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A Simple Method for Computing Soliton Statistics: I provide an extremely simple argument that the kink-type solitons in certain
theories are fermionic. The argument is based on the Witten index, but can in
fact be used to determine soliton statistics in non-supersymmetric theories as
well.
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On the Covariant Quantization of the 2nd-Ilk Superparticle: This paper is devoted to the quantization of the second-ilk superparticle
using the Batalin-Vilkovisky method. We show the full structure of the master
action. By imposing gauge conditions on the gauge fields rather than on
coordinates we find a gauge-fixed quantum action which is free. The structure
of the BRST charge is exhibited and the BRST cohomology yields the same
physical spectrum as the light- cone quantization of the usual superparticle.
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Aharonov-Bohm phase for an electromagnetic wave background: The canonical Aharonov-Bohm effect is usually studied with time-independent
potentials. In this work, we investigate the Aharonov-Bohm phase acquired by a
charged particle moving in {\it time-dependent} potentials . In particular, we
focus on the case of a charged particle moving in the time varying field of a
plane electromagnetic wave. We work out the Aharonov-Bohm phase using both the
potential ({\it i.e.} $\oint A_\mu dx ^\mu$) and field ({\it i.e.}
$\frac{1}{2}\int F_{\mu \nu} d \sigma ^{\mu \nu}$) forms of the Aharanov-Bohm
phase. We give conditions in terms of the parameters of the system (frequency
of the electromagnetic wave, the size of the space-time loop, amplitude of the
electromagnetic wave) under which the time varying Aharonov-Bohm effect could
be observed.
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Ordinary-derivative formulation of conformal totally symmetric arbitrary
spin bosonic fields: Conformal totally symmetric arbitrary spin bosonic fields in flat space-time
of even dimension greater than or equal to four are studied. Second-derivative
(ordinary-derivative) formulation for such fields is developed. We obtain gauge
invariant Lagrangian and the corresponding gauge transformations. Gauge
symmetries are realized by involving the Stueckelberg and auxiliary fields.
Realization of global conformal boost symmetries on conformal gauge fields is
obtained. Modified de Donder gauge condition and de Donder-Stueckelberg gauge
condition are introduced. Using the de Donder-Stueckelberg gauge frame,
equivalence of the ordinary-derivative and higher-derivative approaches is
demonstrated. On-shell degrees of freedom of the arbitrary spin conformal field
are analyzed. Ordinary-derivative light-cone gauge Lagrangian of conformal
fields is also presented. Interrelations between the ordinary-derivative gauge
invariant formulation of conformal fields and the gauge invariant formulation
of massive fields are discussed.
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Higher Order Conformal Invariance of String Backgrounds Obtained by
O(d,d) Transformations: Proposals that $O(d,d)$ boosts of trivial backgrounds lead to non-trivial
conformally invariant backgrounds are checked to two loop order. We find that
conformal invariance can be achieved by adding simple higher order corrections
to the metric and dilaton.
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The Noncommutative S-Matrix: As a simple example of how recently developed on-shell techniques apply to
nonlocal theories, we study the S-matrix of noncommutative gauge theories. In
the complex plane, this S-matrix has essential singularities that signal the
nonlocal behavior of the theory. In spite of this, we show that tree-level
amplitudes may be obtained by BCFW type recursion relations. At one loop we
find a complete basis of master integrals (this basis is larger than the
corresponding basis in the ordinary theory). Any one-loop noncommutative
amplitude may be written as a linear combination of these integrals with
coefficients that we relate to products of tree amplitudes. We show that the
noncommutative N=4 SYM theory has a structurally simple S-matrix, just like the
ordinary N=4 SYM theory.
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Canonical quantization of the D=2n dimensional relativistic spinning
particle with anomalous magnetic moment in the external electromagnetic field: The pseudoclassical hamiltonian and action of the $D=2n$ dimensional Dirac
particle with anomalous magnetic moment interacting with the external
electromagnetic field is found. The Bargmann-Michel-Telegdi equation of motion
for the Pauli-Lubanski vector is deduced. The canonical quantization of $D=2n$
dimensional Dirac spinning particle with anomalous magnetic moment in the
external electromagnetic field is carried out in the gauge which allows to
describe simultaneously particles and antiparticles (massive and massless)
already at the classical level. Pseudoclassical Foldy-Wouthuysen transformation
is used to obtain canonical (Newton-Wigner) coordinates and in terms of this
variables the theory is quantized. The connection of this quantization with the
deGroot and Suttorp's description of Dirac particle with anomalous magnetic
moment in the external electromagnetic field is discussed.
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Holographic Bulk Reconstruction And Cosmological Singularities: We study the structure of entanglement wedges in the Kasner-AdS geometry,
which provides an example of AdS/CFT engineered cosmological singularity. We
investigate the specific limitations of causal reconstruction methods, imposed
by the presence of the cosmological singularities, and we show the supremacy of
modular reconstruction. This model provides an example where modular
reconstruction based on a proper operator subalgebra is more powerful than the
strongest possible causal reconstruction, based on the complete operator
algebra.
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Black hole as fireplace: limited communications across the horizon: An insightful viewpoint was proposed by Susskind about AMPS firewall: the
region behind the firewall does not exist and the firewall is an extension of
the singularity. In this work, we provided a possible picture of this idea by
combining Newman's complex metric and Dvali-Gomez BEC black holes, which are
Bose-Einstein condensates of N gravitons. The inner space behind the horizon is
a realized imaginary space encrusted by the real space outside the horizon. In
this way, the singularity extents to the horizon to make a firewall for the
infalling observer. Some gravitons escape during the fluctuation of the BEC
black hole, resulting in a micro-transparent horizon which makes the firewall
exposes slightly to an observer outside the horizon. This picture allows
limited communications across the horizon.
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Non-conformal supercurrents in six dimensions: Non-conformal supercurrents in six dimensions are described, which contain
the trace of the energy-momentum tensor and the gamma-trace of the
supersymmetry current amongst their component fields. Within the superconformal
approach to ${\cal N} = (1, 0)$ supergravity, we present various distinct
non-conformal supercurrents, one of which is associated with an ${\cal O}(2)$
(or linear) multiplet compensator, while another with a tensor multiplet
compensator. We also derive an infinite class of non-conformal supercurrents
involving ${\cal O}(n)$ multiplets with $n > 2$. As an illustrative example we
construct the relaxed hypermultiplet in supergravity. Finally, we put forward a
non-conformal supercurrent in the ${\cal N} = (2, 0)$ supersymmetric case.
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On the BV formulation of boundary superstring field theory: We propose a Batalin-Vilkovisky (BV) formulation of boundary superstring
field theory. The superstring field action is defined in terms of a closed
one-form in the space of couplings, and we compute it explicitly for exactly
solvable tachyon perturbations. We also argue that the superstring field action
defined in this way is the partition function on the disc, in accord with a
previous proposal.
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$R^4$ terms in supergravity and M-theory: Higher-order invariants and their role as possible counterterms for
supergravity theories are reviewed. It is argued that N=8 supergravity will
diverge at 5 loops. The construction of $R^4$ superinvariants in string and
M-theory is discussed.
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New Kaluza-Klein Instantons and Decay of AdS Vacua: We construct a generalization of Witten's Kaluza-Klein instanton, where a
higher-dimensional sphere (rather than a circle as in Witten's instanton)
collapses to zero size and the geometry terminates at a bubble of nothing, in a
low energy effective theory of M theory. We use the solution to exhibit
instability of non-supersymmetric AdS_5 vacua in M Theory compactified on
positive Kaehler-Einstein spaces, providing a further evidence for the recent
conjecture that any non-supersymmetric anti-de Sitter vacuum supported by
fluxes must be unstable.
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BPS Operators in N=4 SYM: Calogero Models and 2D Fermions: A connection between the gauge fixed dynamics of protected operators in
superconformal Yang-Mills theory in four dimensions and Calogero systems is
established. This connection generalizes the free Fermion description of the
chiral primary operators of the gauge theory formed out of a single complex
scalar to more general operators. In particular, a detailed analysis of
protected operators charged under an su(1|1)contained in psu(2,2|4) is carried
out and a class of operators is identified, whose dynamics is described by the
rational super-Calogero model. These results are generalized to arbitrary BPS
operators charged under an su(2|3) of the superconformal algebra. Analysis of
the non-local symmetries of the super-Calogero model is also carried out, and
it is shown that symmetry for a large class of protected operators is a
contraction of the corresponding Yangian algebra to a loop algebra.
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Modified Dynamical Supergravity Breaking and Off-Diagonal Super-Higgs
Effects: We argue that generic off-diagonal vacuum and nonvacuum solutions for
Einstein manifolds mimic physical effects in modified gravity theories (MGTs)
and encode certain models of the $f(R,T,...)$, Ho\v{r}ava type with dynamical
Lorentz symmetry breaking, induced effective mass for the graviton etc. Our
main goal is to investigate the dynamical breaking of local supersymmetry
determined by off-diagonal solutions in MGTs and encoded as effective Einstein
spaces. This includes the Deser-Zumino super-Higgs effect, for instance, for a
one-loop potential in a (simple but representative) model of $\mathcal{N}=1,
D=4$ supergravity. We develop and apply new geometrical techniques which allows
us to decouple the gravitational field equations and integrate them in a very
general form with the metric and vielbein fields depending on all the spacetime
coordinates via means of various generating and integration functions and
parameters. We study how solutions in MGTs may be related to the dynamical
generation of a gravitino mass and supersymmetry breaking.
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Effective scalar fields in Yang-Mills theories: Scalar fields play a crucial role in the Standard model. On the other hand,
in the weak-coupling regime there is an unsolved problem of the quadratic
divergence of scalar masses. Thus, it is natural to turn to composite, or
effective scalar fields in the strong-coupling regime. Lattice simulations
provide information on the "actually existing" scalar fields in Yang-Mills
theories. On the continuum-theory side, dual models predict existence of
various low-dimension vacuum defects, including probably scalar particles. We
are looking for correspondence between the two frameworks, of lattice
phenomenology and dual models, and discuss possible applications to the theory
of the Yang-Mills plasma in the deconfining phase. It is not ruled out that the
effective scalars play important role in the plasma dynamics.
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Self-Duality and Self-Similarity of Little String Orbifolds: We study a class of ${\cal N}=(1,0)$ little string theories obtained from
orbifolds of M-brane configurations. These are realised in two different ways
that are dual to each other: either as $M$ parallel M5-branes probing a
transverse $A_{N-1}$ singularity or $N$ M5-branes probing an $A_{M-1}$
singularity. These backgrounds can further be dualised into toric, non-compact
Calabi-Yau threefolds $X_{N,M}$ which have double elliptic fibrations and thus
give a natural geometric description of T-duality of the little string
theories. The little string partition functions are captured by the topological
string partition function of $X_{N,M}$. We analyse in detail the free energies
$\Sigma_{N,M}$ associated with the latter in a special region in the K\"ahler
moduli space of $X_{N,M}$ and discover a remarkable property: in the
Nekrasov-Shatashvili-limit, $\Sigma_{N,M}$ is identical to $NM$ times
$\Sigma_{1,1}$. This entails that the BPS degeneracies for any $(N,M)$ can
uniquely be reconstructed from the $(N,M)=(1,1)$ configuration, a property we
refer to as self-similarity. Moreover, as $\Sigma_{1,1}$ is known to display a
number of recursive structures, BPS degeneracies of little string
configurations for arbitrary $(N,M)$ as well acquire additional symmetries.
These symmetries suggest that in this special region the two little string
theories described above are self-dual under T-duality.
