothermodynamic technique to provide a new perspective on
studying the nature of interactions between black hole microstructures,
revealing a non-trivial impact of nonextensive entropies.
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Non-BPS D-brane Near NS5-branes: We use tachyon field theory effective action to study the dynamics of a
non-BPS Dp-brane propagating in the vicinity of k NS5-branes. For the time
dependent tachyon condensation we will concentrate on the case of the large
tachyon and the case when a non-BPS D-brane is close to NS5-branes. For spatial
dependent tachyon condensation we will argue that the problem reduces to the
study of the motion of an array of D(p-1)-branes and D(p-1)-antibranes in the
vicinity of k NS5-branes.
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Dynamical Conifold Transitions and Moduli Trapping in M-Theory Cosmology: We study five-dimensional Kasner cosmologies in the vicinity of a conifold
locus occurring in a time-dependent Calabi-Yau compactification of M-theory.
The dynamics of M2-brane winding modes, which become light in this region, is
taken into account using a suitable gauged supergravity action. We find
cosmological solutions which interpolate between the two branches of the
transition, establishing that conifold transitions can be realized dynamically.
However, generic solutions do not correspond to transitions, but to the moduli
getting trapped close to the conifold locus. This effect results from an
interplay between the scalar potential and Hubble friction. We show that the
dynamics does not depend on the details of the potential, but only on its
overall shape.
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Soliton stability in some knot soliton models: We study the issue of stability of static soliton-like solutions in some
non-linear field theories which allow for knotted field configurations.
Concretely, we investigate the AFZ model, based on a Lagrangian quartic in
first derivatives with infinitely many conserved currents, for which infinitely
many soliton solutions are known analytically. For this model we find that
sectors with different (integer) topological charge (Hopf index) are not
separated by an infinite energy barrier. Further, if variations which change
the topological charge are allowed, then the static solutions are not even
critical points of the energy functional. We also explain why soliton solutions
can exist at all, in spite of these facts. In addition, we briefly discuss the
Nicole model, which is based on a sigma-model type Lagrangian. For the Nicole
model we find that different topological sectors are separated by an infinite
energy barrier.
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Simplifying Multiloop Integrands and Ultraviolet Divergences of Gauge
Theory and Gravity Amplitudes: We use the duality between color and kinematics to simplify the construction
of the complete four-loop four-point amplitude of N=4 super-Yang-Mills theory,
including the nonplanar contributions. The duality completely determines the
amplitude's integrand in terms of just two planar graphs. The existence of a
manifestly dual gauge-theory amplitude trivializes the construction of the
corresponding N=8 supergravity integrand, whose graph numerators are double
copies (squares) of the N=4 super-Yang-Mills numerators. The success of this
procedure provides further nontrivial evidence that the duality and double-copy
properties hold at loop level. The new form of the four-loop four-point
supergravity amplitude makes manifest the same ultraviolet power counting as
the corresponding N=4 super-Yang-Mills amplitude. We determine the amplitude's
ultraviolet pole in the critical dimension of D=11/2, the same dimension as for
N=4 super-Yang-Mills theory. Strikingly, exactly the same combination of vacuum
integrals (after simplification) describes the ultraviolet divergence of N=8
supergravity as the subleading-in-1/N_c^2 single-trace divergence in N=4
super-Yang-Mills theory.
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Planar scattering amplitudes from Wilson loops: We derive an expression for parton scattering amplitudes of planar gauge
theory in terms of sums of Wilson loops. We study in detail the example of
Yang-Mills theory with an adjoint Higgs field. The expression exhibits the
T-duality performed by Alday and Maldacena in the AdS dual as a Fourier
transform in loop space. When combined with the AdS/CFT correspondence for
Wilson loops and a strong coupling argument for the dominance of 1PI diagrams,
this leads to a derivation of the Alday-Maldacena holographic prescription for
scattering amplitudes in terms of momentum Wilson loops. The formula leads to a
conjecture for a relationship between position-space and momentum-space Wilson
loops in N=4 SYM at finite coupling.
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Space and time dimensions of algebras with applications to Lorentzian
noncommutative geometry and quantum electrodynamics: An analogy with real Clifford algebras on even-dimensional vector spaces
suggests to assign a couple of space and time dimensions modulo 8 to any
algebra (represented over a complex Hilbert space) containing two self-adjoint
involutions and an anti-unitary operator with specific commutation relations.
It is shown that this assignment is compatible with the tensor product: the
space and time dimensions of the tensor product are the sums of the space and
time dimensions of its factors. This could provide an interpretation of the
presence of such algebras in PT-symmetric Hamiltonians or the description of
topological matter.
This construction is used to build an indefinite (i.e. pseudo-Riemannian)
version of the spectral triples of noncommutative geometry, defined over Krein
spaces instead of Hilbert spaces. Within this framework, we can express the
Lagrangian (both bosonic and fermionic) of a Lorentzian almost-commutative
spectral triple. We exhibit a space of physical states that solves the
fermion-doubling problem. The example of quantum electrodynamics is described.
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String integrability of defect CFT and dynamical reflection matrices: The D3-D5 probe-brane system is holographically dual to a defect CFT which is
known to be integrable. The evidence comes mainly from the study of correlation
functions at weak coupling. In the present work we shed light on the emergence
of integrability on the string theory side. We do so by constructing the double
row transfer matrix which is conserved when the appropriate boundary conditions
are imposed. The corresponding reflection matrix turns out to be dynamical and
depends both on the spectral parameter and the string embedding coordinates.
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Low energy effective theory for two branes system: We derive the low energy effective theory for two branes system solving the
bulk geometry formally in the covariant curvature formalism developed by
Shiromizu, Maeda and Sasaki. As expected, the effective theory looks like a
Einstein-scalar system. Using this theory we can discuss the cosmology and
non-linear gravity at low energy scales.
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Phenomenology in minimal theory of massive gravity: We investigate the minimal theory of massive gravity (MTMG) recently
introduced. After reviewing the original construction based on its Hamiltonian
in the vielbein formalism, we reformulate it in terms of its Lagrangian in both
the vielbein and the metric formalisms. It then becomes obvious that, unlike
previous attempts in the literature of Lorentz-violating massive gravity, not
only the potential but also the kinetic structure of the action is modified
from the de Rham-Gabadadze-Tolley (dRGT) massive gravity theory. We confirm
that the number of physical degrees of freedom in MTMG is two at fully
nonlinear level. This proves the absence of various possible pathologies such
as superluminality, acausality and strong coupling. Afterwards, we discuss the
phenomenology of MTMG in the presence of a dust fluid. We find that on a flat
homogeneous and isotropic background we have two branches. One of them
(self-accelerating branch) naturally leads to acceleration without the genuine
cosmological constant or dark energy. For this branch both the scalar and the
vector modes behave exactly as in general relativity (GR). The phenomenology of
this branch differs from GR in the tensor modes sector, as the tensor modes
acquire a non-zero mass. Hence, MTMG serves as a stable nonlinear completion of
the self-accelerating cosmological solution found originally in dRGT theory.
The other branch (normal branch) has a dynamics which depends on the
time-dependent fiducial metric. For the normal branch, the scalar mode sector,
even though as in GR only one scalar mode is present (due to the dust fluid),
differs from the one in GR, and, in general, structure formation will follow a
different phenomenology. The tensor modes will be massive, whereas the vector
modes, for both branches, will have the same phenomenology as in GR.
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One loop radiative corrections to the translation-invariant
noncommutative Yukawa Theory: We elaborate in this paper a translation-invariant model for fermions in
4-dimensional noncommutative Euclidean space. The construction is done on the
basis of the renormalizable noncommutative translation-invariant Phi4 theory
introduced by R. Gurau et al. We combine our model with the scalar model, in
order to study the noncommutative pseudo-scalar Yukawa theory. After we derive
the Feynman rules of the theory, we perform an explicit calculation of the
quantum corrections at one loop level to the propagators and vertices.
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Corner symmetry and quantum geometry: By virtue of the Noether theorems, the vast gauge redundancy of general
relativity provides us with a rich algebra of boundary charges that generate
physical symmetries. These charges are located at codimension-2 entangling
surfaces called corners. The presence of non-trivial corner symmetries
associated with any entangling cut provides stringent constraints on the
theory's mathematical structure and a guide through quantization. This report
reviews new and recent results for non-perturbative quantum gravity, which are
natural consequences of this structure. First, we establish that the corner
symmetry derived from the gauge principle encodes quantum entanglement across
internal boundaries. We also explain how the quantum representation of the
corner symmetry algebra provides us with a notion of quantum geometry. We then
focus our discussion on the first-order formulation of gravity and show how
many results obtained in the continuum connect naturally with previous results
in loop quantum gravity. In particular, we show that it is possible to get,
purely from quantization and without discretization, an area operator with
discrete spectrum, which is covariant under local Lorentz symmetry. We
emphasize that while loop gravity correctly captures some of the gravitational
quantum numbers, it does not capture all of them, which points towards
important directions for future developments. Finally, we discuss the
understanding of the gravitational dynamics along null surfaces as a
conservation of symmetry charges associated with a Carrollian fluid.
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From Feynman graphs to Witten diagrams: We investigate the possibility of generalizing Gopakumar's microscopic
derivation [1] of Witten diagrams in large N free quantum field theory to
interacting theories. For simplicity we consider a massless, matrix valued real
scalar field with $\Phi^h$ interaction in d-dimensions. Using Schwinger's
proper time formulation and organizing the sum over Feynman graphs by the
number of loops $\ell$, we show that the two-point function can be expressed as
a sum over boundary-to-boundary propagators of bulk scalars in $AdS_{d+1}$ with
mass determined by $\ell$.
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Effective Field Theories of Post-Newtonian Gravity: A comprehensive
review: [Abridged] This review article presents the progress made over the last
decade, since the introduction of effective field theories (EFTs) into
post-Newtonian (PN) gravity. These have been put forward in the context of
gravitational waves (GWs) from the compact binary inspiral. The mature
development of this interdisciplinary field has resulted in significant
advances of wide interest to physics at several levels serving various
purposes. The field has firmly demonstrated, that seemingly disparate physical
domains, such as quantum field theory and classical gravity, are related, and
that the EFT framework is a universal one, where it has been proven to supply a
robust methodology to boost progress in the development of PN theory. The
review is aimed at a broad audience, from general readers new to the field, to
specialists and experts in related subjects.
The review begins with an overview of the introduction of EFTs into classical
gravity and their development. Then, the basic ideas, which form the conceptual
foundation of EFTs, are provided, and the strategy of a multi-stage EFT
framework, which is utilized for the PN binary inspiral problem, is outlined.
The main body of the review is then dedicated to presenting in detail the study
of each of the effective theories at each of the intermediate scales in the
problem, up to the actual GW observables. The review is concluded with the
multiple prospects of building on the progress in the field, and using further
modern field theory insights and tools, to specifically address the study of
GWs, as well as to broadly expand our fundamental understanding of gauge and
gravity theories across the classical and quantum regimes.
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Positivity, entanglement entropy, and minimal surfaces: The path integral representation for the Renyi entanglement entropies of
integer index n implies these information measures define operator correlation
functions in QFT. We analyze whether the limit $n\rightarrow 1$, corresponding
to the entanglement entropy, can also be represented in terms of a path
integral with insertions on the region's boundary, at first order in $n-1$.
This conjecture has been used in the literature in several occasions, and
specially in an attempt to prove the Ryu-Takayanagi holographic entanglement
entropy formula. We show it leads to conditional positivity of the entropy
correlation matrices, which is equivalent to an infinite series of polynomial
inequalities for the entropies in QFT or the areas of minimal surfaces
representing the entanglement entropy in the AdS-CFT context. We check these
inequalities in several examples. No counterexample is found in the few known
exact results for the entanglement entropy in QFT. The inequalities are also
remarkable satisfied for several classes of minimal surfaces but we find
counterexamples corresponding to more complicated geometries. We develop some
analytic tools to test the inequalities, and as a byproduct, we show that
positivity for the correlation functions is a local property when supplemented
with analyticity. We also review general aspects of positivity for large N
theories and Wilson loops in AdS-CFT.
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Einstein-Yang-Mills theory : I. Asymptotic symmetries: Asymptotic symmetries of the Einstein-Yang-Mills system with or without
cosmological constant are explicitly worked out in a unified manner. In
agreement with a recent conjecture, one finds a Virasoro-Kac-Moody type algebra
not only in three dimensions but also in the four dimensional asymptotically
flat case.
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Smeared and unsmeared chiral vertex operators: We prove unboundedness and boundedness of the unsmeared and smeared chiral
vertex operators, respectively. We use elementary methods in bosonic Fock
space, only. Possible applications to conformal two - dimensional quantum field
theory, perturbation thereof, and to the perturbative construction of the
sine-Gordon model by the Epstein-Glaser method are discussed. From another
point of view the results of this paper can be looked at as a first step
towards a Hilbert space interpretation of vertex operator algebras.