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Generalized structures of ten-dimensional supersymmetric solutions: Four-dimensional supersymmetric type II string theory vacua can be described
elegantly in terms of pure spinors on the generalized tangent bundle T+T*. In
this paper, we apply the same techniques to any ten-dimensional supersymmetric
solution (not necessarily involving a factor with an AdS4 or Minkowski4 metric)
in type II theories. We find a system of differential equations in terms of a
form describing a "generalized ISpin(7) structure". This system is equivalent
to unbroken supersymmetry, in both IIA and IIB. One of the equations reproduces
in one fell swoop all the pure spinors equations for four-dimensional vacua.
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Chaotic dynamics of string around the conformal black hole: In this paper, we make a systematical and in-depth study on the chaotic
dynamics of the string around the conformal black hole. Depending on the
characteristic parameter of the conformal black hole and the initial position
of the string, there are three kinds of dynamical behaviors: ordered, chaotic
and being captured, chaotic but not being captured. A particular interesting
observation is that there is a sharp transition in chaotic dynamics when the
black hole horizon disappears, which is indepent of the initial position of the
string. It provides a possible way to probe the horizon structure of the
massive body. We also examine the generalized MSS (Maldacena, Shenker and
Stanford) inequality, which is proposed in holographic dual field theory, and
find that the generalized MSS inequality holds even in the asymptotically flat
black hole background. Especially, as the initial position of the string
approaches the black hole horizon, the Lyapunov exponent also approaches the
upper bound of the generalized MSS inequality.
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The curvature-induced gauge potential and the geometric momentum for a
particle on a hypersphere: A particle that is constrained to freely move on a hyperspherical surface in
an $N\left( \geq 2\right) $ dimensional flat space experiences a
curvature-induced gauge potential, whose form was given long ago (J. Math.
Phys. \textbf{34}(1993)2827). We demonstrate that the momentum for the particle
on the hypersphere is the geometric one including the gauge potential and its
components obey the commutation relations $\left[ p_{i},p_{j}\right] =-i\hbar
J_{ij}/r^{2}$, in which $\hbar $ is the Planck's constant, and $p_{i}$
($i,j=1,2,3,...N$) denotes the $i-$th component of the geometric momentum, and
$J_{ij}$ specifies the $ij-$th component of the generalized\textit{\ angular
momentum} containing both the orbital part and the coupling of the generators
of continuous rotational symmetry group $% SO(N-1)$ and curvature, and $r$
denotes the radius of the $N-1$ dimensional hypersphere.
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Global symmetry and conformal bootstrap in the two-dimensional $O(n)$
model: We define the two-dimensional $O(n)$ conformal field theory as a theory that
includes the critical dilute and dense $O(n)$ models as special cases, and
depends analytically on the central charge. For generic values of
$n\in\mathbb{C}$, we write a conjecture for the decomposition of the spectrum
into irreducible representations of $O(n)$.
We then explain how to numerically bootstrap arbitrary four-point functions
of primary fields in the presence of the global $O(n)$ symmetry. We determine
the needed conformal blocks, including logarithmic blocks, including in
singular cases. We argue that $O(n)$ representation theory provides upper
bounds on the number of solutions of crossing symmetry for any given four-point
function.
We study some of the simplest correlation functions in detail, and determine
a few fusion rules. We count the solutions of crossing symmetry for the $30$
simplest four-point functions. The number of solutions varies from $2$ to $6$,
and saturates the bound from $O(n)$ representation theory in $21$ out of $30$
cases.
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Effective Field Theory for Massive Gravitons and Gravity in Theory Space: We introduce a technique for restoring general coordinate invariance into
theories where it is explicitly broken. This is the analog for gravity of the
Callan-Coleman-Wess-Zumino formalism for gauge theories. We use this to
elucidate the properties of interacting massless and massive gravitons. For a
single graviton with a Planck scale Mpl and a mass mg, we find that there is a
sensible effective field theory which is valid up to a high-energy cutoff
Lambda parametrically above mg. Our methods allow for a transparent
understanding of the many peculiarities associated with massive gravitons,
among them the need for the Fierz-Pauli form of the Lagrangian, the presence or
absence of the van Dam-Veltman-Zakharov discontinuity in general backgrounds,
and the onset of non-linear effects and the breakdown of the effective theory
at large distances from heavy sources. The natural sizes of all non-linear
corrections beyond the Fierz-Pauli term are easily determined. The cutoff
scales as Lambda ~ (mg^4 Mpl)^(1/5) for the Fierz-Pauli theory, but can be
raised to Lambda ~ (mg^2 Mpl)^(1/3) in certain non-linear extensions. Having
established that these models make sense as effective theories, there are a
number of new avenues for exploration, including model building with gravity in
theory space and constructing gravitational dimensions.
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Generalised holonomies and K(E$_9$): The involutory subalgebra K(E$_9$) of the affine Kac-Moody algebra E$_9$ was
recently shown to admit an infinite sequence of unfaithful representations of
ever increasing dimensions arXiv:2102.00870. We revisit these representations
and describe their associated ideals in more detail, with particular emphasis
on two chiral versions that can be constructed for each such representation.
For every such unfaithful representation we show that the action of K(E$_9$)
decomposes into a direct sum of two mutually commuting (`chiral' and
`anti-chiral') parabolic algebras with Levi subalgebra
$\mathfrak{so}(16)_+\,\oplus\,\mathfrak{so}(16)_-$. We also spell out the
consistency conditions for uplifting such representations to unfaithful
representations of K(E$_{10}$). From these results it is evident that the
holonomy groups so far discussed in the literature are mere shadows (in a
Platonic sense) of a much larger structure.
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Supersymmetry and Fermionic Modes in an Oscillon Background: The excitations referred to as oscillons are long-lived time-dependent field
configurations which emerge dynamically from non-linear field theories. Such
long-lived solutions are of interest in applications that include systems of
Condensed Matter Physics, the Standard Model of Particle Physics,
Lorentz-symmetry violating scenarios and Cosmology. In this work, we show how
oscillons may be accommodated in a supersymmetric scenario. We adopt as our
framework simple ($\mathcal{N}=1$) supersymmetry in $D=1+1$ dimensions. We
focus on the bosonic sector with oscillon configurations and their (classical)
effects on the corresponding fermionic modes, (supersymmetric) partners of the
oscillons. The particular model we adopt to pursue our investigation displays
cubic self-interactions in the scalar sector.
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From D3-Branes to Lifshitz Space-Times: We present a simple embedding of a z=2 Lifshitz space-time into type IIB
supergravity. This is obtained by considering a stack of D3-branes in type IIB
supergravity and deforming the world-volume by a plane wave. The plane wave is
sourced by the type IIB axion. The superposition of the plane wave and the
D3-branes is 1/4 BPS. The near horizon geometry of this configuration is a
5-dimensional z=0 Schroedinger space-time times a 5-sphere. This geometry is
also 1/4 BPS. Upon compactification along the direction in which the wave is
traveling the 5-dimensional z=0 Schroedinger space-time reduces to a
4-dimensional z=2 Lifshitz space-time. The compactification is such that the
circle is small for weakly coupled type IIB string theory. This reduction
breaks the supersymmetries. Further, we propose a general method to construct
analytic z=2 Lifshitz black brane solutions. The method is based on deforming
5-dimensional AdS black strings by an axion wave and reducing to 4-dimensions.
We illustrate this method with an example.
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An Algorithmic Approach to Heterotic String Phenomenology: We briefly review the recent programme to construct, systematically and
algorithmically, large classes of heterotic vacua, as well as the search for
the MSSM therein. Specifically, we outline the monad construction of vector
bundles over complete intersection Calabi-Yau threefolds, their classification,
stability, equivariant cohomology and subsequent relevance to string
phenomenology. It is hoped that this top-down algorithmic approach will isolate
special corners in the heterotic landscape.
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AdS_4/CFT_3 duals from M2-branes at hypersurface singularities and their
deformations: We construct three-dimensional N=2 Chern-Simons-quiver theories which are
holographically dual to the M-theory Freund-Rubin solutions AdS_4 x V_{5,2}/Z_k
(with or without torsion G-flux), where V_{5,2} is a homogeneous
Sasaki-Einstein seven-manifold. The global symmetry group of these theories is
generically SU(2) x U(1) x U(1)_R, and they are hence non-toric. The field
theories may be thought of as the n=2 member of a family of models, labelled by
a positive integer n, arising on multiple M2-branes at certain hypersurface
singularities. We describe how these models can be engineered via generalized
Hanany-Witten brane constructions. The AdS_4 x V_{5,2}/Z_k solutions may be
deformed to a warped geometry R^{1,2} x T^* S^4/Z_k, with self-dual G-flux
through the four-sphere. We show that this solution is dual to a supersymmetric
mass deformation, which precisely modifies the classical moduli space of the
field theory to the deformed geometry.
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On tensionless string field theory in AdS$_3$: We report on progress in formulating a field theory of tensionless strings in
$AdS_3$, starting from the dual large-$N$ symmetric orbifold CFT. We propose a
set of field equations which are gauge invariant under the higher spin algebra
of the theory, the `Higher Spin Square'. The massless higher spin sector is
captured by a Chern-Simons gauge field, while the matter sector is described by
unfolded equations similar to those appearing in Vasiliev theory. Our equations
incorporate the full perturbative spectrum of the theory, including states
coming from the twisted sectors, and capture some of the interactions fixed by
gauge invariance. We also discuss the spectrum of the bulk theory and explain
how linearization around $AdS_3$ gives rise to the expected set of decoupled
wave equations. Our results can be generalized to describe bulk duals of other
large-$N$ symmetric orbifolds.
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Fermion in the Nonabelian Gauge Field Theory in 2+1 Dimensions: The massive SU(2) gauge field theory coupled with fermions is considered in
2+1 dimensions. Quark energy spectrum and radiative shift in constant external
nonabelian field, being exact solution of the gauge field equations with the
Chern-Simons term, are calculated. Under the condition $m = \theta/4$ the quark
state is shown to be supersymmetric.
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Colored HOMFLY-PT polynomials of quasi-alternating $3$-braid knots: Obtaining a closed-form expression for the colored HOMFLY-PT polynomials of
knots from $3$-strand braids carrying arbitrary $SU(N)$ representation is a
challenging problem. In this paper, we confine our interest to twisted
generalized hybrid weaving knots which we denote hereafter by
$\hat{Q}_3(m_1,-m_2,n,\ell)$. This family of knots not only generalizes the
well-known class of weaving knots but also contains an infinite family of
quasi-alternating knots. Interestingly, we obtain a closed-form expression for
the HOMFLY-PT polynomial of $\hat{Q}_3(m_1,-m_2,n,\ell)$ using a modified
version of the Reshitikhin-Turaev method. In addition, we compute the exact
coefficients of the Jones polynomials and the Alexander polynomials of
quasi-alternating knots $\hat{Q}_3(1,-1,n,\pm 1)$. For these homologically-thin
knots, such coefficients are known to be the ranks of their Khovanov and link
Floer homologies, respectively. We also show that the asymptotic behaviour of
the coefficients of the Alexander polynomial is trapezoidal. On the other hand,
we compute the $[r]$-colored HOMFLY-PT polynomials of quasi alternating knots
for small values of $r$. Remarkably, the study of the determinants of certain
twisted weaving knots leads to establish a connection with enumerative geometry
related to $m^{th}$ Lucas numbers, denoted hereafter as $L_{m,2n}$. At the end,
we verify that the reformulated invariants satisfy Ooguri-Vafa conjecture and
we express certain BPS integers in terms of hyper-geometric functions ${}_2
{\bf F}_1\left[a,b, c;z\right]$.
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Bloch electrons on honeycomb lattice and toric Calabi-Yau geometry: We find a new relation between the spectral problem for Bloch electrons on a
two-dimensional honeycomb lattice in a uniform magnetic field and that for
quantum geometry of a toric Calabi-Yau threefold. We show that a difference
equation for the Bloch electron is identical to a quantum mirror curve of the
Calabi-Yau threefold. As an application, we show that bandwidths of the
electron spectra in the weak magnetic flux regime are systematically calculated
by the topological string free energies at conifold singular points in the
Nekrasov-Shatashvili limit.
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Looking for structure in the cobordism conjecture: The cobordism conjecture of the swampland program states that the bordism
group of quantum gravity must be trivial. We investigate this statement in
several directions, on both the mathematical and physical side. We consider the
Whitehead tower construction as a possible organising principle for the
topological structures entering the formulation of the conjecture. We discuss
why and how to include geometric structures in bordism groups, such as higher
U(1)-bundles with connection. The inclusion of magnetic defects is also
addressed in some detail. We further elaborate on how the conjecture could
predict Kaluza--Klein monopoles, and we study the gravity decoupling limit in
the cobordism conjecture, with a few observations on NSNS string backgrounds.
We end with comments in relation to T-duality, as well as the finiteness
conjecture.
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Open Perturbatively Long-Range Integrable gl(N) Spin Chains: We construct the most general perturbatively long-range integrable spin chain
with spins transforming in the fundamental representation of gl(N) and open
boundary conditions. In addition to the previously determined bulk moduli we
find a new set of parameters determining the reflection phase shift. We also
consider finite-size contributions and comment on their determination.
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Metric of the multiply wound rotating string: We consider a string wrapped many times around a compact circle in space, and
let this string carry a right moving wave which imparts momentum and angular
momentum to the string. The angular momentum causes the strands of the
`multiwound' string to separate and cover the surface of a torus. We compute
the supergravity solution for this string configuration. We map this solution
by dualities to the D1-D5 system with angular momentum that has been recently
studied. We discuss how constructing this multiwound string solution may help
us to relate the microscopic and macroscopic pictures of black hole absorption.
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Weak cosmic censorship conjecture in Einstein-Born-Infeld black holes: Recently, Sorce and Wald have suggested a new version of the gedanken
experiments to overspin or overcharge the Kerr-Newman black holes in
Einstein-Maxwell gravity. Following their setup, in this paper, we investigate
the weak cosmic censorship conjecture (WCCC) in the static Einstein-Born-Infeld
black holes for the Einstein gravity coupled to nonlinear electrodynamics.
First of all, we derive the first two order perturbation inequalities of the
charged collision matter in the Einstein-Born-Infeld gravity based on the
Iyer-Wald formalism as well as the null energy conditions of the matter fields
and show that they share the same form as these in Einstein-Maxwell gravity. As
a result, we find that the static Einstein-Born-Infeld black holes cannot be
overcharged under the second-order approximation after considering these
inequalities. Our result at some level hints at the validity of the weak cosmic
censorship conjecture for string theory.
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GLSM's for partial flag manifolds: In this paper we outline some aspects of nonabelian gauged linear sigma
models. First, we review how partial flag manifolds (generalizing
Grassmannians) are described physically by nonabelian gauged linear sigma
models, paying attention to realizations of tangent bundles and other aspects
pertinent to (0,2) models. Second, we review constructions of Calabi-Yau
complete intersections within such flag manifolds, and properties of the gauged
linear sigma models. We discuss a number of examples of nonabelian GLSM's in
which the Kahler phases are not birational, and in which at least one phase is
realized in some fashion other than as a complete intersection, extending
previous work of Hori-Tong. We also review an example of an abelian GLSM
exhibiting the same phenomenon. We tentatively identify the mathematical
relationship between such non-birational phases, as examples of Kuznetsov's
homological projective duality. Finally, we discuss linear sigma model moduli
spaces in these gauged linear sigma models. We argue that the moduli spaces
being realized physically by these GLSM's are precisely Quot and hyperquot
schemes, as one would expect mathematically.
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Type IIB flux vacua from G-theory II: We find analytic solutions of type IIB supergravity on geometries that
locally take the form $\text{Mink}\times M_4\times \mathbb{C}$ with $M_4$ a
generalised complex manifold. The solutions involve the metric, the dilaton,
NSNS and RR flux potentials (oriented along the $M_4$) parametrised by
functions varying only over $\mathbb{C}$. Under this assumption, the
supersymmetry equations are solved using the formalism of pure spinors in terms
of a finite number of holomorphic functions. Alternatively, the solutions can
be viewed as vacua of maximally supersymmetric supergravity in six dimensions
with a set of scalar fields varying holomorphically over $\mathbb{C}$. For a
class of solutions characterised by up to five holomorphic functions, we
outline how the local solutions can be completed to four-dimensional flux vacua
of type IIB theory. A detailed study of this global completion for solutions
with two holomorphic functions has been carried out in the companion paper [1].
The fluxes of the global solutions are, as in F-theory, entirely codified in
the geometry of an auxiliary $K3$ fibration over $\mathbb{CP}^1$. The results
provide a geometric construction of fluxes in F-theory.
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Dynamical gap from holography in the charged dilaton black hole: We study the holographic non-relativistic fermions in the presence of bulk
dipole coupling in charged dilatonic black hole background. We explore the
nontrivial effects of the bulk dipole coupling, the fermion charge as well as
the dilaton field on the flat band, the Fermi surface and the emergence of the
gap by investigating the spectral function of the non-relativistic fermion
system. In particular, we find that the presence of the flat band in the
non-relativistic case will suppress the Fermi momentum. Besides, we observe
that the effect of the dipole coupling in the dilaton gravity is more explicit.
Finally, we consider the non-relativistic fermions at nonzero temperature. A
phase transition from insulator to a conducting state is observed as the
fermion system becomes hotter.
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A Background Independent Formulation of Noncritical String Theory: Using the string field theory recently proposed by the authors and
collaborators, we give a background independent formulation of rational
noncritical string theories with $c\leq 1$. With a little modification of the
string field Hamiltonians previously constructed, we obtain string field
theories which include various rational noncritical string theories as
classical backgrounds.
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Refined, Motivic, and Quantum: It is well known that in string compactifications on toric Calabi-Yau
manifolds one can introduce refined BPS invariants that carry information not
only about the charge of the BPS state but also about the spin content. In this
paper we study how these invariants behave under wall crossing. In particular,
by applying a refined wall crossing formula, we obtain the refined BPS
degeneracies for the conifold in different chambers. The result can be
interpreted in terms of a new statistical model that counts `refined' pyramid
partitions; the model provides a combinatorial realization of wall crossing and
clarifies the relation between refined pyramid partitions and the refined
topological vertex. We also compare the wall crossing behavior of the refined
BPS invariants with that of the motivic Donaldson-Thomas invariants introduced
by Kontsevich-Soibelman. In particular, we argue that, in the context of BPS
state counting, the three adjectives in the title of this paper are essentially
synonymous.
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Large-density field theory, viscosity, and "$2k_F$" singularities from
string duals: We analyze systems where an effective large-N expansion arises naturally in
gauge theories without a large number of colors: a sufficiently large charge
density alone can produce a perturbative string ('tHooft) expansion. One
example is simply the well-known NS5/F1 system dual to $AdS_3\times T^4\times
S^3$, here viewed as a 5+1 dimensional theory at finite density. This model is
completely stable, and we find that the existing string-theoretic solution of
this model yields two interesting results. First, it indicates that the shear
viscosity is not corrected by $\alpha'$ effects in this system. For flow
perpendicular to the F1 strings the viscosity to entropy ratio take the usual
value $1/4\pi$, but for flow parallel to the F1's it vanishes as $T^2$ at low
temperature. Secondly, it encodes singularities in correlation functions coming
from low-frequency modes at a finite value of the momentum along the $T^4$
directions. This may provide a strong coupling analogue of finite density
condensed matter systems for which fermionic constituents of larger operators
contribute so-called "$2k_F$" singularities. In the NS5/F1 example, stretched
strings on the gravity side play the role of these composite operators. We
explore the analogue for our system of the Luttinger relation between charge
density and the volume bounded by these singular surfaces. This model provides
a clean example where the string-theoretic UV completion of the gravity dual to
a finite density field theory plays a significant and calculable role.
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Holographic anyonization: A systematic approach: Anyons have garnered substantial interest theoretically as well as
experimentally. Due to the intricate nature of their interactions, however,
even basic notions such as the equation of state for any kind of anyon gas have
eluded a profound understanding so far. Using holography as a guiding
principle, we propose a general method for an alternative quantization of
electromagnetic degrees of freedom in the gravitational dual to obtain an
effective physical description of strongly correlated anyonic systems. We then
demonstrate the application of this prescription in a toy model of an anyonic
fluid at finite charge density and magnetic field, dual to a dyonic black brane
in AdS_4, and compute the equation of state and various transport coefficients
explicitly.
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On Degenerate Metrics and Electromagnetism: A theory of degenerate metrics is developed and applied to the problem of
unifying gravitation with electromagnetism. The approach is similar to the
Kaluza-Klein approach with a fifth dimension, however no ad hoc conditions are
needed to explain why the extra dimension is not directly observable under
everyday conditions. Maxwell's theory is recovered with differences only at
very small length scales, and a new formula is found for the Coulomb potential
that is regular everywhere.
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Baryon Charges in 4d Superconformal Field Theories and Their AdS Duals: We consider general aspects of the realization of R and non-R flavor
symmetries in the AdS_5 x H_5 dual of 4d N=1 superconformal field theories. We
find a general prescription for computing the charges under these symmetries
for baryonic operators, which uses only topological information (intersection
numbers) on H_5. We find and discuss a new correspondence between the nodes of
the SCFT quiver diagrams and certain divisors in the associated geometry. We
also discuss connections between the non-R flavor symmetries and the enhanced
gauge symmetries in non-conformal theories obtained by adding wrapped branes.
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Glueball instability and thermalization driven by dark radiation: We study glueballs in the holographic gauge theories living in a curved
space-time. The dual bulk is obtained as a solution of the type IIB superstring
theory with two parameters, which correspond to four dimensional (4D)
cosmological constant $\lambda$ and the dark radiation $C$ respectively. The
theory is in the confining phase for $\lambda <0$ and small $C$, then we
observe stable glueball states in this theory. However, the stability of the
glueball states is lost when the density of the dark radiation ($C$) increases
and exceeds a critical point. Above this point, the dark radiation works as the
heat bath of the Yang-Mills theory since the event horizon appears. Thus the
system is thermalized, and the theory is in a finite temperature deconfinement
phase, namely in the QGP phase. We observe this transition process through the
glueball spectra which varies dramatically with $C$. We also examined the
entanglement entropy of the system to find a clue of this phase transition and
the role of the dark radiation $C$ in the entanglement entropy.
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Exotic Dark Spinor Fields: Exotic dark spinor fields are introduced and investigated in the context of
inequivalent spin structures on arbitrary curved spacetimes, which induces an
additional term on the associated Dirac operator, related to a Cech cohomology
class. For the most kinds of spinor fields, any exotic term in the Dirac
operator can be absorbed and encoded as a shift of the electromagnetic vector
potential representing an element of the cohomology group H^1(M, Z_2). The
possibility of concealing such an exotic term does not exist in case of dark
(ELKO) spinor fields, as they cannot carry electromagnetic charge, so that the
full topological analysis must be evaluated. Since exotic dark spinor fields
also satisfy Klein-Gordon propagators, the dynamical constraints related to the
exotic term in the Dirac equation can be explicitly calculated. It forthwith
implies that the non-trivial topology associated to the spacetime can
drastically engender --- from the dynamics of dark spinor fields ---
constraints in the spacetime metric structure. Meanwhile, such constraints may
be alleviated, at the cost of constraining the exotic spacetime topology.