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Bulk scalar emission from a rotating black hole pierced by a tense brane: We study the emission of scalar fields into the bulk from a six-dimensional
rotating black hole pierced by a 3-brane. We determine the angular eigenvalues
in the presence of finite brane tension by using the continued fraction method.
The radial equation is integrated numerically, giving the absorption
probability (graybody factor) in a wider frequency range than in the
preexisting literature. We then compute the power and angular momentum emission
spectra for different values of the rotation parameter and brane tension, and
compare their relative behavior in detail. As is expected from the earlier
result for a nonrotating black hole, the finite brane tension suppresses the
emission rates. As the rotation parameter increases, the power spectra are
reduced at low frequencies due to the smaller Hawking temperature and are
enhanced at high frequencies due to superradiance. The angular momentum spectra
are enhanced over the whole frequency range as the rotation parameter
increases. The spectra and the amounts of energy and angular momentum radiated
away into the bulk are thus determined by the interplay of these effects.
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Pure-Higgs states from the Lefschetz-Sommese theorem: We consider a special class of N=4 quiver quantum mechanics relevant in the
description of BPS states of D4D0 branes in type II Calabi-Yau
compactifications and the corresponding 4-dimensional black holes. These
quivers have two abelian nodes in addition to an arbitrary number of
non-abelian nodes and satisfy some simple but stringent conditions on the set
of arrows, in particular closed oriented loops are always present. The Higgs
branch can be described as the vanishing locus of a section of a vector bundle
over a product of a projective space with a number of Grassmannians. The
Lefschetz-Sommese theorem then allows to separate induced from singular
cohomology which leads to the notion of pure-Higgs states. We compute explicit
formulae for an index counting these pure-Higgs states and prove -- for this
special class of quivers -- some previously stated conjectures about them.
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Superconformal Field Theories for Compact Manifolds with Spin(7)
Holonomy: We present a construction of superconformal field theories for manifolds with
Spin(7) holonomy. Geometrically these models correspond to the realization of
Spin(7) manifolds as anti-holomorphic quotients of Calabi-Yau fourfolds.
Describing the fourfolds as Gepner models and requiring anomaly cancellation we
determine the resulting Betti numbers of the Spin(7) superconformal field
theory. As in the G_2 case, we find that the Gepner model and the geometric
result disagree.
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Brane universe and holography in spacetime of charged AdS dilaton black
hole: In the background of a charged AdS dilaton black hole, we investigate the
movement of a self-graviting 3-brane and relevant holographic effects as the
brane move close to the AdS boundary. The induced metric on brane corresponds
to an exact FLRW geometry, while the evolution of brane is determined by Israel
junction condition and the effective Einstein field equation on brane together.
When the brane approaches the AdS boundary, AdS/CFT correspondence implies that
a radiation dominated FLRW-universe ($P=\frac{1}{3}\rho$) should be given.
According to the holographic renormalization procedure, we involve an
appropriate surface counterterm into the gravitational action for achieving
$P=\frac{1}{3}\rho$ on brane. This surface counterterm also plays a important
role in caculating the mass of charged AdS dilaton black hole. Finally, we
obtain the thermodynamic quantities and give an extend Cardy-Verlinde formula
on brane.
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An approach to quantum gravity from 4-$ε$ dimension: A calculational scheme of quantum-gravitational effects on the physical
quantities is proposed. The calculations are performed in 4-$\epsilon$
dimension with $1/N$-expansion scheme, where the Einstein gravity is
renormalizable and it has an ultraviolet fixed-point within the 1/N-expansion.
In order to perform a consistent perturbation in $4-\epsilon$ dimension,
spin-3/2 fields should be adopted as the N matter-fields whose loop-corrections
are included in the effective action. After calculating the physical quantities
at $4-\epsilon$ dimension, the four-dimensional aspects of them can be seen by
taking the limit of $\epsilon=0$. In taking this limit, any higher derivative
terms are not introduced as the counter terms since no divergence appears at
$\epsilon=0$ in our scheme. According to this approach, we have examined the
effective potential of a scalar field to see the possibility of the spontaneous
symmetry breaking due to the gravitational loop corrections.
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Solution of N=2 Gauge Theories via Compactification to Three Dimensions: A number of N=2 gauge theories can be realized by brane configurations in
Type IIA string theory. One way of solving them involves lifting the brane
configuration to M-theory. In this paper we present an alternative way of
analyzing a subclass of these theories (elliptic models). We observe that upon
compactification on a circle one can use a version of mirror symmetry to map
the original brane configuration into one containing only D-branes.
Simultaneously the Coulomb branch of the four-dimensional theory is mapped to
the Higgs branch of a five-dimensional theory with three-dimensional
impurities. The latter does not receive quantum corrections and can be analyzed
exactly. The solution is naturally formulated in terms of an integrable system,
which is a version of a Hitchin system on a punctured torus.
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Solving N=3 super-Yang-Mills equations in harmonic superspace: We analyze the superfield constraints of the D=4, N=3 SYM-theory using
light-cone gauge conditions. The SU(3)/U(1)xU(1) harmonic variables are
interpreted as auxiliary spectral parameters, and the transform to the
harmonic-superspace representation is considered. Our nilpotent gauge for the
basic harmonic superfield simplifies the SYM-equations of motion. A partial
Grassmann decomposition of these equations yields the solvable linear system of
iterative equations.
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Meromorphic Scaling Flow of N=2 Supersymmetric SU(2) Yang-Mills with
Matter: Beta-functions are derived for the flow of N=2 SUSY SU(2) Yang-Mills in
4-dimensions with massless matter multiplets in the fundamental representation
of the gauge group. The beta-functions represent the flow of the couplings as
the VEV of the Higgs field is lowered and are modular forms of weight -2. They
have the correct asymptotic behaviour at both the strong and weak coupling
fixed points. Corrections to the massless beta-functions when masses are turned
on are discussed.
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Numerical simulation of non-extensive Boltzmann equation: We present first results of the development of a test particle simulation for
solving non-extensive extensions of the elastic two-particle Boltzmann
equation. Stationary one-particle energy distributions with power-law tail are
obtained.
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Complex Monopoles in the Georgi-Glashow-Chern-Simons Model: We investigate the three dimensional Georgi-Glashow model with a Chern-Simons
term. We find that there exist complex monopole solutions of finite action.
They dominate the path integral and disorder the Higgs vacuum, but electric
charges are not confined. Subtleties in the gauge fixing procedure in the path
integral and issues related to Gribov copies are noted.
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The particle spectrum of the Tricritical Ising Model with spin reversal
symmetric perturbations: We analyze the evolution of the particle spectrum of the Tricritical Ising
Model by varying the couplings of the energy and vacancy density fields. The
particle content changes from the spectrum of a supersymmetric theory (either
of an exact or a spontaneously broken supersymmetric theory) to the spectrum of
seven particles related to the underlying E_7 structure. In the low temperature
phase some of these excitations are topologically charged particles that are
stable under an arbitrary variation of the parameters. The high and low
temperature phases of the model are related by duality. In some regions of the
two couplings there are also present false vacua and sequences of bound states.
In order to study the non-integrable features of this model we employ the Form
Factor Perturbation Theory and the Truncated Conformal Space Approach.
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Correlations vs connectivity in R-charge: The holographic relation between quantum correlations and connectivity of
spacetime is explored for single R-charged AdS$_5$ black holes and their
half-BPS limits (superstars). In a two boundary set-up, the wormhole between
both universes reduces to a designable and computable quantum mechanical
correlation between the dual microscopic degrees of freedom in the BPS limit.
This quantum connectivity is seen as a naked singularity by a single sided
observer. In a single boundary set-up, as a small step towards the description
of entangled black holes, we describe quantum teleportation between two labs in
different locations of the transverse 5-sphere using entangled gravitons in a
reference state that provides a classical channel between both labs.
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YANG-MILLS-HIGGS versus CONNES-LOTT: By a suitable choice of variables we show that every Connes-Lott model is a
Yang-Mills-Higgs model. The contrary is far from being true. Necessary
conditions are given. Our analysis is pedestrian and illustrated by examples.
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Peculiar properties of a charged dilatonic black hole in AdS_5: We study a charged dilatonic black hole in AdS_5, derived from a lagrangian
involving a gauge field whose kinetic term is modified by the exponential of a
neutral scalar. This black hole has two properties which one might reasonably
demand of the dual of a Fermi liquid: Its entropy is proportional to
temperature at low temperature, and its extremal limit supports normal modes of
massless, charged bulk fermions. The black hole we study has a simple analytic
form because it can be embedded in type IIB string theory as the near-horizon
limit of D3-branes with equal spins in two of the three independent transverse
planes. Two further properties can be deduced from this embedding: There is a
thermodynamic instability, reminiscent of ferromagnetism, at low temperatures;
and there is an AdS_3 factor in the extremal near-horizon geometry which
accounts for the linear dependence of entropy on temperature. Altogether, it is
plausible that the dilatonic black hole we study, or a relative of it with
similar behavior in the infrared, is the dual of a Fermi liquid; however, the
particular embedding in string theory that we consider is unlikely to have such
a dual description, unless through some unexpected boson-fermion equivalence at
large N.
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On genus expansion of superpolynomials: Recently it was shown that the (Ooguri-Vafa) generating function of HOMFLY
polynomials is the Hurwitz partition function, i.e. that the dependence of the
HOMFLY polynomials on representation R is naturally captured by symmetric group
characters (cut-and-join eigenvalues). The genus expansion and expansion
through Vassiliev invariants explicitly demonstrate this phenomenon. In the
present letter we claim that the superpolynomials are not functions of such a
type: symmetric group characters do not provide an adequate linear basis for
their expansions. Deformation to superpolynomials is, however, straightforward
in the multiplicative basis: the Casimir operators are \beta-deformed to
Hamiltonians of the Calogero-Moser-Sutherland system. Applying this trick to
the genus and Vassiliev expansions, we observe that the deformation is fully
straightforward only for the thin knots. Beyond the family of thin knots
additional algebraically independent terms appear in the Vassiliev and genus
expansions. This can suggest that the superpolynomials do in fact contain more
information about knots than the colored HOMFLY and Kauffman polynomials.
However, even for the thin knots the beta-deformation is non-innocent: already
in the simplest examples it seems inconsistent with the postivity of colored
superpolynomials in non-(anti)symmetric representations, which also happens in
I.Cherednik's (DAHA-based) approach to the torus knots.
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A non-Fock fermion toy model: Recent progress in mathematical theory of random processes provides us with
non-Fock product systems (continuous tensor products of Hilbert spaces) used
here for constructing a toy model for fermions. Some state vectors describe
infinitely many particles in a finite region; the particles accumulate to a
point. Electric charge can be assigned to the particles, the total charge being
zero. Time dynamics is not considered yet, only kinematics (a single time
instant).
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Semiclassical Methods in Curved Spacetime and Black Hole Thermodynamics: Improved semiclassical techniques are developed and applied to a treatment of
a real scalar field in a $D$-dimensional gravitational background. This
analysis, leading to a derivation of the thermodynamics of black holes, is
based on the simultaneous use of: (i) a near-horizon description of the scalar
field in terms of conformal quantum mechanics; (ii) a novel generalized WKB
framework; and (iii) curved-spacetime phase-space methods. In addition, this
improved semiclassical approach is shown to be asymptotically exact in the
presence of hierarchical expansions of a near-horizon type. Most importantly,
this analysis further supports the claim that the thermodynamics of black holes
is induced by their near-horizon conformal invariance.
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Kaluza-Kelin Higher Derivative Gravity and Friedmann-Robertson-Walker
Cosmology: Kaluza-Klein approach in an N(=1+3+D)-dimensional Friedmann-Robertson-Walker
type space is often adopted in the literature. We derive a compact expression
for the Friedmann equation in a (1+3+D)-dimensional space. The redundancy of
the associated field equations due to the Bianchi identity is analyzed. We also
study the dilaton gravity theory with higher-derivative gravitational
couplings. It turns out that higher-order terms will not affect the Friedmann
equation in a constant flat internal space. This is true only for the flat-De
Sitter external space. The inflationary solution in an induced-gravity model is
also discussed as an application.
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Aharonov-Bohm Scattering of a Localized Wave Packet: Analysis of the
Forward Direction: The Aharonov-Bohm scattering of a localized wave packet is considered. A
careful analysis of the forward direction points out new results: according to
the time-dependent solution obtained by means of the asymptotic representation
for the propagator (kernel), a phenomenon of auto-interference occurs along the
forward direction, where, also, the probability density current is evaluated
and found finite.
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Heterotic G_2-manifold compactifications with fluxes and fermionic
condensates: We consider flux compactifications of heterotic string theory in the presence
of fermionic condensates on M_{1,2} times X_7 with both factors carrying a
Killing spinor. In other words, M_{1,2} is either de Sitter, anti-de Sitter or
Minkowski, and X_7 possesses a nearly parallel G_2-structure or has
G_2-holonomy. We solve the complete set of field equations and the Bianchi
identity to order alpha'. The latter is satisfied via a non-standard embedding
by choosing the gauge field to be a G_2-instanton. It is shown that none of the
solutions to the field equations is supersymmetric.