Besides being prime candidates to the dark matter problem, dark spinor fields
are shown to be potential candidates to probe non-trivial topologies in
spacetime, as well as probe the spacetime metric structure.
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$N=2$ Superconformal Field Theories in $4$ Dimensions and A-D-E
Classification: Making use of the exact solutions of the $N=2$ supersymmetric gauge theories
we construct new classes of superconformal field theories (SCFTs) by
fine-tuning the moduli parameters and bringing the theories to critical points.
In the case of SCFTs constructed from pure gauge theories without matter $N=2$
critical points seem to be classified according to the A-D-E classification as
in the two-dimensional SCFTs.
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Do Our Observations Depend upon the Quantum State of the Universe?: Generically the probabilities of observational results depend upon both the
quantum state and the rules for extracting the probabilities from it. It is
often argued that inflation may make our observations independent of the
quantum state. In a framework in which one considers the state and the rules as
logically separate, it is shown how it is possible that the probabilities are
indeed independent of the state, but the rules for achieving this seem somewhat
implausible.
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The Dimensional-Reduction Anomaly in Spherically Symmetric Spacetimes: In D-dimensional spacetimes which can be foliated by n-dimensional
homogeneous subspaces, a quantum field can be decomposed in terms of modes on
the subspaces, reducing the system to a collection of (D-n)-dimensional fields.
This allows one to write bare D-dimensional field quantities like the Green
function and the effective action as sums of their (D-n)-dimensional
counterparts in the dimensionally reduced theory. It has been shown, however,
that renormalization breaks this relationship between the original and
dimensionally reduced theories, an effect called the dimensional-reduction
anomaly. We examine the dimensional-reduction anomaly for the important case of
spherically symmetric spaces.
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$SL(2,R)\times U(1)$ symmetry and quasinormal modes in the self-dual
warped AdS black hole: The algebraic approach to the spectrum of quasinormal modes has been made as
simple as possible for the BTZ black hole by the strategy developed in
\cite{Zhang}. By working with the self-dual warped AdS black hole, we
demonstrate in an explicit way that such a strategy can be well adapted to
those warped AdS balck holes with the $SL(2,R)\times U(1)$ isometry. To this
end, we first introduce two associated tensor fields with the quadratic Casimir
of $SL(2,R)\times U(1)$ Lie algebra in the self-dual warped AdS black hole and
show that they correspond essentially to the metric and volume element up to a
constant prefactor, respectively. Then without appealing to any concrete
coordinate system, we can further show that the solutions to the equations of
motion for the scalar, vector, spinor fields all fall into the representations
of the $SL(2,R)\times U(1)$ Lie algebra by a purely abstract tensor and spinor
analysis. Accordingly, the corresponding spectrum of quasinormal modes for each
fixed azimuthal quantum number can be derived algebraically as the infinite
tower of descendants of the highest weight mode of the $SL(2,R)$ Lie
subalgebra.
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Brane-World Inflation and the Transition to Standard Cosmology: In the context of a five-dimensional brane-world model motivated from
heterotic M-theory, we develop a framework for potential-driven brane-world
inflation. Specifically this involves a classification of the various
background solutions of (A)dS_5 type, an analysis of five-dimensional slow-roll
conditions and a study of how a transition to the flat vacuum state can be
realized. It is shown that solutions with bulk potential and both bane
potentials positive exist but are always non-separating and have a non-static
orbifold. It turns out that, for this class of backgrounds, a transition to the
flat vacuum state during inflation is effectively prevented by the rapidly
expanding orbifold. We demonstrate that such a transition can be realized for
solutions where one boundary potential is negative. For this case, we present
two concrete inflationary models which exhibit the transition explicitly.
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Correlation functions of local composite operators from generalized
unitarity: We describe the use of generalized unitarity for the construction of
correlation functions of local gauge-invariant operators in general quantum
field theories and illustrate this method with several calculations in N=4
super-Yang-Mills theory involving BPS and non-BPS operators. Form factors of
gauge-invariant operators and their multi-operator generalization play an
important role in our construction. We discuss various symmetries of the
momentum space presentation of correlation functions, which is natural in this
framework and give examples involving non-BPS and any number of BPS operators.
We also discuss the calculation of correlators describing the energy flow in
scattering processes as well as the construction of the effective action of a
background gravitational field.
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Matrix Cosmology: Some speculative preliminary ideas relating matrix theory and cosmology are
discussed.
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Landau-Khalatnikov-Fradkin transformation of the fermion propagator in
massless reduced QED: We study the gauge-covariance of the massless fermion propagator in reduced
Quantum Electrodynamics (QED). Starting from its value in some gauge, we
evaluate an all order expression for it in another gauge by means of the
Landau-Khalatnikov-Fradkin transformation. We find that the weak coupling
expansions thus derived are in perfect agreement with the exact calculations.
We also prove that the fermion anomalous dimension of reduced QED is gauge
invariant to all orders of perturbation theory except for the first one.
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Lorentz violation, Möller scattering and finite temperature: Lorentz and CPT symmetries may be violated in new physics that emerges at
very high energy scale, i.e., at the Planck scale. The differential cross
section of the M\"oller scattering, due to Lorentz violation at finite
temperature is calculated. Lorentz-violating effects emerge from an interaction
vertex due to a CPT-odd nonminimal coupling in the covariant derivative. The
finite temperature effects are determined using the Thermo Field Dynamics (TFD)
formalism.
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The Cosmological Dynamics of Interacting Holographic Dark Energy Model: Motivated by the recent observations for the cosmic acceleration and the
suitable evolution of the Universe provided an interaction (decay of dark
energy to matter) is incorporated in a cosmological model, we study the
cosmological evolution of the Interacting Holographic Dark Energy scenario.
Critical points are derived and their corresponding cosmological models are
presented. The dynamical character of these models is revealed.
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Holographic Butterfly Effect at Quantum Critical Points: When the Lyapunov exponent $\lambda_L$ in a quantum chaotic system saturates
the bound $\lambda_L\leqslant 2\pi k_BT$, it is proposed that this system has a
holographic dual described by a gravity theory. In particular, the butterfly
effect as a prominent phenomenon of chaos can ubiquitously exist in a black
hole system characterized by a shockwave solution near the horizon. In this
paper we propose that the butterfly velocity can be used to diagnose quantum
phase transition (QPT) in holographic theories. We provide evidences for this
proposal with an anisotropic holographic model exhibiting metal-insulator
transitions (MIT), in which the derivatives of the butterfly velocity with
respect to system parameters characterizes quantum critical points (QCP) with
local extremes in zero temperature limit. We also point out that this proposal
can be tested by experiments in the light of recent progress on the measurement
of out-of-time-order correlation function (OTOC).
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Low-energy $6D$, ${\cal N}=(1,1)$ SYM effective action beyond the
leading approximation: For $6D$, ${\cal N}=(1,1)$ SYM theory formulated in ${\cal N}=(1,0)$ harmonic
superspace as a theory of interacting gauge multiplet and hypermultiplet we
construct the ${\cal N}=(1,1)$ supersymmetric Heisenberg-Euler-type superfield
effective action. The effective action is computed for the slowly varying
on-shell background fields and involves, in the bosonic sector, all powers of a
constant abelian strength.
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Bi-Hamiltonian Sturcture of Super KP Hierarchy: We obtain the bi-Hamiltonian structure of the super KP hierarchy based on the
even super KP operator $\Lambda = \theta^{2} + \sum^{\infty}_{i=-2}U_{i}
\theta^{-i-1}$, as a supersymmetric extension of the ordinary KP bi-Hamiltonian
structure. It is expected to give rise to a universal super $W$-algebra
incorporating all known extended superconformal $W_{N}$ algebras by reduction.
We also construct the super BKP hierarchy by imposing a set of anti-self-dual
constraints on the super KP hierarchy.
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High frequency quasi-normal modes for black holes with generic
singularities II: Asymptotically non-flat spacetimes: The possibility that the asymptotic quasi-normal mode (QNM) frequencies can
be used to obtain the Bekenstein-Hawking entropy for the Schwarzschild black
hole -- commonly referred to as Hod's conjecture -- has received considerable
attention. To test this conjecture, using monodromy technique, attempts have
been made to analytically compute the asymptotic frequencies for a large class
of black hole spacetimes. In an earlier work, two of the current authors
computed the high frequency QNMs for scalar perturbations of $(D+2)$
dimensional spherically symmetric, asymptotically flat, single horizon
spacetimes with generic power-law singularities. In this work, we extend these
results to asymptotically non-flat spacetimes. Unlike the earlier analyses, we
treat asymptotically flat and de Sitter spacetimes in a unified manner, while
the asymptotic anti-de Sitter spacetimes is considered separately. We obtain
master equations for the asymptotic QNM frequency for all the three cases. We
show that for all the three cases, the real part of the asymptotic QNM
frequency -- in general -- is not proportional to ln(3) thus indicating that
the Hod's conjecture may be restrictive.
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Non-Invertible Duality Interfaces in Field Theories with Exotic
Symmetries: In recent years, the concept of global symmetry has generalized considerably.
Two dramatic examples of this generalization are the exotic symmetries that
govern theories with fractons and non-invertible symmetries, which do not fuse
according to a group law. Only recently has the interplay between these two
been examined. In this paper, we provide further examples of the interplay in
the XY plaquette model, XY cube model, 1+1 d theory with global dipole
symmetry, and the 2+1 d Lifshitz theory. They are analogs of the duality
symmetries in 2d CTFs and are constructed by first gauging a finite subgroup of
the momentum symmetry on half of spacetime and then performing a duality
transformation. We analyze the fusion rules of the symmetries and find that
they are condensation defects from an analog of higher gauging exotic
symmetries. We also address their dependence on the UV cutoff when relevant.
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At the horizon of a supersymmetric AdS_5 black hole: Isometries and
half-BPS giants: The near-horizon geometry of an asymptotically AdS_5 supersymmetric black
hole discovered by Gutowski and Reall is analysed. After lifting the solution
to 10 dimensions, we explicitly solve the Killing spinor equations in both
Poincare and global coordinates. It is found that exactly four supersymmetries
are preserved which is twice the number for the full black hole. The full set
of isometries is constructed and the isometry supergroup is shown to be
SU(1,1|1) X SU(2) X U(3). We further study half-BPS configurations of D3-branes
in the near-horizon geometry in Poincare and global coordinates. Both giant
graviton probes and dual giant graviton probes are found.
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Supersymmetry Breaking and Inflation from Higher Curvature Supergravity: The generic embedding of the $R+R^2$ higher curvature theory into old-minimal
supergravity leads to models with rich vacuum structure in addition to its
well-known inflationary properties. When the model enjoys an exact R-symmetry,
there is an inflationary phase with a single supersymmetric Minkowski vacuum.
This appears to be a special case of a more generic set-up, which in principle
may include R-symmetry violating terms which are still of pure supergravity
origin. By including the latter terms, we find new supersymmetry breaking vacua
compatible with single-field inflationary trajectories. We discuss explicitly
two such models and we illustrate how the inflaton is driven towards the
supersymmetry breaking vacuum after the inflationary phase. In these models the
gravitino mass is of the same order as the inflaton mass. Therefore, pure
higher curvature supergravity may not only accommodate the proper inflaton
field, but it may also provide the appropriate hidden sector for supersymmetry
breaking after inflation has ended.