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Unfolded Equations for Current Interactions of 4d Massless Fields as a
Free System in Mixed Dimensions: Interactions of massless fields of all spins in four dimensions with currents
of any spin is shown to result from a solution of the linear problem that
describes a gluing between rank-one (massless) system and rank-two (current)
system in the unfolded dynamics approach. Since the rank-two system is dual to
a free rank-one higher-dimensional system, that effectively describes conformal
fields in six space-time dimensions, the constructed system can be interpreted
as describing a mixture between linear conformal fields in four and six
dimensions. Interpretation of the obtained results in spirit of AdS/CFT
correspondence is discussed.
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The first law of heterotic stringy black hole mechanics at zeroth order
in alpha prime: We re-derive the first law of black hole mechanics in the context of the
Heterotic Superstring effective action compactified on a torus to leading order
in alpha prime, using Wald's formalism, covariant Lie derivatives and momentum
maps. The Kalb-Ramond field strength of this theory has Abelian Chern-Simons
terms which induce Nicolai-Townsend transformations of the Kalb-Ramond field.
We show how to deal with all these gauge symmetries deriving the first law in
terms of manifestly gauge-invariant quantities. In presence of Chern-Simons
terms, several definitions of the conserved charges exist, but the formalism
picks up only one of them to play a role in the first law.
This work is a first step towards the derivation of the first law at first
order in alpha prime where, more complicated, non-Abelian, Lorentz
("gravitational") and Yang-Mills Chern-Simons terms are included in the
Kalb-Ramond field strength. The derivation of a first law is a necessary step
towards the derivation of a manifestly gauge-invariant entropy formula which is
still lacking in the literature. In its turn, this entropy formula is needed to
compare unambiguously macroscopic and microscopic black hole entropies.
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The second law of thermodynamics, TCP, and Einstein causality in anti-de
Sitter space-time: If the vacuum is passive for uniformly accelerated observers in anti-de
Sitter space-time (i.e. cannot be used by them to operate a "perpetuum
mobile"), they will (a) register a universal value of the Hawking-Unruh
temperature, (b) discover a TCP symmetry, and (c) find that observables in
complementary wedge-shaped regions are commensurable (local) in the vacuum
state. These results are model independent and hold in any theory which is
compatible with some weak notion of space-time localization.
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TASI Lectures on Supergravity and String Vacua in Various Dimensions: These lectures aim to provide a global picture of the spaces of consistent
quantum supergravity theories and string vacua in higher dimensions. The
lectures focus on theories in the even dimensions 10, 8, and 6. Supersymmetry,
along with with anomaly cancellation and other quantum constraints, places
strong limitations on the set of physical theories which can be consistently
coupled to gravity in higher-dimensional space-times. As the dimensionality of
space-time decreases, the range of possible supergravity theories and the set
of known string vacuum constructions expand. These lectures develop the basic
technology for describing a variety of string vacua, including heterotic,
intersecting brane, and F-theory compactifications. In particular, a systematic
presentation is given of the basic elements of F-theory. In each dimension, we
summarize the current state of knowledge regarding the extent to which
supergravity theories not realized in string theory can be shown to be
inconsistent.
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The asymptotic growth of states of the 4d N=1 superconformal index: We show that the superconformal index of N=1 superconformal field theories in
four dimensions has an asymptotic growth of states which is exponential in the
charges. Our analysis holds in a Cardy-like limit of large charges, for which
the index is dominated by small values of chemical potentials. In this limit we
find the saddle points of the integral that defines the superconformal index
using two different methods. One method, valid for finite N, is to first take
the Cardy-like limit and then find the saddle points. The other method is to
analyze the saddle points at large N and then take the Cardy-like limit. The
result of both analyses is that the asymptotic growth of states of the
superconformal index exactly agrees with the Bekenstein-Hawking entropy of
supersymmetric black holes in the dual AdS$_5$ theory.
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Kondo effect from a Lorentz-violating domain wall description of
superconductivity: We extend recent results on domain wall description of superconductivity in
an Abelian Higgs model by introducing a particular Lorentz-violating term. The
temperature of the system is interpreted through the fact that the soliton
following accelerating orbits is a Rindler observer experiencing a thermal
bath. We show that this term can be associated with the {\sl Kondo effect},
that is, the Lorentz-violating parameter is closely related to the
concentration of magnetic impurities living on a superconducting domain wall.
We also found that the critical temperature decreasing with the impurity
concentration as a non single-valued function, for the case $T_K < T_{c0}$,
develops a negative curvature and presents deviations from the Abrikosov and
Gor'kov theory, a phenomenon already supported by experimental evidence.
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Spinflation with Angular Potentials: We investigate in detail the cosmological consequences of realistic angular
dependent potentials in the brane inflation scenario. Embedding a warped throat
into a compact Calabi-Yau space with all moduli stabilized breaks the no-scale
structure and induces angular dependence in the potential of the probe
D3-brane. We solve the equations of motion from the DBI action in the warped
deformed conifold including linearized perturbations around the imaginary
self-dual solution. Our numerical solutions show that angular dependence is a
next to leading order correction to the dominant radial motion of the brane,
however, just as angular motion typically increases the amount of inflation
(spinflation), having additional angular dependence also increases the amount
of inflation. We also derive an analytic approximation for the number of
e-foldings along the DBI trajectory in terms of the compactification
parameters.
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An Alternative to Exact Renormalization and Cosmological Solutions in
String Theory: In this work we review the application of a functional method, serving as an
alternative to the Wilsonian Exact Renormalization approach, to stringy bosonic
$\sigma$-models with metric and dilaton backgrounds on a spherical world sheet
[1]. We derive an exact evolution equation for the dilaton with the amplitude
of quantum fluctuations, driven by the kinetic term of the two-dimensional
world-sheet theory. The linear dilaton conformal field theory, corresponding to
a linearly (in cosmic Einstein-frame time) expanding Universe, appears as a
trivial fixed point of this equation. With the help of conformal-invariance
conditions, we find a logarithmic dilaton as another, exact and non trivial,
fixed-point solution. Cosmological implications of our solutions are briefly
discussed, in particular the transition (exit) from the expanding Universe of
the linear dilaton to the Minkowski vacuum, corresponding to the non-trivial
fixed point of our generalised flow. This novel renormalization-group method
may therefore offer new insights into exact properties of string theories of
physical significance.
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Non-Equilibrium Critical Phenomena From Probe Brane Holography in
Schrödinger Spacetime: We study the non-equilibrium steady-state phase transition from probe brane
holography in $z=2$ Schr\"odinger spacetime. Concerning differential
conductivity, a phase transition could occur in the conductor state.
Considering constant current operator as the external field and the
conductivity as an order parameter, we derive scaling behavior of order
parameter near the critical point. We explore the critical exponents of the
non-equilibrium phase transition in two different Schr\"odinger spacetimes,
which originated $1)$ from supergravity, and $2)$ from AdS blackhole in the
light-cone coordinates. Interestingly, we will see that even at the zero charge
density, in our first geometry, the dynamical critical exponent of $z=2$ has a
major effect on the critical exponents.
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Strings on Orientifolds: We construct several examples of compactification of Type IIB theory on
orientifolds and discuss their duals. In six dimensions we obtain models with
$N=1$ supersymmetry, multiple tensor multiplets, and different gauge groups. In
nine dimensions we obtain a model that is dual to M-theory compactified on a
Klein bottle.
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Positive-definite states of a Klein-Gordon type particle: A possible way for the consistent probability interpretation of the
Klein-Gordon equation is proposed. It is assumed that some states of a scalar
charged particle cannot be physically realized. The rest of quantum states are
proven to have positive-definite probability distributions.
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Small dark energy without small parameters: We present a prototype model that resolves the cosmological constant problem
using matter alone, i.e., without modifying gravity. Its generic cosmological
solutions adjust an arbitrarily large, negative dark energy to a positive value
parametrically suppressed by an initial field velocity. Inflationary initial
conditions lead to a positive dark energy exponentially smaller in magnitude
than any model parameter, or any scale in the initial conditions.
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Extended supersymmetry for the Bianchi-type cosmological models: In this paper we propose a superfield description for all Bianchi-type
cosmological models. The action is invariant under world-line local $n=4$
supersymmetry with $SU(2)_{local}XSU(2)_{global}$ internal symmetry. Due to the
invariance of the action we obtain the constraints, which form a closed
superalgebra of the $n=4$ supersymmetric quantum mechanics. This procedure
provides the inclusion of supermatter in a sistematic way.
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Discretizing Gravity in Warped Spacetime: We investigate the discretized version of the compact Randall-Sundrum model.
By studying the mass eigenstates of the lattice theory, we demonstrate that for
warped space, unlike for flat space, the strong coupling scale does not depend
on the IR scale and lattice size. However, strong coupling does prevent us from
taking the continuum limit of the lattice theory. Nonetheless, the lattice
theory works in the manifestly holographic regime and successfully reproduces
the most significant features of the warped theory. It is even in some respects
better than the KK theory, which must be carefully regulated to obtain the
correct physical results. Because it is easier to construct lattice theories
than to find exact solutions to GR, we expect lattice gravity to be a useful
tool for exploring field theory in curved space.
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A tunneling picture of dual giant Wilson loop: We further discuss a rotating dual giant Wilson loop (D3-brane) solution
constructed in Lorentzian AdS by Drukker et al. The solution is shown to be
composed of a dual giant Wilson loop and a dual giant graviton by minutely
examining its shape. This observation suggests that the corresponding
gauge-theory operator should be a k-th symmetric Wilson loop with the
insertions of dual giant graviton operators. To support the correspondence, the
classical action of the solution should be computed and compared with the
gauge-theory result. For this purpose we first perform a Wick rotation to the
Lorentzian solution by following the tunneling prescription and obtain
Euclidean solutions corresponding to a circular or a straight-line Wilson loop.
In Euclidean signature boundary terms can be properly considered in the
standard manner and the classical action for the Euclidean solutions can be
evaluated. The result indeed reproduces the expectation value of the k-th
symmetric Wilson loop as well as the power-law behavior of the correlation
function of dual giant graviton operators.
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Pulling the Boundary into the Bulk: Motivated by the ability to consistently apply the Ryu-Takayanagi
prescription for general convex surfaces and the relationship between
entanglement and geometry in tensor networks, we introduce a novel, covariant
bulk object - the holographic slice. The holographic slice is found by
considering the continual removal of short range information in a boundary
state. It thus provides a natural interpretation as the bulk dual of a series
of coarse-grained holographic states. The slice possesses many desirable
properties that provide consistency checks for its boundary interpretation.
These include monotonicity of both area and entanglement entropy, uniqueness,
and the inability to probe beyond late-time black hole horizons. Additionally,
the holographic slice illuminates physics behind entanglement shadows, as
minimal area extremal surfaces anchored to a coarse-grained boundary may probe
entanglement shadows. This lets the slice flow through shadows. To aid in
developing intuition for these slices, many explicit examples of holographic
slices are investigated. Finally, the relationship to tensor networks and
renormalization (particularly in AdS/CFT) is discussed.
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A Nonabelian Particle-Vortex Duality: We define a nonabelian particle-vortex duality as a $3-$dimensional analogue
of the usual $2-$dimensional worldsheet nonabelian T-duality. The
transformation is defined in the presence of a global $SU(2)$ symmetry and,
although derived from a string theoretic setting, we formulate it generally. We
then apply it to so-called "semilocal strings" in an $SU(2)_{G}\times U(1)_{L}$
gauge theory, originally discovered in the context of cosmic string physics.
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Gauged WZW models for space-time groups and gravitational actions: In this paper we investigate gauged Wess-Zumino-Witten models for space-time
groups as gravitational theories, following the trend of recent work by
Anabalon, Willison and Zanelli. We discuss the field equations in any dimension
and study in detail the simplest case of two space-time dimensions and gauge
group SO(2,1). For this model we study black hole solutions and we calculate
their mass and entropy which resulted in a null value for both.
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Operator spectroscopy for 4d SCFTs with a=c: We study a rich set of four-dimensional superconformal field theories (SCFTs)
with both central charges identical: $a = c$. These are constructed via the
diagonal $\mathcal{N}=2$ or $\mathcal{N}=1$ gauging of the flavor symmetry $G$
of a collection of $\mathcal{N}=2$ Argyres-Douglas theories of type
$\mathcal{D}_p(G)$, with or without adjoint chiral multiplets, in
arXiv:2106.12579 and arXiv:2111.12092. We compute superconformal indices of
some theories where the rank of $G$ is low, performing a refined test for
unitarity, and further determine the relevant and marginal operator content in
detail. We find that most of these theories flow to interacting SCFTs with
$a=c$ in the infrared.
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The canonical structure of Podolsky's generalized electrodynamics on the
Null-Plane: In this work we will develop the canonical structure of Podolsky's
generalized electrodynamics on the null-plane. This theory has second-order
derivatives in the Lagrangian function and requires a closer study for the
definition of the momenta and canonical Hamiltonian of the system. On the
null-plane the field equations also demand a different analysis of the
initial-boundary value problem and proper conditions must be chosen on the
null-planes. We will show that the constraint structure, based on Dirac
formalism, presents a set of second-class constraints, which are exclusive of
the analysis on the null-plane, and an expected set of first-class constraints
that are generators of a U(1) group of gauge transformations. An inspection on
the field equations will lead us to the generalized radiation gauge on the
null-plane, and Dirac Brackets will be introduced considering the problem of
uniqueness of these brackets under the chosen initial-boundary condition of the
theory.
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Conformal perturbation of off-critical correlators in the 3D Ising
universality class: Thanks to the impressive progress of conformal bootstrap methods we have now
very precise estimates of both scaling dimensions and OPE coefficients for
several 3D universality classes. We show how to use this information to obtain
similarly precise estimates for off-critical correlators using conformal
perturbation. We discuss in particular the $< \sigma (r) \sigma (0) >$, $<
\epsilon (r) \epsilon (0) >$ and $< \sigma (r) \epsilon (0) >$ two point
functions in the high and low temperature regimes of the 3D Ising model and
evaluate the leading and next to leading terms in the $s = t r^{\Delta_{t}}$
expansion, where $t$ is the reduced temperature. Our results for $< \sigma (r)
\sigma (0) >$ agree both with Monte Carlo simulations and with a set of
experimental estimates of the critical scattering function.
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Fluid-gravity correspondence and causal first-order relativistic viscous
hydrodynamics: The fluid-gravity correspondence is a duality between anti-de Sitter Einstein
gravity and a relativistic fluid living at the conformal boundary. We show that
one can accommodate the causal first-order viscous hydrodynamics recently
developed by Bemfica, Disconzi, Noronha, and Kovtun in this framework, by
requiring a set of natural conditions for the geometric data at the horizon.
The latter hosts an induced Carrollian fluid, whose equations of motion are
shown to be tightly tied to the ones describing the fluid at the boundary.
Functional expressions for the transport coefficients are found --with those
associated to viscosity and heat flux uniquely determined--, satisfying a set
of known causality requirements for the underlying equations of motion.
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Vacuum block thermalization in semi-classical 2d CFT: The universal nature of black hole collapse in asymptotically $AdS_3$
gravitational theories suggests that its holographic dual process,
thermalization, should similarly be fixed by the universal features of 2d CFT
with large central charge $c$. It is known that non-equilibrium states with
scaling dimensions of order $c$ can be sorted into states that eventually
thermalize and those that fail to do so. By proving an equivalence between
bounded Virasoro coadjoint orbits and certain (in)stability intervals of Hill's
equation it is shown that a state that fails to thermalize can be promoted to a
thermalizing state by preparing the system beforehand with an energy greater
than an appropriate threshold energy. It is generally a difficult problem to
ascertain whether a state will thermalize or not. As partial progress to this
problem a set of lower bounds are presented for the treshold energy, which can
alternatively be interpreted as criteria for thermalization.
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Generalized W-algebras and Integrable Hierarchies: We report on generalizations of the KdV-type integrable hierarchies of
Drinfel'd and Sokolov. These hierarchies lead to the existence of new classical
$W$-algebras, which arise as the second Hamiltonian structure of the
hierarchies. In particular, we present a construction of the $W_n^{(l)}$
algebras.
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Type II/F-theory Superpotentials and Ooguri-Vafa Invariants of Compact
Calabi-Yau Threefolds with Three Deformations: We calculate the D-brane superpotentials for two Calabi-Yau manifolds with
three deformations by the generalized hypergeometric GKZ systems, which give
rise to the flux superpotentials $\mathcal{W}_{GVW}$ of the dual F-theory
compactification on the relevant Calabi-Yau fourfolds in the weak decoupling
limit. We also compute the Ooguri-Vafa invariants from A-model expansion with
mirror symmetry, which are related to the open Gromov-Witten invariants.
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THE NUMBER OF SPHALERON INSTABILITIES OF THE BARTNIK-McKINNON SOLITONS
AND NON-ABELIAN BLACK HOLES: It is proven that there are precisely $n$ odd-parity sphaleron-like unstable
modes of the $n$-th Bartnik-McKinnon soliton and the $n$-th non-abelian black
hole solution of the Einstein-Yang-Mills theory for the gauge group $SU(2)$.
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Projectively-Compact Spinor Vertices and Space-Time Spin-Locality in
Higher-Spin Theory: The concepts of compact and projectively-compact spin-local spinor vertices
are introduced. Vertices of this type are shown to be space-time spin-local,
i.e. their restriction to any finite subset of fields is space-time local. The
known spinor spin-local cubic vertices with the minimal number of space-time
derivatives are verified to be projectively-compact. This has the important
consequence that spinor spin-locality of the respective quartic vertices would
imply their space-time spin-locality. More generally, it is argued that the
proper class of solutions of the non-linear higher-spin equations that leads to
the minimally non-local (presumably space-time spin-local) vertices is
represented by the projectively-compact vertices. The related aspects of the
higher-spin holographic correspondence are briefly discussed.
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(S)QCD on R^3 x S^1: Screening of Polyakov loop by fundamental quarks
and the demise of semi-classics: Recently, it was argued that the thermal deconfinement transition in pure
Yang-Mills theory is continuously connected to a quantum phase transition in
softly-broken N=1 SYM theory on R^3 x S^1. The transition is semiclassically
calculable at small S^1 size L, occurs as the soft mass m_soft and L vary, and
is driven by a competition between perturbative effects and nonperturbative
topological molecules. These are correlated instanton--anti-instanton tunneling
events, whose constituents are monopole-instantons "bound" by attractive
long-range forces. The mechanism driving the transition is universal for all
simple gauge groups, with or without a center, such as SU(N) or G_2. Here, we
consider theories with fundamental quarks. We examine the role topological
objects play in determining the fate of the (exact or approximate)
center-symmetry in SU(2) SQCD, with or without soft-breaking terms. In theories
whose large-m_soft limit is thermal nonsupersymmetric QCD with massive quarks,
we find a crossover of the Polyakov loop, from approximately center-symmetric
at small 1/L to maximally center-broken at larger 1/L, as seen in lattice
thermal QCD with massive quarks and T=1/L. We argue that in all calculable
cases, including SQCD with exact center symmetry, quarks deform
instanton-monopoles by their quantum fluctuations and do not contribute to
their binding. The semiclassical approximation and the molecular picture of the
vacuum fail, upon decreasing the quark mass, precisely when quarks would begin
mediating a long-range attractive force between monopole-instantons, calling
for a dual description of the resulting strong-coupling theory.
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A note on unparticle in lower dimensions: Using the gauge-invariant but path-dependent variables formalism, we examine
the effect of the space-time dimensionality on a physical observable in the
unparticle scenario. We explicitly show that long-range forces between
particles mediated by unparticles are still present whenever we go over into
lower dimensions.
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Hawking radiation from z=3 and z=1-Lifshitz black holes: The Hawking radiation considered as a tunneling process, by using a
Hamilton-Jacobi prescription, is discussed for both z=3 and z=1-Lifshitz black
holes. We have found that the tunneling rate (which is not thermal but related
to the change of entropy) for the z=3-Lifshitz black hole (which does not
satisfy the Area/4-law) does not yield (give us) the ecpected tunneling rate:
$\Gamma\simeq exp(\Delta S)$, where $\Delta S$ is the change of black hole
entropy, if we compare with the z=1-Lifshitz black hole (BTZ black hole, which
satisfies the Area/4-law).
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Manifest gravitational duality near anti de Sitter space-time: We derive a manifestly duality-invariant formulation of the action principle
for linearized gravity on anti de Sitter background. The analysis is based on
the two-potential formalism, obtained upon resolution of the constraints in the
Hamiltonian formulation. We discuss the relevance of our result in the context
of holography.
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Shadows of 5D Black Holes from String Theory: We study the shadow behaviors of five dimensional (5D) black holes embedded
in type IIB superstring/supergravity inspired spacetimes by considering
solutions with and without rotations. Geometrical properties as shapes and
sizes are analyzed in terms of the D3-brane number and the rotation parameter.
Concretely, we find that the shapes are indeed significantly distorted by such
physical parameters and the size of the shadows decreases with the brane or
"color" number and the rotation. Then, we investigate geometrical observables
and energy emission rate aspects.
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W-representations of the fermionic matrix and Aristotelian tensor models: We show that the fermionic matrix model can be realized by
$W$-representation. We construct the Virasoro constraints with higher algebraic
structures, where the constraint operators obey the Witt algebra and null
3-algebra. The remarkable feature is that the character expansion of the
partition function can be easily derived from such Virasoro constraints. It is
a $\tau$-function of the KP hierarchy. We construct the fermionic Aristotelian
tensor model and give its $W$-representation. Moreover, we analyze the
fermionic red tensor model and present the $W$-representation and character
expansion of the partition function.
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DBI Genesis: An Improved Violation of the Null Energy Condition: We show that the DBI conformal galileons, derived from the world-volume
theory of a 3-brane moving in an AdS bulk, admit a background, stable under
quantum corrections, which violates the Null Energy Condition (NEC). The
perturbations around this background are stable and propagate subluminally.
Unlike other known examples of NEC violation, such as ghost condensation and
conformal galileons, this theory also admits a stable, Poincare-invariant
vacuum, with a Lorentz-invariant S-matrix satisfying standard analyticity
conditions. Like conformal galileons, perturbations around deformations of the
Poincare invariant vacuum propagate superluminally.
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Emergence of a Big Bang singularity in an exact string background: The origin of Big Bang singularity in 3+1 dimensions can be understood in an
exact string theory background obtained by an analytic continuation of a cigar
like geometry with a nontrivial dilaton. In a T-dual conformal field theory
picture there exists a closed string tachyon potential which excises the
singular space-time of a strongly coupled regime to ensure that a higher
dimensional universe has no curvature singularity. However in 3+1 dimensions
the universe exhibits all the pathology of a standard Big Bang cosmology. The
emergence of a singularity now owes to a higher dimensional orbifold
singularity which does not have a curvature singularity in higher dimensions,
suggesting that close to the compactification scale an effective description of
3+1 dimensions breaks down and bouncing universe emerges in 5 and higher
dimensions.
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Traversable wormhole without interaction: We show that strong quantum entanglement can support a stable traversable
wormhole without any explicit interaction or tunnelling term between the two
boundary theories of the wormhole. Specifically we work with two complex SYK
models. The entangled state is prepared using a tunnelling term in imaginary
time but the tunnelling term is removed from the time evolution operator so the
two complex SYK models are not coupled. Low temperature states show revival
dynamics which is the hallmark of a traversable wormhole geometry. To send any
meaningful information from one system to the other, one only needs to turn on
a very small interaction term. The technique that we are employing can be
applied to other systems to study aspects of quantum entanglement.
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Dyons with potentials: duality and black hole thermodynamics: A modified version of the double potential formalism for the electrodynamics
of dyons is constructed. Besides the two vector potentials, this manifestly
duality invariant formulation involves four additional potentials, scalar
potentials which appear as Lagrange multipliers for the electric and magnetic
Gauss constraints and potentials for the longitudinal electric and magnetic
fields. In this framework, a static dyon appears as a Coulomb-like solution
without string singularities. Dirac strings are needed only for the Lorentz
force law, not for Maxwell's equations. The magnetic charge no longer appears
as a topological conservation law but as a surface integral on a par with
electric charge. The theory is generalized to curved space. As in flat space,
the string singularities of dyonic black holes are resolved. As a consequence
all singularities are protected by the horizon and the thermodynamics is shown
to follow from standard arguments in the grand canonical ensemble.
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Recent Trends in Superstring Phenomenology: We review for non-experts possible phenomenological scenari in String Theory.
In particular we focus on vacuum configurations with intersecting and/or
magnetized unoriented D-branes. We will show how a TeV scale tension may be
compatible with the existence of Large Extra Dimensions and how anomalous
U(1)'s can give rise to interesting signatures at LHC or in cosmic rays.
Finally, we discuss unoriented D-brane instantons as a source of
non-perturbative effects that can contribute to moduli stabilization and susy
braking in combination with fluxes. We conclude with an outlook and directions
for future work.
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The Timelike Tube Theorem in Curved Spacetime: The timelike tube theorem asserts that in quantum field theory without
gravity, the algebra of observables in an open set U is the same as the
corresponding algebra of observables in its ``timelike envelope'' E(U), which
is an open set that is in general larger. The theorem was originally proved in
the 1960's by Borchers and Araki for quantum fields in Minkowski space. Here we
sketch the proof of a version of the theorem for quantum fields in a general
real analytic spacetime. Details have appeared elsewhere.