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Relativistic Gravity and Parity-Violating Non-Relativistic Effective
Field Theories: We show that the relativistic gravity theory can offer a framework to
formulate the non-relativistic effective field theory in a general coordinate
invariant way. We focus on the parity violating case in 2+1 dimensions which is
particularly appropriate for the study on quantum Hall effects and chiral
superfluids. We discuss how the non-relativistic spacetime structure emerges
from relativistic gravity. We present covariant maps and constraints that
relate the field contents in the two theories, which also serve as the
holographic dictionary in context of gauge/gravity duality. A low energy
effective action for fractional quantum Hall states is constructed, which
captures universal geometric properties and generates non-universal corrections
systematically. We give another holographic example with dyonic black brane
background to calculate thermodynamic and transport properties of strongly
coupled non-relativistic fluids in magnetic field. In particular, by
identifying the shift function in the gravity as minus of guiding center
velocity, we obtain the Hall viscosity with its relation to Landau orbital
angular momentum density proportional to Wen-Zee shift. Our formalism has a
good projection to lowest Landau level.
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Covariant Hamiltonian field theory. Path integral quantization: The Hamiltonian counterpart of classical Lagrangian field theory is covariant
Hamiltonian field theory where momenta correspond to derivatives of fields with
respect to all world coordinates. In particular, classical Lagrangian and
covariant Hamiltonian field theories are equivalent in the case of a
hyperregular Lagrangian, and they are quasi-equivalent if a Lagrangian is
almost-regular. In order to quantize covariant Hamiltonian field theory, one
usually attempts to construct and quantize a multisymplectic generalization of
the Poisson bracket. In the present work, the path integral quantization of
covariant Hamiltonian field theory is suggested. We use the fact that a
covariant Hamiltonian field system is equivalent to a certain Lagrangian system
on a phase space which is quantized in the framework of perturbative field
theory. We show that, in the case of almost-regular quadratic Lagrangians, path
integral quantizations of associated Lagrangian and Hamiltonian field theories
are equivalent.
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Causality Bounds in Quadratic Inflation from Purely Virtual Particles: The "$\phi^2$" slow roll inflation combined with General Relativity is
largely excluded by Planck data. In this paper, we consider the same potential
combined with the $R+C^2$ gravity of purely virtual particles (or fakeons),
where the would-be ghost introduced by the Weyl tensor term, $C^2$, is
quantized with the fakeon prescription. We compute the tensor power spectrum in
the full theory by means of the Cosmic Renormalization Group formalism and
critically examine its physical meaning. In particular, we show that it is not
possible to retrieve the power spectrum of the fakeon free-theory by
considering the decoupling limit of the purely virtual particles. We provide a
physical explanation in terms of the causal structure of the theory to infer
that a model of quadratic inflation from purely virtual particles is also
discarded from a phenomenological point of view.
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Holographic Butterfly Velocities in Brane Geometry and
Einstein-Gauss-Bonnet Gravity with Matters: In the first part of the paper we generalize the butterfly velocity formula
to anisotropic spacetime. We apply the formula to evaluate the butterfly
velocities in M-branes, D-branes and strings backgrounds. We show that the
butterfly velocities in M2-branes, M5-branes and the intersection M2$\bot$M5
equal to those in fundamental strings, D4-branes and the intersection
F1$\bot$D4 backgrounds, respectively. These observations lead us to conjecture
that the butterfly velocity is generally invariant under a double-dimensional
reduction. In the second part of the paper, we study the butterfly velocity for
Einstein-Gauss-Bonnet gravity with arbitrary matter fields. A general formula
is obtained. We use this formula to compute the butterfly velocities in
different backgrounds and discuss the associated properties.
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SUSY-Extended Field Theory: A field model on fibre bundles can be extended in a standard way to the
BRS-invariant SUSY field model which possesses the Lie supergroup ISp(2) of
symmetries.
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On Gauge Invariant Wilsonian Flows: We investigate non-Abelian gauge theories within a Wilsonian Renormalisation
Group approach. Our main question is: How close can one get to a gauge
invariant flow, despite the fact that a Wilsonian coarse-graining seems to be
incompatible with gauge invariance? We discuss the possible options in the case
of quantum fluctuations, and argue that for thermal fluctuations a fully gauge
invariant implementation can be obtained.
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Complete Solution of SU(2) Chern-Simons Theory: Explicit and complete topological solution of SU(2) Chern-Simons theory on
S^3 is presented.
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Playing with the index of M-theory: Motivated by M-theory, we study rank n K-theoretic Donaldson-Thomas theory on
a toric threefold X. In the presence of compact four-cycles, we discuss how to
include the contribution of D4-branes wrapping them. Combining this with a
simple assumption on the (in)dependence on Coulomb moduli in the 7d theory, we
show that the partition function factorizes and, when X is Calabi-Yau and it
admits an ADE ruling, it reproduces the 5d master formula for the geometrically
engineered theory on A(n-1) ALE space, thus extending the usual geometric
engineering dictionary to n>1. We finally speculate about implications for
instanton counting on Taub-NUT.
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D2-brane RR-charge on SU(2): We compute RR charges of D2-branes on a background with H-field which belongs
to a nontrivial cohomology class. We discover that the RR charge depends on the
configuration of the background `electric' RR field. This result explains the
ambiguity in the definition of the RR charge previously observed in the SU(2)
WZW model.
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The R-matrix bootstrap for the 2d O(N) bosonic model with a boundary: The S-matrix bootstrap is extended to a 1+1d theory with $O(N)$ symmetry and
a boundary in what we call the R-matrix bootstrap since the quantity of
interest is the reflection matrix (R-matrix). Given a bulk S-matrix, the space
of allowed R-matrices is an infinite dimensional convex space from which we
plot a two dimensional section given by a convex domain on a 2d plane. In
certain cases, at the boundary of the domain, we find vertices corresponding to
integrable R-matrices with no free parameters. In other cases, when there is a
one-parameter family of integrable R-matrices, the whole boundary represents
integrable theories. We also consider R-matrices which are analytic in an
extended region beyond the physical cuts, thus forbidding poles (resonances) in
that region. In certain models, this drastically reduces the allowed space of
R-matrices leading to new vertices that again correspond to integrable
theories. We also work out the dual problem, in particular in the case of
extended analyticity, the dual function has cuts on the physical line whenever
unitarity is saturated. For the periodic Yang-Baxter solution that has zero
transmission, we computed the R-matrix initially using the bootstrap and then
derived its previously unknown analytic form.
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The N=2 cascade revisited and the enhancon bearings: Supergravity backgrounds with varying fluxes generated by fractional branes
at non-isolated Calabi-Yau singularities had escaped a precise dual field
theory interpretation so far. In the present work, considering the prototypical
example of such models, the C*C^2/Z_2 orbifold, we propose a solution for this
problem, and show that the known cascading solution corresponds to a vacuum on
the Coulomb branch of the corresponding quiver gauge theory involving a
sequence of strong coupling transitions reminiscent of the baryonic root of N=2
SQCD. We also find a slight modification of this cascading vacuum which upon
mass deformation is expected to flow to the Klebanov-Strassler cascade.
Finally, we discuss an infinite class of vacua on the Coulomb branch whose RG
flows include infinitely coupled conformal regimes, and explain their
gravitational manifestation in terms of new geometric structures that we dub
enhancon bearings. Repulson-free backgrounds dual to all the vacua we analyse
are explicitly provided.
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Near-horizon brane-scan revived: In 1987 two versions of the brane-scan of D-dimensional super p-branes were
put forward. The first pinpointed those (p,D) slots consistent with
kappa-symmetric Green-Schwarz type actions; the second generalized the
"membrane at the end of the universe" idea to all those superconformal groups
describing p-branes on the boundary of AdS_{p+2} x S^{D-p-2}. Although the
second version predicted D3 and M5 branes in addition to those of the first, it
came unstuck because the 1/2 BPS solitonic branes failed to exhibit the
required symmetry enhancement in the near-horizon limit, except in the
non-dilatonic cases (p=2,D=11), (p=3,D=10) and (p=5,D=11). Just recently,
however, it has been argued that the fundamental D=10 heterotic string does
indeed display a near-horizon enhancement to OSp(8|2) as predicted by the
brane-scan, provided alpha' corrections are taken into account. If this logic
could be extended to the other strings and branes, it would resolve this
21-year-old paradox and provide new AdS/CFT dualities, which we tabulate.
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Coordinate and Kähler $σ$-Model Anomalies and Their
Cancellation in String Effective Field Theories: We discuss the complete set of one-loop triangle graphs involving the
Yang-Mills gauge connection, the \Kahler\ connection and the $\sigma$-model
coordinate connection in the effective field theory of $(2,2)$ symmetric $Z_N$
orbifolds. That is, we discuss pure gauge, pure \Kahler\ and pure
$\sigma$-model coordinate anomalies as well as the mixed anomalies, such as
\Kahler-gauge, some of which have been discussed elsewhere. We propose a
mechanism for restoring both \Kahler\ and $\sigma$-model coordinate symmetry
based upon the introduction of two types of counterterms. Finally, we enlarge
the $\sigma$-model generalization of the Green-Schwarz mechanism to allow the
removal of the universal parts of a wider class of anomalies than those
previously discussed.
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Dynamical mass generation of spin-2 fields in de Sitter space for an
$O(N)$ symmetric model at large $N$: We consider the strong-coupling phase in a model of $O(N)$ spin-2 field
theory in de Sitter spacetime and the effective mass of spin-2 fields therein.
In the strong-coupling phase, the Higuchi bound limits the mass parameter in
the theory. The analysis using the large $N$ approximation finds the critical
value of the mass parameter with numerical calculation.
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Perturbative region on non-Gaussian parameter space in single-field
inflation: We calculate one-loop correction to the two-point functions of curvature
perturbation in single-field inflation generated by cubic self-interaction.
Incorporating the observed red-tilted spectrum of curvature perturbation, the
relevant one-loop correction takes a finite value and inversely proportional to
the spectral tilt. Requiring one-loop correction to be much smaller than the
tree-level contribution leads to an upper bound on primordial non-Gaussianity.
While observationally allowed region of non-Gaussian parameter space is found
to be entirely included by the region, where one-loop correction is smaller
than the tree-level contribution, an appreciably large region has one-loop
correction larger than 1% or even 10% of the latter. If future observations
conclude non-Gaussianity falls in such a region, then it would be important to
incorporate higher-order corrections to the spectrum in order to achieve
precise cosmology. In some extreme cases, where one-loop correction has a
comparable magnitude to the tree-level contribution, it might indicate
breakdown of the cosmological perturbation theory in the context of
single-field inflation.
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The E(2) Particle: Recently it has been advocated [1] that for describing nature within the
minimal symmetry requirement, certain subgroups of Lorentz group may play a
fundamental role. One such group is E(2) which induces a Lie algebraic
Non-Commutative spacetime [4] where translation invariance is not fully
maintained. We have constructed a consistent structure of Non-commutative phase
space for this system and furthermore we have studied an appropriate point
particle action on it. Interestingly, the Einstein dispersion relation
$p^2=m^2$ remains intact. The model is constructed by exploiting a dual
canonical phase space following the scheme developed by us earlier [8].