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New Charged Black Holes with Conformal Scalar Hair: A new class of four-dimensional, hairy, stationary solutions of the
Einstein-Maxwell-Lambda system with a conformally coupled scalar field is
constructed in this paper. The metric belongs to the Plebanski-Demianski family
and hence its static limit has the form of the charged C-metric. It is shown
that, in the static case, a new family of hairy black holes arises. They turn
out to be cohomogeneity-two, with horizons that are neither Einstein nor
homogenous manifolds. The conical singularities in the C-metric can be removed
due to the back reaction of the scalar field providing a new kind of regular,
radiative spacetime. The scalar field carries a continuous parameter
proportional to the usual acceleration present in the C-metric. In the
zero-acceleration limit, the static solution reduces to the dyonic
Bocharova-Bronnikov-Melnikov-Bekenstein solution or the dyonic extension of the
Martinez-Troncoso-Zanelli black holes, depending on the value of the
cosmological constant.
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Supersymmetry on Three-dimensional Lorentzian Curved Spaces and Black
Hole Holography: We study N <= 2 superconformal and supersymmetric theories on Lorentzian
threemanifolds with a view toward holographic applications, in particular to
BPS black hole solutions. As in the Euclidean case, preserved supersymmetry for
asymptotically locally AdS solutions implies the existence of a (charged)
"conformal Killing spinor" on the boundary. We find that such spinors exist
whenever there is a conformal Killing vector which is null or timelike. We
match these results with expectations from supersymmetric four-dimensional
asymptotically AdS black holes. In particular, BPS bulk solutions in global AdS
are known to fall in two classes, depending on their graviphoton magnetic
charge, and we reproduce this dichotomy from the boundary perspective. We
finish by sketching a proposal to find the dual superconformal quantum
mechanics on the horizon of the magnetic black holes.
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Saturating unitarity bounds at U-duality symmetric points: It has recently been shown that the leading Wilson coefficient in type II
string theory can take (almost) all values allowed by unitarity, crossing
symmetry and maximal supersymmetry in D=10 and D=9 dimensions. This suggests
that string theory might define the unique consistent quantum theory of gravity
with maximal supersymmetry. We study the minima of the leading Wilson
coefficient in D=6, 7 and 8 dimensions and find the global minimum at the point
in moduli space with maximal symmetry. The minimum value turns out to always be
negative for D<8.
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Forms and algebras in (half-)maximal supergravity theories: The forms in D-dimensional (half-)maximal supergravity theories are discussed
for 3 $\leq$ D $\leq$ 11. Superspace methods are used to derive consistent sets
of Bianchi identities for all the forms for all degrees, and to show that they
are soluble and fully compatible with supersymmetry. The Bianchi identities
determine Lie superalgebras that can be extended to Borcherds superalgebras of
a special type. It is shown that any Borcherds superalgebra of this type gives
the same form spectrum, up to an arbitrary degree, as an associated Kac-Moody
algebra. For maximal supergravity up to D-form potentials, this is the very
extended Kac-Moody algebra E11. It is also shown how gauging can be carried out
in a simple fashion by deforming the Bianchi identities by means of a new
algebraic element related to the embedding tensor. In this case the appropriate
extension of the form algebra is a truncated version of the so-called tensor
hierarchy algebra.
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Matched Asymptotic Expansion for Caged Black Holes - Regularization of
the Post-Newtonian Order: The "dialogue of multipoles" matched asymptotic expansion for small black
holes in the presence of compact dimensions is extended to the Post-Newtonian
order for arbitrary dimensions. Divergences are identified and are regularized
through the matching constants, a method valid to all orders and known as
Hadamard's partie finie. It is closely related to "subtraction of
self-interaction" and shows similarities with the regularization of quantum
field theories. The black hole's mass and tension (and the "black hole
Archimedes effect") are obtained explicitly at this order, and a Newtonian
derivation for the leading term in the tension is demonstrated. Implications
for the phase diagram are analyzed, finding agreement with numerical results
and extrapolation shows hints for Sorkin's critical dimension - a dimension
where the transition turns second order.
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Applications of the Weyl-Wigner formalism to noncommutative geometry: In this dissertation the Weyl-Wigner approach is presented as a map between
functions on a real cartesian symplectic vector space and a set of operators on
a Hilbert space, to analyse some aspects of the relations between quantum and
classical formalism, both as a quantization, and as a classical limit. It is
presented an extension of this formalism to the case of a more general
classical phase space, namely one whose configuration space is a compact simple
Lie group. In the second part, it is used to develop a fuzzy approximation to
the algebra of functions on a disc. This is the first example of a fuzzy space
originating from a classical space which has a boundary. It is analysed how
this approximation copes the presence of ultraviolet divergences even in
noninteracting field theories on a disc.
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Yangian Invariant Scattering Amplitudes in Supersymmetric Chern-Simons
Theory: We propose a generating function for scattering amplitudes of N=6
super-Chern-Simons theory which parallels a recent work on N=4 super-Yang-Mills
theory by Arkani-Hamed et al. Our result suggests that the scattering
amplitudes of the super-Chern-Simons theory exhibit Yangian invariance.
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Sigma-model soliton intersections from exceptional calibrations: A first-order `BPS' equation is obtained for 1/8 supersymmetric intersections
of soliton-membranes (lumps) of supersymmetric (4+1)-dimensional massless sigma
models, and a special non-singular solution is found that preserves 1/4
supersymmetry. For 4-dimensional hyper-K\"ahler target spaces ($HK_4$) the BPS
equation is shown to be the low-energy limit of the equation for a
Cayley-calibrated 4-surface in $\bE^4\times HK_4$. Similar first-order
equations are found for stationary intersections of Q-lump-membranes of the
massive sigma model, but now generic solutions preserve either 1/8
supersymmetry or no supersymmetry, depending on the time orientation.
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Three-loop universal anomalous dimension of the Wilson operators in N=4
SUSY Yang-Mills model: We present results for the three-loop universal anomalous dimension of Wilson
twist-2 operators in the N=4 Supersymmetric Yang-Mills model. These results are
obtained by extracting the most complicated contributions from the three loop
non-singlet anomalous dimensions in QCD which were calculated recently. Their
singularities at j=1 agree with the predictions obtained from the BFKL equation
for N=4 SYM in the next-to-leading order. The asymptotics of universal
anomalous dimension at large j is in an agreement with the expectations based
on an interpolation between weak and strong coupling regimes in the framework
of the AdS/CFT correspondence.
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Phenomenology from the Landscape of String Vacua: This article is the author's PhD thesis. After a review of string vacua
obtained through compactification (with and wothout fluxes), it presents and
describes various aspects of the Landscape of string vacua. At first it gives
an introduction and an overview of the statistical study of the set of four
dimensional string vacua, giving the detailed study of one corner of this set
(G2-holonomy compactifications of M-theory). Then it presents the ten
dimensional approach to string vacua, concentrating on the ten dimensional
description of the Type IIA flux vacua. Finally it gives two examples of models
having some interesting and characteristic phenomenological features, and that
belong to two different corners of the Landscape: warped compactifications of
Type IIB String Theory and M-theory compactifications on G2-holonomy manifolds.
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Low's Subleading Soft Theorem as a Symmetry of QED: It was shown by F. Low in the 1950s that the subleading terms of soft photon
S-matrix elements obey a universal linear relation. In this paper we give a new
interpretation to this old relation, for the case of massless QED, as an
infinitesimal symmetry of the S-matrix. The symmetry is shown to be locally
generated by a vector field on the conformal sphere at null infinity. Explicit
expressions are constructed for the associated charges as integrals over null
infinity and shown to generate the symmetry. These charges are local
generalizations of electric and magnetic dipole charges.
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Lagrangian formulation of massive fermionic totally antisymmetric tensor
field theory in AdS_d space: We apply the BRST approach, developed for higher spin field theories, to
Lagrangian construction for totally antisymmetric massive fermionic fields in
AdS_d space. As well as generic higher spin massive theories, the obtained
Lagrangian theory is a reducible gauge model containing, besides the basic
field, a number of auxiliary (Stuckelberg) fields and the order of reducibility
grows with the value of the rank of the antisymmetric field. However, unlike
the generic higher spin theory, for the special case under consideration we
show that one can get rid of all the auxiliary fields and the final Lagrangian
for fermionic antisymmetric field is formulated only in terms of basic field.
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From giant gravitons to black holes: We study AdS$_5$ black holes from a recently suggested giant graviton
expansion formula for the index of $U(N)$ maximal super-Yang-Mills theory. We
compute the large $N$ entropy at fixed charges and giant graviton numbers $n_I$
by a saddle point analysis, and further maximize it in $n_I$. This agrees with
the dual black hole entropy in the small black hole limit. To get black holes
at general sizes, one should note that various giant graviton indices cancel
because gauge theory does not suffer from a Hagedorn-like pathology by an
infinite baryonic tower. With one assumption on the mechanism of this
cancellation, we account for the dual black hole entropy at general sizes. We
interpret our results as analytic continuations of the large $N$ free energies
of SCFTs, and based on it compute the entropies of AdS$_{4,7}$ black holes from
M5, M2 giant gravitons.
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Quasi-normal modes of a dielectric ball and some their implications: It is shown that the quasi-normal modes arise, in a natural way, when
considering the oscillations in unbounded regions by imposing the radiation
condition at spatial infinity with a complex wave vector $k$. Hence
quasi-normal modes are not peculiarities of gravitation problems only (black
holes and relativistic stars). It is proposed to consider the space form of the
quasi-normal modes with allowance for their time dependence. As a result, the
problem of their unbounded increase when $r\to \infty$ is not encountered more.
The properties of quasi-normal modes of a compact dielectric sphere are
discussed in detail. It is argued that the spatial form of these modes
(especially so-called surface modes) should be taken into account, for example,
when estimating the potential health hazards due to the use of portable
telephones.
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Loop Corrections in Double Field Theory: Non-trivial Dilaton Potentials: It is believed that the invariance of the generalised diffeomorphisms
prevents any non-trivial dilaton potential from double field theory. It is
therefore difficult to include loop corrections in the formalism. We show that
by redefining a non-local dilaton field, under strong constraint which is
necessary to preserve the gauge invariance of double field theory, the theory
does permit non-constant dilaton potentials and loop corrections. If the fields
have dependence on only one single coordinate, the non-local dilaton is
identical to the ordinary one with an additive constant.
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Two dimensional QCD is a one dimensional Kazakov-Migdal model: We calculate the partition functions of QCD in two dimensions on a cylinder
and on a torus in the gauge $\partial_{0} A_{0} = 0$ by integrating explicitly
over the non zero modes of the Fourier expansion in the periodic time variable.
The result is a one dimensional Kazakov-Migdal matrix model with eigenvalues on
a circle rather than on a line. We prove that our result coincides with the
standard expansion in representations of the gauge group. This involves a non
trivial modular transformation from an expansion in exponentials of $g^2$ to
one in exponentials of $1/g^2$. Finally we argue that the states of the $U(N)$
or $SU(N)$ partition function can be interpreted as a gas of N free fermions,
and the grand canonical partition function of such ensemble is given explicitly
as an infinite product.
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Natural Cutoffs effect on Charged Rotating TeV-Scale Black Hole
Thermodynamics: We study the thermodynamics of charged rotating black hole in large extra
dimensions scenario where quantum gravity effects are taken into account. We
consider the effects of minimal length, minimal momentum, and maximal momentum
as natural cutoffs on the thermodynamics of charged rotating TeV-scale black
holes. In this framework the effect of the angular momentum and charge on the
thermodynamics of the black hole are discussed. We focus also on frame dragging
and Sagnac effect of the micro black holes.
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Relativistic Elasticity of Stationary Fluid Branes: Fluid mechanics can be formulated on dynamical surfaces of arbitrary
co-dimension embedded in a background space-time. This has been the main object
of study of the blackfold approach in which the emphasis has primarily been on
stationary fluid configurations. Motivated by this approach we show under
certain conditions that a given stationary fluid configuration living on a
dynamical surface of vanishing thickness and satisfying locally the first law
of thermodynamics will behave like an elastic brane when the surface is subject
to small deformations. These results, which are independent of the number of
space-time dimensions and of the fluid arising from a gravitational dual,
reveal the (electro)elastic character of (charged) black branes when
considering extrinsic perturbations.
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P-T phase diagram of a holographic s+p model from Gauss-Bonnet gravity: In this paper, we study the holographic s+p model in 5-dimensional bulk
gravity with the Gauss-Bonnet term. We work in the probe limit and give the
$\Delta$-T phase diagrams at three different values of the Gauss-Bonnet
coefficient to show the effect of the Gauss-Bonnet term. We also construct the
P-T phase diagrams for the holographic system using two different definitions
of the pressure and compare the results.
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On the Stringy Hartle-Hawking State: We argue that non-perturbative $\alpha'$ stringy effects render the
Hartle-Hawking state associated with the $SL(2)/U(1)$ eternal black hole
singular at the horizon. We discuss implications of this observation on
firewalls in string theory.
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Cosmic microwave background polarization, Faraday rotation and
stochastic gravity-waves backgrounds: A magnetic field, coherent over the horizon size at the decoupling and strong
enough to rotate the polarization plane of the CMBR, can be generated from the
electromagnetic vacuum fluctuations amplified by the space-time evolution of
the dilaton coupling. The possible relevance of this result for superstring
inspired cosmological models is discussed. Particular attention will be paid to
the connection between Faraday rotation signals and stochastic gravity-wave
backgrounds.
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Supersymmetric solutions of N=2 d=4 sugra: the whole ungauged shebang: In this article we complete the classification of the supersymmetric
solutions of N=2 D=4 ungauged supergravity coupled to an arbitrary number of
vector- and hypermultiplets. We find that in the timelike case the
hypermultiplets cause the constant-time hypersurfaces to be curved and have
su(2) holonomy identical to that of the hyperscalar manifold. The solutions
have the same structure as without hypermultiplets but now depend on functions
which are harmonic in the curved 3-dimensional space. We discuss an example
obtained from a hyper-less solution via the c-map. In the null case we find
that the hyperscalars can only depend on the null coordinate and the solutions
are essentially those of the hyper-less case.
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Covariant representation theory of the Poincaré algebra and some of
its extensions: There has been substantial calculational progress in the last few years for
gauge theory amplitudes which involve massless four dimensional particles. One
of the central ingredients in this has been the ability to keep precise track
of the Poincare algebra quantum numbers of the particles involved. Technically,
this is most easily done using the well-known four dimensional spinor helicity
method. In this article a natural generalization to all dimensions higher than
four is obtained based on a covariant version of the representation theory of
the Poincare algebra. Covariant expressions for all possible polarization
states, both bosonic and fermionic, are constructed. For the fermionic states
the analysis leads directly to pure spinors. The natural extension to the
representation theory of the on-shell supersymmetry algebra results in an
elementary derivation of the supersymmetry Ward identities for scattering
amplitudes with massless or massive legs in any integer dimension from four
onwards. As a proof-of-concept application a higher dimensional analog of the
vanishing helicity-equal amplitudes in four dimensions is presented in (super)
Yang-Mills theory, Einstein (super-)gravity and superstring theory in a flat
background.
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Noncommutative Momentum for Arbitrary Spin Polarization: There have been comments on the starting paper, hep-th/0106074, which point
out unclear motivation and definitions on noncommutative momentum introduced.
Therefore, to give more clear presentation, this paper is withdrawn.
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Ghost-free higher derivative unimodular gravity: The unimodular version of the ghost-free higher derivative gravity is
obtained. It is the unimodular reduction of some particular lagrangians
quadratic in curvature.
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Dynamical Decay of Brane-Antibrane and Dielectric Brane: Using D-brane effective field theories, we study dynamical decay of unstable
brane systems : (i) a parallel brane-antibrane pair with separation l and (ii)
a dielectric brane. In particular we give explicitly the decay width of these
unstable systems, and describe how the decay proceeds after the tunnel effect.
The decay (i) is analysed by the use of a tachyon effective action on the
Dp-Dpbar. A pair annihilation starts by nucleation of a bubble of a tachyon
domain wall which represents a throat connecting these branes, and the
tunneling decay width is found to be proportional to exp(-l^{p+1} T_{Dp}). We
study also the decay leaving topological defects corresponding to
lower-dimensional branes, which may be relevant for recent inflationary
braneworld scenario. As for the decay (ii), first we observe that Dp-branes
generically ``curl up'' in a nontrivial RR field strength. Using this
viewpoint, we compute the decay width of the dielectric D2-branes by
constructing relevant Euclidean bounce solutions in the shape of a funnel. We
also give new solutions in doughnut shape which are involved with nucleation of
dielectric branes from nothing.
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Topological couplings in higher derivative extensions of supersymmetric
three-form gauge theories: We consider a topological coupling between a pseudo-scalar field and a 3-form
gauge field in ${\cal N}=1$ supersymmetric higher derivative 3-form gauge
theories in four spacetime dimensions. We show that ghost/tachyon-free higher
derivative Lagrangians with the topological coupling can generate various
potentials for the pseudo-scalar field by solving the equation of motion for
the 3-form gauge field. We give two examples of higher derivative Lagrangians
and the corresponding potentials: one is a quartic order term of the field
strength and the other is the term which can generate a cosine-type potential
of the pseudo-scalar field.
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Current Algebra and Bosonization in Three Dimensions: We consider the fermion-boson mapping in three dimensional space-time, in the
Abelian case, from the current algebra point of view. We show that in a
path-integral framework one can derive a general bosonization recipe leading,
in the bosonic language, to the correct equal-time current commutators of the
original free fermionic theory.
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On Bogomolny equations in generalized gauged baby BPS Skyrme models: Using the concept of strong necessary conditions (CSNC), we derive Bogomolny
equations and BPS bounds for two modifications of the gauged baby BPS Skyrme
model: the nonminimal coupling to the gauge field and k-deformed model. In
particular, we study, how the Bogomolny equations and the equation for the
potential, reflect these two modifications. In both examples, the CSNC method
shows to be a very useful tool.
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Vacuum Radiation in Conformally Invariant Quantum Field Theory: Although the whole conformal group $SO(4,2)$ can be considered as a symmetry
in a classical massless field theory, the subgroup of special conformal
transformations (SCT), usually related to transitions to uniformly accelerated
frames, causes vacuum radiation in the corresponding quantum field theory, in
analogy to the Fulling-Unruh effect. The spectrum of the outgoing particles can
be calculated exactly and proves to be a generalization of the Planckian one.
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Retrofitting and the mu Problem: One of the challenges of supersymmetry (SUSY) breaking and mediation is
generating a mu term consistent with the requirements of electro-weak symmetry
breaking. The most common approach to the problem is to generate the mu term
through a SUSY breaking F-term. Often these models produce unacceptably large B
mu terms as a result. We will present an alternate approach, where the mu term
is generated directly by non-perturtative effects. The same non-perturbative
effect will also retrofit the model of SUSY breaking in such a way that mu is
at the same scale as masses of the Standard Model superpartners. Because the mu
term is not directly generated by SUSY breaking effects, there is no associated
B mu problem. These results are demonstrated in a toy model where a stringy
instanton generates mu.
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Gravity Dual of Two-Dimensional $\mathcal{N} = (2,2)^*$ Supersymmetric
Yang-Mills Theory and Integrable Models: The 2D $\mathcal{N}=(2,2)^*$ supersymmetric Yang-Mills theory can be obtained
from the 2D $\mathcal{N}=(4,4)$ theory with a twisted mass deformation. In this
paper we construct the gravity dual theory of the 2D $\mathcal{N}=(2,2)^*$
supersymmetric $U(N)$ Yang-Mills theory at the large $N$ and large 't Hooft
coupling limit using the 5D gauged supergravity. In the UV regime, this
construction also provides the gravity dual of the 2D $\mathcal{N}=(2,2)^*$
$U(N)$ topological Yang-Mills-Higgs theory. We propose a triality in the UV
regime among integrable model, gauge theory and gravity, and we make some
checks of this relation at classical level.
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Homage to Ettore Majorana: Homage is paid to E. Majorana by dedicating our recent work in his memory.
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Black Hole Geometries in Noncommutative String Theory: We obtain a generalized Schwarzschild (GS-) and a generalized
Reissner-Nordstrom (GRN-) black hole geometries in (3+1)-dimensions, in a
noncommutative string theory. In particular, we consider an effective theory of
gravity on a curved $D_3$-brane in presence of an electromagnetic (EM-) field.
Two different length scales, inherent in its noncommutative counter-part, are
exploited to obtain a theory of effective gravity coupled to an U(1)
noncommutative gauge theory to all orders in $\Theta$. It is shown that the
GRN-black hole geometry, in the Planckian regime, reduces to the GS-black hole.
However in the classical regime it may be seen to govern both
Reissner-Nordstrom and Schwarzschild geometries independently. The emerging
notion of 2D black holes evident in the frame-work are analyzed. It is argued
that the $D$-string in the theory may be described by the near horizon 2D black
hole geometry, in the gravity decoupling limit. Finally, our analysis explains
the nature of the effective force derived from the nonlinear EM-field and
accounts for the Hawking radiation phenomenon in the formalism.
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High-Energy theory for close Randall Sundrum branes: We obtain an effective theory for the radion dynamics of the two-brane
Randall Sundrum model, correct to all orders in brane velocity in the limit of
close separation, which is of interest for studying brane collisions and early
Universe cosmology. Obtained via a recursive solution of the Bulk equation of
motions, the resulting theory represents a simple extension of the
corresponding low-energy effective theory to the high energy regime. The
four-dimensional low-energy theory is indeed not valid when corrections at
second order in velocity are considered. This extension has the remarkable
property of including only second derivatives and powers of first order
derivatives. This important feature makes the theory particularly easy to
solve. We then extend the theory by introducing a potential and detuning the
branes.
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Lattice Landau gauge via Stereographic Projection: The complete cancellation of Gribov copies and the Neuberger 0/0 problem of
lattice BRST can be avoided in modified lattice Landau gauge. In compact U(1),
where the problem is a lattice artifact, there remain to be Gribov copies but
their number is exponentially reduced. Moreover, there is no cancellation of
copies there as the sign of the Faddeev-Popov determinant is positive. Applied
to the maximal Abelian subgroup this avoids the perfect cancellation amongst
the remaining Gribov copies for SU(N) also. In addition, based on a definition
of gauge fields on the lattice as stereographically-projected link variables,
it provides a framework for gauge fixed Monte-Carlo simulations. This will
include all Gribov copies in the spirit of BRST. Their average is not zero, as
demonstrated explicitly in simple models. This might resolve present
discrepancies between gauge-fixed lattice and continuum studies of QCD Green's
functions.
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Density matrices in quantum gravity: We study density matrices in quantum gravity, focusing on topology change. We
argue that the inclusion of bra-ket wormholes in the gravity path integral is
not a free choice, but is dictated by the specification of a global state in
the multi-universe Hilbert space. Specifically, the Hartle-Hawking (HH) state
does not contain bra-ket wormholes. It has recently been pointed out that
bra-ket wormholes are needed to avoid potential bags-of-gold and strong
subadditivity paradoxes, suggesting a problem with the HH state. Nevertheless,
in regimes with a single large connected universe, approximate bra-ket
wormholes can emerge by tracing over the unobserved universes. More drastic
possibilities are that the HH state is non-perturbatively gauge equivalent to a
state with bra-ket wormholes, or that the third-quantized Hilbert space is
one-dimensional. Along the way we draw some helpful lessons from the well-known
relation between worldline gravity and Klein-Gordon theory. In particular, the
commutativity of boundary-creating operators, which is necessary for
constructing the alpha states and having a dual ensemble interpretation, is
subtle. For instance, in the worldline gravity example, the Klein-Gordon field
operators do not commute at timelike separation.
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From Simplified BLG Action to the First-Quantized M-Theory: Concise summary of the recent progress in the search for the world-volume
action for multiple M2 branes. After a recent discovery of simplified version
of BLG action, which is based on the ordinary Lie-algebra structure, does not
have coupling constants and extra dynamical fields, attention should be
switched to the study of M2 brane dynamics. A viable brane analogue of Polyakov
formalism and Belavin-Knizhnik theorem for strings can probably be provided by
Palatini formalism for 3d (super)gravity.
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TBA Equations and Quantization Conditions: It has been recently realized that, in the case of polynomial potentials, the
exact WKB method can be reformulated in terms of a system of TBA equations. In
this paper we study this method in various examples. We develop a graphical
procedure due to Toledo, which provides a fast and simple way to study the
wall-crossing behavior of the TBA equations. When complemented with exact
quantization conditions, the TBA equations can be used to solve spectral
problems exactly in Quantum Mechanics. We compute the quantum corrections to
the all-order WKB periods in many examples, as well as the exact spectrum for
many potentials. In particular, we show how this method can be used to
determine resonances in unbounded potentials.
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"Self-tuning" and Conformality: We consider an infinite-volume brane world setup where a codimension one
brane is coupled to bulk gravity plus a scalar field with vanishing potential.
The latter is protected by bulk supersymmetry, which is intact even if brane
supersymmetry is completely broken as the volume of the extra dimension is
infinite. Within this setup we discuss a flat solution with a ``self-tuning''
property, that is, such a solution exists for a continuous range of values for
the brane tension. This infinite-volume solution is free of any singularities,
and has the property that the brane cosmological constant is protected by bulk
supersymmetry. We, however, also point out that consistency of the coupling
between bulk gravity and brane matter generically appears to require that the
brane world-volume theory be conformal.
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Radiation from SU(3) monopole scattering: The energy radiated during the scattering of SU(3) monopoles is estimated as
a function of their asymptotic velocity v. In a typical scattering process the
total energy radiated is of order v^3 as opposed to v^5 for SU(2) monopoles.