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Continuity, Localization, and Cosmology in Warped Geometry: This is the first of two papers studying localization of massive bulk fields
on a bane in 5D anti-de Sitter spacetime, and some of their cosmological
consequences. Here we focus on a massive 5D scalar, which is known to lack a
localized mode, and discuss how a seeming discontinuity between this theory and
the massless theory - known to support a localized zero mode - is resolved
thanks to peculiar analytic properties of the massive two-point amplitude.
Furthermore, we propose a boundary term that leads to the emergence of a
massless localized mode in the massive theory. Last but not least, we consider
the case when the brane world-volume is de Sitter spacetime, and prove the
existence of a localized massive mode. We discuss how these results, taken
collectively, can be used to describe the accelerated expansion due to the
massive 5D scalar field in an early, or in a late-time universe.
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Twisted Poincaré Symmetry and Some Implications on Noncommutative
Quantum Field Theory: The concept of twisted Poincar\'e symmetry, as well as some implications, are
reviewed. The spin-statistics relation and the nonlocality of NC QFT are
discussed in the light of this quantum symmetry. The possibility of a twisted
symmetry principle for quantum field and gauge theories formulated on a
noncommutative space-time is also explored.
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Exact Operator Solution for Liouville Theory with $q$ A Root of Unity: The exact operator solution for quantum Liouville theory constructed for the
generic quantum deformation parameter $q$ is extended to the case with $q$
being a root of unity. The screening charge operator becomes nilpotent in such
cases and arbitrary Liouville exponentials can be obtained in finite
polynomials of the screening charge.
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High temperature asymptotics of thermodynamic functions of
electromagnetic field subjected to boundary conditions on a sphere and
cylinder: The high temperature asymptotics of thermodynamic functions of
electromagnetic field subjected to boundary conditions with spherical and
cylindrical symmetries are constructed by making use of a general expansion in
terms of heat kernel coefficients and the related determinant. For this, some
new heat kernel coefficients and determinants had to be calculated for the
boundary conditions under consideration. The obtained results reproduce all the
asymptotics derived by other methods in the problems at hand and involve a few
new terms in the high temperature expansions. An obvious merit of this approach
is its universality and applicability to any boundary value problem correctly
formulated.
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Quantum vacuum fluctuations and the principle of virtual work in
inhomogeneous backgrounds: We discuss several aspects of the stress-energy tensor for a quantum scalar
field in an inhomogeneous background, the latter being modeled by a variable
mass. Using a perturbative approach, dimensional regularization and adiabatic
subtraction, we present all-order formal expressions for the stress-energy
tensor. Importantly, we provide an explicit proof of the principle of virtual
work for Casimir forces, taking advantage of the conservation law for the
renormalized stress-energy tensor. We discuss also discontinuity-induced
divergences. For the particular case of planar inhomogeneities, we corroborate
the perturbative results with a WKB-inspired expansion.
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Introduction to Random Matrices: These notes provide an introduction to the theory of random matrices. The
central quantity studied is $\tau(a)= det(1-K)$ where $K$ is the integral
operator with kernel $1/\pi} {\sin\pi(x-y)\over x-y} \chi_I(y)$. Here
$I=\bigcup_j(a_{2j-1},a_{2j})$ and $\chi_I(y)$ is the characteristic function
of the set $I$. In the Gaussian Unitary Ensemble (GUE) the probability that no
eigenvalues lie in $I$ is equal to $\tau(a)$. Also $\tau(a)$ is a tau-function
and we present a new simplified derivation of the system of nonlinear
completely integrable equations (the $a_j$'s are the independent variables)
that were first derived by Jimbo, Miwa, M{\^o}ri, and Sato in 1980. In the case
of a single interval these equations are reducible to a Painlev{\'e} V
equation. For large $s$ we give an asymptotic formula for $E_2(n;s)$, which is
the probability in the GUE that exactly $n$ eigenvalues lie in an interval of
length $s$.
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Topological mass in seven dimensions and dualities in four dimensions: The massive topologically and self dual theories en seven dimensions are
considered. The local duality between these theories is established and the
dimensional reduction lead to the different dualities for massive antisymmetric
fields in four dimensions.
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A numerical algorithm for efficiently obtaining a Feynman parameter
representation of one-gluon loop QCD Feynman diagrams for a large number of
external gluons: A numerical program is presented which facilitates a computation pertaining
to the full set of one-gluon loop diagrams (including ghost loop
contributions), with M attached external gluon lines in all possible ways. The
feasibility of such a task rests on a suitably defined master formula, which is
expressed in terms of a set of Grassmann and a set of Feynman parameters. The
program carries out the Grassmann integration and performs the Lorentz trace on
the involved functions, expressing the result as a compact sum of parametric
integrals. The computation is based on tracing the structure of the final
result, thus avoiding all intermediate unnecessary calculations and directly
writing the output. Similar terms entering the final result are grouped
together. The running time of the program demonstrates its effectiveness,
especially for large M.
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The Nuts and Bolts of Einstein-Maxwell Solutions: We find new non-supersymmetric solutions of five-dimensional ungauged
supergravity coupled to two vector multiplets. The solutions are regular,
horizonless and have the same asymptotic charges as non-extremal charged black
holes. An essential ingredient in our construction is a four-dimensional
Euclidean base which is a solution to Einstein-Maxwell equations. We construct
stationary solutions based on the Euclidean dyonic Reissner-Nordstrom black
hole as well as a six-parameter family with a dyonic Kerr-Newman-NUT base.
These solutions can be viewed as compactifications of eleven-dimensional
supergravity on a six-torus and we discuss their brane interpretation.
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Twisted Superalgebras and Cohomologies of the N=2 Superconformal Quantum
Mechanics: We prove that the invariance of the N=2 superconformal quantum mechanics is
controlled by subalgebras of a given twisted superalgebra made of 6 fermionic
(nilpotent) generators and 6 bosonic generators (including a central charge).
The superconformal quantum mechanics actions are invariant under this quite
large twisted superalgebra. On the other hand, they are fully determined by a
subalgebra with only 2 fermionic and 2 bosonic (the central charge and the
ghost number) generators. The invariant actions are Q_i-exact (i=1,2,...,6),
with a Q_{i'}-exact (i'\neq i) antecedent for all 6 fermionic generators. It
follows that the superconformal quantum mechanics actions with Calogero
potentials are uniquely determined even if, in its bosonic sector, the twisted
superalgebra does not contain the one-dimensional conformal algebra sl(2), but
only its Borel subalgebra. The general coordinate covariance of the non-linear
sigma-model for the N=2 supersymmetric quantum mechanics in a curved target
space is fully implied only by its worldline invariance under a pair of the 6
twisted supersymmetries. The transformation connecting the ordinary and twisted
formulations of the N=2 superconformal quantum mechanics is explicitly
presented.
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A new, exact, gauge-invariant RG-flow equation: This paper has been withdrawn by the authors.
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Induced self-interactions in the spacetime of a global monopole with
finite core: In this paper we analyze induced self-interactions for point-like particles
with electric and scalar charges placed at rest in the spacetime of a global
monopole admitting a general spherically symmetric inner structure to it. In
order to develop this analysis we calculate the three-dimensional Green
function associated with the physical system under consideration. As we shall
see for the charged particle outside the monopole core, the corresponding Green
functions are composed by two distinct contributions, the firsts ones are
induced by the non-trivial topology of the global monopole considered as a
point-like defect and the seconds are corrections induced by the non-vanishing
inner structure attributed to it. For both cases, the self-energies present a
similar structure, having also two distinct contributions as well. For a
specific model considered for region inside the monopole, named flower-pot, we
shall see that the particle with electric charge will be always subject to a
repulsive self-force with respect to the monopole core's boundary, on the other
scalar charged particle exhibits peculiar behavior. Depending on the curvature
coupling the self-force can be repulsive or attractive with respect to the
core's boundary. Moreover, the contribution due to the point-like global
monopole vanishes for massless particle conformally coupled with three
dimensional space section of the manifold, and the only contribution comes from
the core-induced part.
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Monopoles, Polyakov-Loops and Gauge Fixing on the Torus: We consider pure Yang Mills theory on the four torus. A set of non-Abelian
transition functions is presented which encompass all instanton sectors. It is
argued that these transition functions are a convenient starting point for
gauge fixing. In particular, we give an extended Abelian projection with
respect to the Polyakov loop, where $A_0$ is independent of time and in the
Cartan subalgebra. In the non-perturbative sectors such gauge fixings are
necessarily singular. These singularities can be restricted to Dirac strings
joining monopole and anti-monopole like ``defects''.
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High temperature behavior of non-local observables in boosted strongly
coupled plasma: A holographic study: In this work, we perform a holographic analysis to study non local
observables associated to a uniformly \textit{boosted} strongly coupled large
$N$ thermal plasma in $d$-dimensions. In order to accomplish the holographic
analysis, the appropriate dual bulk theory turns out to be $d+1$ dimensional
\textit{boosted} AdS-Schwarzschild blackhole background. In particular, we
compute entanglement entropy of the boosted plasma at high temperature living
inside a strip geometry with entangling width $l$ in the boundary at a
particular instant of time. We also study the two-point correlators in the
boundary by following geodesic approximation method. For analyzing the effect
of boosting on the thermal plasma and correspondingly on both non local
observables, we keep the alignment of the width of region of interest both
parallel and perpendicular to the direction of the boost. We find our results
significantly modified compared to those in un-boosted plasma up to the
quadratic order of the boost velocity $v$. More interestingly, the relative
orientation of the boost and the entangling width plays a crucial role to
quantify the holographic entanglement entropy in the boundary theory. The
breaking of rotational symmetry in the boundary theory due to the boosting of
the plasma along a specific flat direction causes this interesting feature.
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Holographic applications of logarithmic conformal field theories: We review the relations between Jordan cells in various branches of physics,
ranging from quantum mechanics to massive gravity theories. Our main focus is
on holographic correspondences between critically tuned gravity theories in
Anti-de Sitter space and logarithmic conformal field theories in various
dimensions. We summarize the developments in the past five years, include some
novel generalizations and provide an outlook on possible future developments.
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How to get from imaginary to real chemical potential: Using the exactly solvable Gross-Neveu model as theoretical laboratory, we
analyse in detail the relationship between a relativistic quantum field theory
at real and imaginary chemical potential. We find that one can retrieve the
full information about the phase diagram of the theory from an imaginary
chemical potential calculation. The prerequisite is to evaluate and
analytically continue the effective potential for the chiral order parameter,
rather than thermodynamic observables or phase boundaries. In the case of an
inhomogeneous phase, one needs to compute the full effective action, a
functional of the space-dependent order parameter, at imaginary chemical
potential.
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Thermal Aspects of ABJM theory: Currents and Condensations: To study thermal aspects of the ABJM theory in the strongly coupled regime,
we carry out the CP3 invariant dimensional reduction of the type IIA
supergravity down to four dimensions. We then investigate zero and finite
temperature responses of the operators which are dual to the AdS scalar and
vector fields. Two scalar operators are shown to have finite-temperature
condensations by coupling of constant source term. The currents dual to the
massless and massive gauge fields are not induced by coupling of constant
boundary vector potential, which implies that the phase described by black
brane background is not superconducting. We also discuss a generalization to
charged (dyonic) black holes.
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Two-Point Superstring Tree Amplitudes Using the Pure Spinor Formalism: We provide a prescription for computing two-point tree amplitudes in the pure
spinor formalism that are finite and agree with the corresponding expression in
the field theories. In [arXiv:1906.06051v1-arXiv:1909.03672v3], same results
were presented for bosonic strings and it was mentioned they can be generalized
to superstrings. The pure spinor formalism is a successful super-Poincare
covariant approach to quantization of superstrings [arXiv:hep-th/0001035v2].