For charge (1,1) monopoles the dipole radiation produced is estimated for all
geodesics on the moduli space. For charge (2,1) monopoles the dipole radiation
is estimated for the axially symmetric geodesic. The power radiated appears to
diverge in the massless limit. The implications of this for the case of
non-Abelian unbroken symmetry are discussed.
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Classification of Singular Spinor Fields and Other Mass Dimension One
Fermions: We investigate the constraint equations of the Lounesto spinor fields
classification and show that it can be used to completely characterize all the
singular classes, which are potential accommodations for further mass dimension
one fermions, beyond the well known Elko spinor fields. This result can be
useful for two purposes: besides a great abridgement in the classification of a
given spinor field, we provide a general form of each class of spinor fields,
which can be used furthermore to search for a general classification of spinors
dynamics.
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Simple variables for AdS$_5 \times S^5$ superspace: We introduce simple variables for describing the AdS$_5\times S^5$
superspace, i. e. $\frac{PSU(2,2|4)}{SO(4,1)\times SO(5)}$. The idea is to
embed the coset superspace into a space described by variables which are in
linear (ray) representations of the supergroup $PSU(2,2|4)$ by imposing certain
supersymmetric quadratic constraints (up to two overall U(1) factors). The
construction can be considered as a supersymmetric generalisation of the
elementary realisations of the $AdS_5$ and the $S^5$ spaces by the SO(4,2) and
SO(6) invariant quadratic constraints on two six-dimensional flat spaces.
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A Canticle on (4,0) Supergravity-Scalar Multiplet Systems for a
``Cognoscente'': Extending prior investigations, we study three of the the four distinct
minimal (4,0) scalar multiplets coupled to (4,0) supergravity. It is found that
the scalar multiplets manifest their differences at the component level by
possessing totally different couplings to the supergravity fields. Only the
SM-I multiplet possesses a conformal coupling. For the remaining multiplets,
terms linear in the world sheet curvature and/or SU(2) gauge field strengths
are required to appear in the action by local supersymmetry.
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Superconnections: an Interpretation of the Standard Model: The mathematical framework of superbundles suggests that one considers the
Higgs field as a natural constituent of a superconnection. I propose to take as
superbundle the exterior algebra obtained from a Hermitian vector bundle of
rank 5 for the Standard Model.
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Hopf Algebraic Structures in the Cutting Rules: Since the Connes--Kreimer Hopf algebra was proposed, revisiting present
quantum field theory has become meaningful and important from algebraic points.
In this paper, the Hopf algebra in the cutting rules is constructed. Its
coproduct contains all necessary ingredients for the cutting equation crucial
to proving perturbative unitarity of the S-matrix. Its antipode is compatible
with the causality principle. It is obtained by reducing the Hopf algebra in
the largest time equation which reflects partitions of the vertex set of a
given Feynman diagram. First of all, the Connes--Kreimer Hopf algebra in the
BPHZ renormalization instead of the dimensional regularization and the minimal
subtraction is described so that the strategy of setting up Hopf algebraic
structures of Feynman diagrams becomes clear.
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Fluctuations in the Entropy of Hawking Radiation: We use the gravitational path integral (GPI) to compute the fluctuations of
the Hawking radiation entropy around the Page curve, in a two-dimensional model
introduced by Penington \emph{et al}. Before the Page time, we find that
$\delta S = e^{-S}/\sqrt{2}$, where $S$ is the black hole entropy. This result
agrees with the Haar-averaged entropy fluctuations of a bipartite system, which
we also compute at leading order. After the Page time, we find that $\delta S
\sim e^{-S}$, up to a prefactor that depends logarithmically on the width of
the microcanonical energy window. This is not symmetric under exchange of
subsystem sizes and so does not agree with the Haar average for a subsystem of
fixed Hilbert space dimension. The discrepancy can be attributed to the fact
that the black hole Hilbert space dimension is not fixed by the state
preparation: even in a microcanonical ensemble with a top-hat smearing
function, the GPI yields an additive fluctuation in the number of black hole
states. This result, and the fact that the Page curve computed by the GPI is
smooth, all point towards an ensemble interpretation of the GPI.
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A-twisted correlators and Hori dualities: The Hori-Tong and Hori dualities are infrared dualities between
two-dimensional gauge theories with $\mathcal{N}{=}(2,2)$ supersymmetry, which
are reminiscent of four-dimensional Seiberg dualities. We provide additional
evidence for those dualities with $U(N_c)$, $USp(2N_c)$, $SO(N)$ and $O(N)$
gauge groups, by matching correlation functions of Coulomb branch operators on
a Riemann surface $\Sigma_g$, in the presence of the topological $A$-twist. The
$O(N)$ theories studied, denoted by $O_+ (N)$ and $O_- (N)$, can be understood
as $\mathbb{Z}_2$ orbifolds of an $SO(N)$ theory. The correlators of these
theories on $\Sigma_g$ with $g > 0$ are obtained by computing correlators with
$\mathbb{Z}_2$-twisted boundary conditions and summing them up with weights
determined by the orbifold projection.
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Exact Combinatorics of Bern-Kosower-type Amplitudes for Two-Loop
$Φ^3$ Theory: Counting the contribution rate of a world-line formula to Feynman diagrams in
$\phi^3$ theory, we explain the idea how to determine precise combinatorics of
Bern-Kosower-like amplitudes derived from a bosonic string theory for $N$-point
two-loop Feynman amplitudes. In this connection we also present a method to
derive simple and compact world-line forms for the effective action.
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Consistent Pauli reduction on group manifolds: We prove an old conjecture by Duff, Nilsson, Pope and Warner asserting that
the NS-NS sector of supergravity (and more general the bosonic string) allows
for a consistent Pauli reduction on any d-dimensional group manifold G, keeping
the full set of gauge bosons of the G x G isometry group of the bi-invariant
metric on G. The main tool of the construction is a particular generalised
Scherk-Schwarz reduction ansatz in double field theory which we explicitly
construct in terms of the group's Killing vectors. Examples include the
consistent reduction from ten dimensions on $S^3\times S^3$ and on similar
product spaces. The construction is another example of globally geometric
non-toroidal compactifications inducing non-geometric fluxes.
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On The Bound States Of Photons In Noncommutative Quantum Electrodynamics: We consider the possibility that photons of noncommutative QED can make bound
states. Using the potential model, developed based on the constituent gluon
picture of QCD glue-balls, arguments are presented in favor of existence of
these bound states. The basic ingredient of potential model is that the
self-interacting massless gauge particles may get mass by inclusion
non-perturbative effects.
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BiHermitian Supersymmetric Quantum Mechanics: BiHermitian geometry, discovered long ago by Gates, Hull and Rocek, is the
most general sigma model target space geometry allowing for (2,2) world sheet
supersymmetry. In this paper, we work out supersymmetric quantum mechanics for
a biHermitian target space. We display the full supersymmetry of the model and
illustrate in detail its quantization procedure. Finally, we show that the
quantized model reproduces the Hodge theory for compact twisted generalized
Kaehler manifolds recently developed by Gualtieri. This allows us to recover
and put in a broader context the results on the biHermitian topological sigma
models obtained by Kapustin and Li.
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A Comparison of Supersymmetry Breaking and Mediation Mechanisms: We give a unified treatment of different models of supersymmetry breaking and
mediation from a four dimensional effective field theory standpoint. In
particular a comparison between GMSB and various gravity mediated versions of
SUSY breaking shows that, once the former is embedded within a SUGRA framework,
there is no particular advantage to that mechanism from the point of view of
FCNC suppression. We point out the difficulties of all these scenarios - in
particular the cosmological modulus problem. We end with a discussion of
possible string theory realizations.
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Currents on Grassmann algebras: We define currents on a Grassmann algebra $Gr(N)$ with $N$ generators as
distributions on its exterior algebra (using the symmetric wedge product). We
interpret the currents in terms of ${\Z}_2$-graded Hochschild cohomology and
closed currents in terms of cyclic cocycles (they are particular multilinear
forms on $Gr(N)$). An explicit construction of the vector space of closed
currents of degree $p$ on $Gr(N)$ is given by using Berezin integration.
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Confined two-dimensional fermions at finite density: We introduce the chemical potential in a system of two-dimensional massless
fermions, confined to a finite region, by imposing twisted boundary conditions
in the Euclidean time direction. We explore in this simple model the
application of functional techniques which could be used in more complicated
situations.
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Near-Conformal Dynamics at Large Charge: We investigate four-dimensional near-conformal dynamics by means of the
large-charge limit. We first introduce and justify the formalism in which
near-conformal invariance is insured by adding a dilaton and then determine the
large-charge spectrum of the theory. The dilaton can also be viewed as the
radial mode of the EFT. We calculate the two-point functions of charged
operators. We discover that the mass of the dilaton, parametrising the
near-breaking of conformal invariance, induces a novel term that is logarithmic
in the charge. One can therefore employ the large-charge limit to explore
near-conformal dynamics and determine dilaton-related properties.
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The Loop Group of E_8 and K-Theory from 11d: We examine the conjecture that an 11d E_8 bundle, appearing in the
calculation of phases in the M-Theory partition function, plays a physical role
in M-Theory, focusing on consequences for the classification of string theory
solitons. This leads for example to a classification of IIA solitons in terms
of that of LE_8 bundles in 10d. Since K(Z,2) approximates LE_8 up to \pi_{14},
this reproduces the K-Theoretic classification of IIA D-branes while treating
NSNS and RR solitons more symmetrically and providing a natural interpretation
of G_0 as the central extension of LE_8.
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The fermion-boson map for large $d$ and its connection to lattice
transformations: I point out that the phase transitions of the $d+1$ Gross-Neveu and
$CP^{N-1}$ models at finite temperature and imaginary chemical potential can be
mapped to transformations of regular hexagonal and regular triangular lattices
to square lattice. The duality elements of two continuous models of fermions
and bosons and two discrete lattice models make their appearance offering a new
view of their phase transitions. I also show that the fermion-boson map in odd
dimensions at finite temperature and imaginary chemical potential has a
generalization for arbitrary $d$ that gives an expression of the transfer
momentum of fundamental particles that behave like Bloch waves. These particles
are travelling inside a periodic potential and scattering from specific
surfaces (hexagonal and triangular kind) with a specific ordered construction
based on golden ratio formula $\phi=\frac{1}{\phi}+1$ and its generalization. I
further argue that this transfer momentum gives us a modified Bragg Law
equation which it has a large $d$ limit to the well known expression for the
transfer momentum when the scattering lattice is square. Interestingly these
surfaces make a family of some first Brillouin zones that interact with
particle beams and the maximum amount of momentum of the beam is transferred to
them for specific angles related to their construction. Their construction is
based on the golden ratio $\phi$ and the Riemann $\zeta(n)$ functions. The
zeros and extrema of the Bloch-Wigner-Ramakrishnan $D_d(z)$ functions and
Clausen $Cl_d(\theta) $ functions play an important role to the analysis since
they allow us not only to study the lattice transformations but also to study
the fermionic theory deep inside the strong coupling regime as the dimension of
the theory increases.
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Calogero-Sutherland Approach to Defect Blocks: Extended objects such as line or surface operators, interfaces or boundaries
play an important role in conformal field theory. Here we propose a systematic
approach to the relevant conformal blocks which are argued to coincide with the
wave functions of an integrable multi-particle Calogero-Sutherland problem.
This generalizes a recent observation in 1602.01858 and makes extensive
mathematical results from the modern theory of multi-variable hypergeometric
functions available for studies of conformal defects. Applications range from
several new relations with scalar four-point blocks to a Euclidean inversion
formula for defect correlators.
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Quantum Gravity, Field Theory and Signatures of Noncommutative Spacetime: A pedagogical introduction to some of the main ideas and results of field
theories on quantized spacetimes is presented, with emphasis on what such field
theories may teach us about the problem of quantizing gravity. We examine to
what extent noncommutative gauge theories may be regarded as gauge theories of
gravity. UV/IR mixing is explained in detail and we describe its relations to
renormalization, to gravitational dynamics, and to deformed dispersion
relations in models of quantum spacetime of interest in string theory and in
doubly special relativity. We also discuss some potential experimental probes
of spacetime noncommutativity.
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Electric/Magnetic Field Deformed Giant Gravitons in Melvin Geometry: The rotating D3-brane in the $AdS_5 \times S^5$ spacetime could be blowed up
to the spherical BPS configuration which has the same energy and quantum number
of the point-like graviton and is called as a giant graviton. The configuration
is stable only if its angular momentum was less than a critical value of $P_c$.
In this paper we investigate the properties of the giant graviton in the
electric/magnetic Melvin geometries of deformed $AdS_5 \times S^5$ spacetime
which was obtained in our previous paper (hep-th/0512117, Phys. Rev. D73 (2006)
026007). We find that in the magnetic Melvin spacetime the giant graviton has
lower energy than the point-like graviton. Also, the critical value of the
angular momentum is an increasing function of the magnetic field flux $B$. In
particular, it is seen that while increasing the angular momentum the radius of
giant graviton is initially an increasing function, then, after it reach its
maximum value it becomes a decreasing function of the angular momentum. During
these regions the giant graviton is still a stable configuration, contrast to
that in the undeformed theory. Finally, beyond the critical value of angular
momentum the giant graviton has higher energy than the point-like graviton and
it eventually becomes unstable. Our analyses show that the electric Melvin
field will always render the giant graviton unstable.
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Non-commutative Gross-Neveu model at large N: The non-commutative O(N) Gross-Neveu model is solved in the large N limit in
two and three space-time dimensions. The commutative version of the two
dimensional model is a renormalizable quantum field theory, both in a coupling
constant expansion and an expansion in 1/N. The non-commutative version has a
renormalizable coupling constant expansion where ultraviolet divergences can be
removed by adjusting counterterms to each order. On the other hand, in a
previous work, we showed that the non-commutative theory is not renormalizable
in the large N expansion. This is argued to be due to a combined effect of
asymptotic freedom and the ultraviolet/infrared mixing that occurs in a
non-commutative field theory. In the present paper we will elaborate on this
result and extend it to study the large N limit of the three dimensional
Gross-Neveu model. We shall see that the large N limit of the three dimensional
theory is also trivial when the ultraviolet cutoff is removed.
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Conformal Dilaton-Higgs Gravity on Warped Spacetimes: Black Hole
Paradoxes revisited: We investigate on a Randall-Sundrum warped spacetime, a Kerr-like black hole
in the conformal dilaton-Higgs $(\omega,\Phi)$ gravity model. We applied the
antipodal boundary condition on the Klein surface using the
$\mathds{Z}_2$-symmetry in the "large" (bulk) extra dimension. It turns out
that the pseudo-Riemannian 5D manifold can be written as an effective 4D
Riemannian brane spacetime, $\mathds{R}^2_+\times\mathds{R}^1\times S^1$, where
$\mathds{R}^2_+$ is conformally flat. The solution in valid on both manifolds.
So the solution can equally well described by an instanton solution. An
advantage is that antipodicity can be maintained without a "cut-and-past"
method or to rely on quantum cloning, when treating the scattering description
of the evaporation process of the Hawking radiation. We need only the
windingnumber as quantum number. Moreover, the equations are invariant under
time reversal. The problem of finding the matching condition of the
near-horizon approximation and the far-away Regge-Wheeler approximation, can
possibly be solved by splitting the spacetime in a dilaton field times an
"un-physical" spacetime, which is conformally flat. In the case of a constant
gauge field, we find that the conform invariant mass term $\sim \Phi^2\omega^2$
in the Lagrangian follows directly from the superfluous dilaton equation by
suitable choice of the scale of the extra dimension.Finally, we bring forward
the relation between the embedded Klein surface in $\mathds{R}^4$ and the
quantum mechanical information paradox.
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The Gribov horizon and the one-loop color-Coulomb potential: We recalculate the color-Coulomb potential to one-loop order, under the
assumption that the effect of the Gribov horizon is to make i) the transverse
gluon propagator less singular; and ii) the color-Coulomb potential more
singular, than their perturbative behavior in the low-momentum limit. As a
first guess, the effect of the Gribov horizon is mimicked by introducing a
transverse momentum-dependent gluon mass term, leading to a propagator of the
Gribov form, with the prescription that the mass parameter should be adjusted
to the unique value where the infrared behavior of the Coulomb potential is
enhanced. We find that this procedure leads to a Coulomb potential rising
asymptotically as a linear term modified by a logarithm.
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Classical Soft Graviton Theorem due to Scalar Fields on 4-D Minkowski
Background: The classical soft graviton theorem expresses the behavior of low-frequency
gravitational radiation. In this paper, simplistic proofs of the classical soft
graviton theorem for massless and massive scalar fields on $4$-D Minkowski
background are presented without considering the correction to the behavior of
scalar fields and gravitational stress-energy tensor due to the perturbation in
the background.
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Supersymmetric Yang-Mills theory in D=6 without anti-commuting variables: Supersymmetric Yang-Mills theory is formulated in six dimensions, without the
use of anti-commuting variables. This is achieved using a new Nicolai map, to
third order in the coupling constant. This is the second such map in six
dimensions and highlights a potential ambiguity in the formalism.
|
Dimers in a Bottle: We revisit D3-branes at toric CY$_3$ singularities with orientifolds and
their description in terms of dimer models. We classify orientifold actions on
the dimer through smooth involutions of the torus. In particular, we describe
new orientifold projections related to maps on the dimer without fixed points,
leading to Klein bottles. These new orientifolds lead to novel $\mathcal{N}=1$
SCFT's that resemble, in many aspects, non-orientifolded theories. For
instance, we recover the presence of fractional branes and some of them trigger
a cascading RG-flow \`a la Klebanov-Strassler. The remaining involutions lead
to non-supersymmetric setups, thus exhausting the possible orientifolds on
dimers.
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Reflected Entropy and Entanglement Wedge Cross Section with the First
Order Correction: We study the holographic duality between the reflected entropy and the
entanglement wedge cross section with the first order correction. In the field
theory side, we consider the reflected entropy for $\rho_{AB}^m$, where
$\rho_{AB}$ is the reduced density matrix for two intervals in the ground
state. The reflected entropy in the 2d holographic conformal field theories is
computed perturbatively up to the first order in $m-1$ by using the
semiclassical conformal block. In the gravity side, we compute the entanglement
wedge cross section in the backreacted geometry by cosmic branes with tension
$T_m$ which are anchored at the AdS boundary. Comparing both results we find a
perfect agreement, showing the duality works with the first order correction in
$m-1$.
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Holographic Bjorken Flow at Large-D: We use gauge/gravity duality to study the dynamics of strongly coupled gauge
theories undergoing boost invariant expansion in an arbitrary number of
space-time dimensions (D). By keeping the scale of the late-time energy density
fixed, we explore the infinite-D limit and study the first few corrections to
this expansion. In agreement with other studies, we find that the large-D
dynamics are controlled by hydrodynamics and we use our computation to
constrain the leading large-D dependence of a certain combination of transport
coefficients up to 6-th order in gradients. Going beyond late time physics, we
discuss how non-hydrodynamic modes appear in the large-D expansion in the form
of a trans-series in D, identical to the non-perturbative contributions to the
gradient expansion. We discuss the consequence of this trans-series in the
non-convergence of the large-D expansion.
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The Strong-Coupling Expansion and the Ultra-local Approximation in Field
Theory: We discuss the strong-coupling expansion in Euclidean field theory. In a
formal representation for the Schwinger functional, we treat the off-diagonal
terms of the Gaussian factor as a perturbation about the remaining terms of the
functional integral. We first study the strong-coupling expansion in the \phi^4
theory and also quantum electrodynamics. Assuming the ultra-local
approximation, we examine the analytic structure of the zero-dimensional
generating functions in the complex coupling constants plane. Second, we
discuss the ultra-local generating functional in two idealized field theory
models. To control the divergences of the strong-coupling perturbative
expansion two different steps are used. First, we introduce a lattice structure
to give meaning to the ultra-local generating functional. Using an analytic
regularization procedure we discuss briefly how it is possible to obtain a
renormalized Schwinger functional associated with these scalar models, going
beyond the ultra-local approximation. Using the strong-coupling perturbative
expansion we show how it is possible to compute the renormalized vacuum energy
of a self-interacting scalar field, going beyond the one-loop level.
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Holography versus Correspondence principle: eternal
Schwarzschild-anti-de Sitter geometry: It is shown that the correspondence principle and the holographic principle
are incompatible in the background of an eternal Schwarzschild-anti-de Sitter
geometry. The argument is based on the observation that algebraic structures of
local quantum field and CFT operators are not equivalent. This implies, in
particular, the bulk CFT must be singular near the black-hole horizon. A CFT
Hilbert space representation is elaborated which may correspond to the AdS
black hole in the dual theory.
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Semi-classical wormholes and time machines are unstable: We show that Lorentzian (traversable) wormholes and time machines with
semi-classical spacetimes are unstable due to their violation of the null
energy condition (NEC). Semi-classicality of the energy-momentum tensor in a
given quantum state (required for semi-classicality of the spacetime) implies
localization of its wavefunction in phase space, leading to evolution according
to the classical equations of motion. Previous results related to violation of
the NEC then require that the configuration is unstable to small perturbations.
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Manipulating the internal structure of Bloch walls: In this work, we describe a procedure to manipulate the internal structure of
localized configurations of the Bloch wall type. We consider a three-field
model and develop a first order formalism based on the minimization of the
energy of the static fields. The results show that the third field may be
decoupled and used to change the geometric arrangement of the Bloch wall,
giving rise to a diversity of modifications of its internal structure. The
procedure captures effects that goes beyond the standard situation and can be
used in several applications of practical interest, in particular, for the
study of the magnetization of magnetic materials at the nanometric scale.
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Notes on the ambient approach to boundary values of AdS gauge fields: The ambient space of dimension d+2 allows to formulate both fields on
AdS(d+1) and conformal fields in d dimensions such that the symmetry algebra
o(d,2) is realized linearly. We elaborate an ambient approach to the boundary
analysis of gauge fields on anti de Sitter spacetime. More technically, we use
its parent extension where fields are still defined on AdS or conformal space
through arbitrary intrinsic coordinates while the ambient construction works in
the target space. In this way, a manifestly local and o(d,2)-covariant
formulation of the boundary behaviour of massless symmetric tensor gauge fields
on AdS(d+1) spacetime is obtained. As a byproduct, we identify some useful
ambient formulation for Fronsdal fields, conformal currents and shadow fields
along with a concise generating-function formulation of the Fradkin-Tseytlin
conformal fields somewhat similar to the one obtained by Metsaev. We also show
how this approach extends to more general gauge theories and discuss its
relation to the unfolded derivation of the boundary dynamics recently proposed
by Vasiliev.
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Decelerating cosmologies are de-scramblers: Stationary observers in static spacetimes see falling objects spread
exponentially fast, or fast-scramble, near event horizons. We generalize this
picture to arbitrary cosmological horizons. We give examples of exponential
fast-scrambling and power-law scrambling and "de-scrambling" as charges
propagate freely near a horizon. In particular we show that when the universe
is decelerating, information hidden behind the apparent horizon is de-scrambled
as it re-enters the view of the observer. In contrast to the de Sitter case,
the power-law scaling suggests that the microscopic dynamics of the horizon are
local.
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Roadmap on Wilson loops in 3d Chern-Simons-matter theories: This is a compact review of recent results on supersymmetric Wilson loops in
ABJ(M) and related theories. It aims to be a quick introduction to the state of
the art in the field and a discussion of open problems. It is divided into
short chapters devoted to different questions and techniques. Some new results,
perspectives and speculations are also presented. We hope this might serve as a
baseline for further studies of this topic.
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Completeness in supergravity constructions: We prove that the supergravity r- and c-maps preserve completeness. As a
consequence, any component H of a hypersurface {h=1} defined by a homogeneous
cubic polynomial such that -d^2 h is a complete Riemannian metric on H defines
a complete projective special Kahler manifold and any complete projective
special Kahler manifold defines a complete quaternionic Kahler manifold of
negative scalar curvature. We classify all complete quaternionic Kahler
manifolds of dimension less or equal to 12 which are obtained in this way and
describe some complete examples in 16 dimensions.
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Regular basis and R-matrices for the su(n)_k Knizhnik-Zamolodchikov
equation: Dynamical R-matrix relations are derived for the group-valued chiral vertex
operators in the SU(n) WZNW model from the KZ equation for a general four-point
function including two step operators. They fit the exchange relations for the
U_q(sl_n) covariant quantum matrix derived previously by solving the dynamical
Yang-Baxter equation. As a byproduct, we extend the regular basis introduced
earlier for SU(2) chiral fields to SU(n) step operators and display the
corresponding triangular matrix representation of the braid group.
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Quenches on thermofield double states and time reversal symmetry: In this paper we study a quench protocol on thermofield double states in the
presence of time-reversal symmetry that is inspired by the work of Gao,
Jafferis and Wall.
The deformation is a product of hermitian operators on the left and right
systems that are identical to each other and that lasts for a small amount of
time.
We study the linear dependence on the quench to the properties of the
deformation under time reversal. If the quench is time symmetric, then the
linear response after the quench of all T-even operators vanishes. This
includes the response of the energy on the left system and all the
thermodynamic expectation values (the time averaged expectation values of the
operators). Also, we show under an assumption of non-degeneracy of the
Hamiltonian that the entanglement entropy between left and right is not
affected to this order. We also study a variation of the quench where an
instantaneous deformation is given by an operator of fixed T-parity and it's
time derivative. It is shown that the sign of the response of the Hamiltonian
is correlated with the T-parity of the operator. We can then choose the sign of
the amplitude of the quench to result in a reduction in the energy. This
implies a reduction of the entanglement entropy between both sides.
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