Because the pure spinor formalism is equivalent to other superstring
formalisms, we explicitly verify the above claim. We introduce a mostly BRST
exact operator in order to achieve this.
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Fuzzy BIons in Curved Spacetimes: The non-abelian Dirac-Born-Infeld action is used to construct the D2-brane
from multiple D0-branes in the curved spacetimes. After choosing the matrix
elements as the coordinates of the D0-branes we obtain a simple formula of the
Lagrangian for the system in a class of the curved background. Using the
formula we first re-examine the system in the flat spacetime and show that, in
addition to the fuzzy tube and fuzzy spike which were found in the previous
literature, there is the fuzzy wormhole solution. Next, we apply the formula to
the system in the geometry of the NS5-branes background. A solution describing
the fuzzy BIon of spike profile is obtained. Our investigations show that the
size of the matrices is finite for the fuzzy spike in the curved spacetimes.
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Two Point Correlation Function of Sine-Liouville Theory: Exact two point correlation functions of sine-Liouville theory are presented
for primary fields with U(1) charge neutral, which may either preserve or break
winding number. Our result is checked with perturbative calculation and is also
consistent with previous one which can be obtained by restricting the action
parameters.
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Dynamical completions of generalized O'Raifeartaigh models: We present gauge theory completions of Wess-Zumino models admitting
supersymmetry breaking vacua with spontaneously broken R-symmetry. Our models
are simple deformations of generalized ITIY models, a supersymmetric theory
with gauge group Sp(N), N+1 flavors plus singlets, with a modified tree level
superpotential which explicitly breaks (part of) the global symmetry. Depending
on the nature of the deformation, we obtain effective O'Raifeartaigh-like
models whose pseudomoduli space is locally stable in a neighborhood of the
origin of field space, or in a region not including it. Hence, once embedded in
direct gauge mediation scenarios, our models can give low energy spectra with
either suppressed or unsuppressed gaugino mass.
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Singular electromagnetic fields in nonlinear electrodynamics with a
constant background field: When exploring equations of nonlinear electrodynamics in effective medium
formed by mutually parallel external electric and magnetic fields, we come to
special static axial-symmetric solutions of two types. The first are comprised
of fields referred to as electric and magnetic responses to a point-like
electric charge when placed into the medium. In electric case, this is a field
determined by the induced charge density. In magnetic case, this is a field
carrying no magnetic charge and determined by an induced current. Fields of
second type require presence of pseudoscalar constants for their existence.
These are singular on the axis drawn along the external fields. In electric
case this is a field of an inhomogeneously charged infinitely thin thread. In
magnetic case this is the magnetic monopole with the Dirac string supported by
solenoidal current. In both cases the necessary pseudoscalar constant is
supplied by field derivatives of nonlinear Lagrangian taken on external fields.
There is also a magnetic thread solution dual to electric thread with null
total magnetic charge.
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Free q-Deformed Relativistic Wave Equations by Representation Theory: In a representation theoretic approach a free q-relativistic wave equation
must be such, that the space of solutions is an irreducible representation of
the q-Poincare algebra. It is shown how this requirement uniquely determines
the q-wave equations. As examples, the q-Dirac equation (including q-gamma
matrices which satisfy a q-Clifford algebra), the q-Weyl equations, and the
q-Maxwell equations are computed explicitly.
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On explicit free field realizations of current algebras: We construct the explicit free field representations of the current algebras
$so(2n)_k$, $so(2n+1)_k$ and $sp(2n)_k$ for a generic positive integer $n$ and
an arbitrary level $k$. The corresponding energy-momentum tensors and screening
currents of the first kind are also given in terms of free fields.
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Near-Extremal Vanishing Horizon AdS5 Black Holes and Their CFT Duals: We consider families of charged rotating asymptotically AdS5 Extremal black
holes with Vanishing Horizon (EVH black holes) whose near horizon geometries
develop locally AdS3 throats. Using the AdS3/CFT2 duality, we propose an
EVH/CFT2 correspondence to describe the near-horizon low energy IR dynamics of
near-EVH black holes involving a specific large N limit of the 4d N = 4 SYM. We
give a map between the UV and IR near-EVH excitations, showing that the UV
first law of thermodynamics reduces to the IR first law satisfied by the near
horizon BTZ black holes in this near-EVH limit. We also discuss the connection
between our EVH/CFT proposal and the Kerr/CFT correspondence in the cases where
the two overlap.
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F-maximization along the RG flows: a proposal: We propose an extension of the F-maximization principle to take into account
the effects of non-superconformality. Guided by a four-dimensional analog, we
formulate a modification of the free energy via the Lagrange multiplier
technique. We conjecture that the Lagrange multiplier plays the same role as
the coupling constant, at least at weak coupling. We check our proposal in many
examples with unitary, symplectic and orthogonal gauge groups.
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Three-point functions in ${\cal N}=4$ SYM: the hexagon proposal at three
loops: Basso, Komatsu and Vieira recently proposed an all-loop framework for the
computation of three-point functions of single-trace operators of ${\cal N}=4$
super-Yang-Mills, the "hexagon program". This proposal results in several
remarkable predictions, including the three-point function of two protected
operators with an unprotected one in the $SU(2)$ and $SL(2)$ sectors. Such
predictions consist of an "asymptotic" part---similar in spirit to the
asymptotic Bethe Ansatz of Beisert and Staudacher for two-point functions---as
well as additional finite-size "wrapping" L\"uscher-like corrections. The focus
of this paper is on such wrapping corrections, which we compute at three-loops
in the $SL(2)$ sector. The resulting structure constants perfectly match the
ones obtained in the literature from four-point correlators of protected
operators.
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Quantization of Nambu Brackets from Operator Formalism in Classical
Mechanics: This paper proposes a novel approach to quantizing Nambu brackets in
classical mechanics using operator formalism. The approach employs the ``Planck
derivative'' to represent Nambu brackets, from which we derive a commutation
relation for their quantization. Notably, this commutation relation aligns with
that emerging from the T-duality of closed strings in a twisted torus with a
B-field, thereby hinting at a potential connection with Double Field Theory.
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Repulsive Casimir Effects: Like Casimir's original force between conducting plates in vacuum, Casimir
forces are usually attractive. But repulsive Casimir forces can be achieved in
special circumstances. These might prove useful in nanotechnology. We give
examples of when repulsive quantum vacuum forces can arise with conducting
materials.
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Semiclassical (Quantum Field Theory) and Quantum (String) de Sitter
Regimes: New Results: We compute the quantum string entropy S_s(m, H) from the microscopic string
density of states rho_s (m,H) of mass m in de Sitter space-time. We find for
high m, a {\bf new} phase transition at the critical string temperature T_s=
(1/2 pi k_B)L c^2/alpha', higher than the flat space (Hagedorn) temperature
t_s. (L = c/H, the Hubble constant H acts at the transition as producing a
smaller string constant alpha' and thus, a higher tension). T_s is the precise
quantum dual of the semiclassical (QFT Hawking-Gibbons) de Sitter temperature
T_sem = hbar c /(2\pi k_B L). We find a new formula for the full de Sitter
entropy S_sem (H), as a function of the usual Bekenstein-Hawking entropy
S_sem^(0)(H). For L << l_{Planck}, ie. for low H << c/l_Planck,
S_{sem}^{(0)}(H) is the leading term, but for high H near c/l_Planck, a new
phase transition operates and the whole entropy S_sem (H) is drastically
different from the Bekenstein-Hawking entropy S_sem^(0)(H). We compute the
string quantum emission cross section by a black hole in de Sitter (or
asymptotically de Sitter) space-time (bhdS). For T_sem ~ bhdS << T_s, (early
evaporation stage), it shows the QFT Hawking emission with temperature T_sem ~
bhdS, (semiclassical regime). For T_sem ~ bhdS near T_{s}, it exhibits a phase
transition into a string de Sitter state of size L_s = l_s^2/L}, l_s=
\sqrt{\hbar alpha'/c), and string de Sitter temperature T_s. Instead of
featuring a single pole singularity in the temperature (Carlitz transition), it
features a square root branch point (de Vega-Sanchez transition). New bounds on
the black hole radius r_g emerge in the bhdS string regime: it can become r_g =
L_s/2, or it can reach a more quantum value, r_g = 0.365 l_s.
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Superspace Duality in Low-Energy Superstrings: We extend spacetime duality to superspace, including fermions in the
low-energy limits of superstrings. The tangent space is a curved, extended
superspace. The geometry is based on an enlarged coordinate space where the
vanishing of the d'Alembertian is as fundamental as the vanishing of the curl
of a gradient.
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Relativistic effect of entanglement in fermion-fermion scattering: We study the properties of entanglement entropy among scattering particles as
observed from different inertial moving frames, based on an exemplary QED
process $e^+e^-\rightarrow\mu^+\mu^-$. By the explicit calculation of the
Wigner rotation, the entanglement entropy of scattering particles is found to
be Lorentz invariant. We also study the behavior of the entanglement between
spin degrees of freedom for scattering particles in moving frames. This
quantity, being found to change with different inertial reference frames, does
not exhibit as a Lorentz invariant.
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Massive and massless monopoles with nonabelian magnetic charges: We use the multimonopole moduli space as a tool for studying the properties
of BPS monopoles carrying nonabelian magnetic charges. For configurations whose
total magnetic charge is purely abelian, the moduli space for nonabelian
breaking can be obtained as a smooth limit of that for a purely abelian
breaking. As the asymptotic Higgs field is varied toward one of the special
values for which the unbroken symmetry is enlarged to a nonabelian group, some
of the fundamental monopoles of unit topological charge remain massive but
acquire nonabelian magnetic charges. The BPS mass formula indicates that others
should become massless in this limit. We find that these do not correspond to
distinct solitons but instead manifest themselves as ``nonabelian clouds''
surrounding the massive monopoles. The moduli space coordinates describing the
position and $U(1)$ phase of these massless monopoles are transformed into an
equal number of nonabelian global gauge orientation and gauge-invariant
structure parameters characterizing the nonabelian cloud. We illustrate this
explicitly in a class of $Sp(2N)$ examples for which the full family of
monopole solutions is known. We show in detail how the unbroken symmetries of
the theory are manifested as isometries of the moduli space metric. We discuss
the connection of these results to the Montonen-Olive duality conjecture,
arguing in particular that the massless monopoles should be understood as the
duals to the massless gauge bosons that appear as the mediators of the
nonabelian forces in the perturbative sector.
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Chiral Gauged WZW Theories and Coset Models in Conformal Field Theory: The Wess-Zumino-Witten (WZW) theory has a global symmetry denoted by
$G_L\otimes G_R$. In the standard gauged WZW theory, vector gauge fields (\ie\
with vector gauge couplings) are in the adjoint representation of the subgroup
$H \subset G$. In this paper, we show that, in the conformal limit in two
dimensions, there is a gauged WZW theory where the gauge fields are chiral and
belong to the subgroups $H_L$ and $H_R$ where $H_L$ and $H_R$ can be different
groups. In the special case where $H_L=H_R$, the theory is equivalent to vector
gauged WZW theory. For general groups $H_L$ and $H_R$, an examination of the
correlation functions (or more precisely, conformal blocks) shows that the
chiral gauged WZW theory is equivalent to $(G/H)_L\otimes (G/H)_R$ coset models
in conformal field theory. The equivalence of the vector gauged WZW theory and
the corresponding $G/H$ coset theory then follows.
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Quadrality for Supersymmetric Matrix Models: We introduce a new duality for $\mathcal{N}=1$ supersymmetric gauged matrix
models. This $0d$ duality is an order 4 symmetry, namely an equivalence between
four different theories, hence we call it Quadrality. Our proposal is motivated
by mirror symmetry, but is not restricted to theories with a D-brane
realization and holds for general $\mathcal{N}=1$ matrix models. We present
various checks of the proposal, including the matching of: global symmetries,
anomalies, deformations and the chiral ring. We also consider quivers and the
corresponding quadrality networks. Finally, we initiate the study of matrix
models that arise on the worldvolume of D(-1)-branes probing toric Calabi-Yau
5-folds.
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Semiclassical Quantisation of Finite-Gap Strings: We perform a first principle semiclassical quantisation of the general
finite-gap solution to the equations of a string moving on R x S^3. The
derivation is only formal as we do not regularise divergent sums over stability
angles. Moreover, with regards to the AdS/CFT correspondence the result is
incomplete as the fluctuations orthogonal to this subspace in AdS_5 x S^5 are
not taken into account. Nevertheless, the calculation serves the purpose of
understanding how the moduli of the algebraic curve gets quantised
semiclassically, purely from the point of view of finite-gap integration and
with no input from the gauge theory side. Our result is expressed in a very
compact and simple formula which encodes the infinite sum over stability angles
in a succinct way and reproduces exactly what one expects from knowledge of the
dual gauge theory. Namely, at tree level the filling fractions of the algebraic
curve get quantised in large integer multiples of hbar = 1/lambda^{1/2}. At
1-loop order the filling fractions receive Maslov index corrections of hbar/2
and all the singular points of the spectral curve become filled with small
half-integer multiples of hbar. For the subsector in question this is in
agreement with the previously obtained results for the semiclassical energy
spectrum of the string using the method proposed in hep-th/0703191.
Along the way we derive the complete hierarchy of commuting flows for the
string in the R x S^3 subsector. Moreover, we also derive a very general and
simple formula for the stability angles around a generic finite-gap solution.
We also stress the issue of quantum operator orderings since this problem
already crops up at 1-loop in the form of the subprincipal symbol.
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Massive symmetric tensor field on AdS: The two-point Green function of a local operator in CFT corresponding to a
massive symmetric tensor field on the AdS background is computed in the
framework of the AdS/CFT correspondence. The obtained two-point function is
shown to coincide with the two-point function of the graviton in the limit when
the mass vanishes.
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Holographic two-point functions in medium: We study two-point correlation function in a medium composed of two kinds of
matter, which is the dual of a three-dimensional generalized $p$-brane gas
geometry. Following the holographic prescription, we calculate temporal and
spatial two-point functions in the medium. In general, the screening effect of
the medium makes two-point functions decrease more rapidly than the CFT's
two-point function. In the extremal limit, however, we find that a temporal
two-point function is still conformal. This indicates that a two-dimensional UV
CFT flows into a one-dimensional quantum mechanics in the IR limit. This is
consistent with the fact that the near horizon geometry in the extremal limit
reduces to AdS$_2$. We also investigate holographic mutual information
representing the correlation between two subsystems. We show that a critical
distance in the IR region, where the mutual information vanishes, leads to a
similar behavior to the correlation length of a two-point function.
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Symanzik's Method Applied To The Fractional Quantum Hall Edge States: In this paper we consider an abelian Chern-Simons theory with plane boundary
and we show, following Symankiz's quite general approach, how the known results
for edge states in the Laughlin series can be derived in a systematic way by
the separability condition. Moreover we show that the conserved boundary
currents find a natural and explicit interpretation in terms of the continuity
equation and the Tomonaga-Luttinger commutation relation for electronic density
is recovered.
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Observable Supertranslations: We show that large gauge transformations in asymptotically flat spacetime can
be implemented by sandwiching a shell containing the ingoing hard particles
between two finite-width shells of soft gauge excitations. Integration of the
graviton Dirac bracket implies that our observable soft degrees of freedom obey
the algebra imposed by Strominger on unobservable boundary degrees of freedom.
Thus, we provide both a derivation and an observable realization of this
algebra. The conservation laws associated with asymptotic symmetries are seen
to arise physically from free propagation of infrared modes. This explains in
physical terms our recent result that soft charges fail to constrain the hard
scattering problem, and so cannot be relevant to the black hole information
paradox.
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Tunneling decay of false domain walls: the silence of the lambs: We study the decay of "false" domain walls, which are metastable states of
the quantum theory where the true vacuum is trapped inside the wall, with the
false vacuum outside. We consider a theory with two scalar fields, a shepherd
field and a field of sheep. The shepherd field serves to herd the solitons of
the sheep field so that they are nicely bunched together. However, quantum
tunnelling of the shepherd field releases the sheep to spread out
uncontrollably. We show how to calculate the tunnelling amplitude for such a
disintegration.
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Renormalizations in softly broken N=1 theories: Slavnov-Taylor
identities: Slavnov-Taylor identities have been applied to perform explicitly the
renormalization procedure for the softly broken N=1 SYM. The result is in
accordance with the previous results obtained at the level of supergraph
technique.
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Nearly Critical Superfluids in Keldysh-Schwinger Formalism: We examine the effective theory of critical dynamics near superfluid phase
transitions in the framework of the Keldysh-Schwinger formalism. We focus on
the sector capturing the dynamics of the complex order parameter and the
conserved current corresponding to the broken global symmetry. After
constructing the theory up to quadratic order in the $a$-fields, we compare the
resulting stochastic system with Model F as well as with holography. We
highlight the role of a time independent gauge symmetry of the effective theory
also known as ``chemical shift". Finally, we consider the limiting behaviour at
energies much lower than the gap of the amplitude mode by integrating out the
high energy degrees of freedom to reproduce the effective theory of
superfluids.
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All point correlation functions in SYK: Large $N$ melonic theories are characterized by two-point function Feynman
diagrams built exclusively out of melons. This leads to conformal invariance at
strong coupling, four-point function diagrams that are exclusively ladders, and
higher-point functions that are built out of four-point functions joined
together. We uncover an incredibly useful property of these theories: the
six-point function, or equivalently, the three-point function of the primary
$O(N)$ invariant bilinears, regarded as an analytic function of the operator
dimensions, fully determines all correlation functions, to leading nontrivial
order in $1/N$, through simple Feynman-like rules. The result is applicable to
any theory, not necessarily melonic, in which higher-point correlators are
built out of four-point functions. We explicitly calculate the bilinear
three-point function for $q$-body SYK, at any $q$. This leads to the bilinear
four-point function, as well as all higher-point functions, expressed in terms
of higher-point conformal blocks, which we discuss. We find universality of
correlators of operators of large dimension, which we simplify through a saddle
point analysis. We comment on the implications for the AdS dual of SYK.
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Five-Brane BPS States in Heterotic M-Theory: We present explicit methods for computing the discriminant curves and the
associated Kodaira type fiber degeneracies of elliptically fibered Calabi-Yau
threefolds. These methods are applied to a specific three-family, SU(5) grand
unified theory of particle physics within the context of Heterotic M-Theory. It
is demonstrated that there is always a region of moduli space where a bulk
space five-brane is wrapped on a pure fiber in the Calabi-Yau threefold.
Restricting the discussion to the smooth parts of the discriminant curve, we
explore the properties of the N=2 BPS supermultiplets that arise on the
worldvolume of this five-brane due to the degeneration of the elliptic fiber.
The associated degenerating M membranes are shown to project to string
junctions in the base space. We use string junction techniques to explicitly
compute the light BPS hyper- and vector multiplet spectrum for each Kodaira
type fiber near the smooth part of the discriminant curve in the SU(5) GUT
theory.
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On the consistency of a class of R-symmetry gauged 6D N=(1,0)
supergravities: R-symmetry gauged 6D (1,0) supergravities free from all local anomalies, with
gauge groups $G\times G_R$ where $G_R$ is the R-symmetry group and $G$ is
semisimple with rank greater than one, and which have no hypermultiplet
singlets, are extremely rare. There are three such models known in which the
gauge symmetry group is $G_1\times G_2 \times U(1)_R$ where the first two
factors are $ \left(E_6/{\mathbb{Z}_3}\right) \times E_7$, $ G_2 \times E_7 $
and $F_4 \times Sp(9)$. These are models with single tensor multiplet, and
hyperfermions in the $(1,912)$, $(14,56)$ and $(52,18)$ dimensional
representations of $G_1\times G_2$, respectively. So far it is not known if
these models follow from string theory. We highlight key properties of these
theories, and examine constraints which may arise from the consistency of the
quantization of anomaly coefficients formulated in their strongest form by
Monnier and Moore. Assuming that the gauged models accommodate dyonic string
excitations, we find that these constraints are satisfied only by the model
with the $F_4 \times Sp(9)\times U(1)_R$ symmetry. We also discuss aspects of
dyonic strings and potential caveats they may pose in applying the stated
consistency conditions to the $R$-symmetry gauged models.
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Quiver Chern-Simons theories and crystals: We consider N=2 quiver Chern-Simons theories described by brane tilings,
whose moduli spaces are toric Calabi-Yau 4-folds. Simple prescriptions to
obtain toric data of the moduli space and a corresponding brane crystal from a
brane tiling are proposed.
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Noncommutative Sugawara Construction: The noncommutative extension of the Sugawara construction for free massless
fermionic fields in two dimensions is studied. We prove that the equivalence of
the noncommutative Sugawara energy-momentum tensor and symmetric
energy-momentum tensor persists in the noncommutative extension. Some relevant
physical results of this equivalence are also discussed.
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Tidal Stresses and Energy Gaps in Microstate Geometries: We compute energy gaps and study infalling massive geodesic probes in the new
families of scaling, microstate geometries that have been constructed recently
and for which the holographic duals are known. We find that in the deepest
geometries, which have the lowest energy gaps, the geodesic deviation shows
that the stress reaches the Planck scale long before the probe reaches the cap
of the geometry. Such probes must therefore undergo a stringy transition as
they fall into microstate geometry. We discuss the scales associated with this
transition and comment on the implications for scrambling in microstate
geometries.
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Super Kähler oscillator from SU(2|1) superspace: We construct a new version of the worldline SU(2|1) superspace as a
deformation of the standard N =4, d=1 superspace and show that it naturally
provides off- and on-shell description of general supersymmetric K\"ahler
oscillator model considered earlier at the classical level within the
Hamiltonian approach. The basic object is a generalized chiral SU(2|1), d=1
superfield with the off-shell field content (2, 4, 2). The frequency of the
oscillator and the strength of external magnetic field are defined by two
parameters: the contraction parameter $m$ and the new parameter $\lambda$ which
reflects the freedom in defining the chiral SU(2|1), d=1 superspace. We treat
both classical and quantum cases.
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Lectures on (abelian) Chern-Simons vortices: Various aspects including the construction and the symmetries of Abelian
Chern-Simons vortices are reviewed. Extended version of the Lectures delivered
at NIKHEF (Amsterdam), July 2006. Typos corrected, some refernces added.
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Appearance of Boulware-Deser ghost in bigravity with doubly coupled
matter: We discuss the ghost freeness in the case when we add matter coupled to two
metrics to the ghost-free bigravity. In this paper we show that the
Boulware-Deser ghost generally revives in the presence of doubly coupled matter
and that ghost freeness strongly restricts the model of kinetically doubly
coupled matter. This result may anticipate difficulties in the attempt to
derive the ghost-free bigravity as a low-energy effective theory, starting with
a model applicable at high energies.
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On integrability of the one-dimensional Hubbard model: We find a family of solutions to Zamolodchikov's tetrahedral algebra
corresponding to the fermionic R-operator for the free fermion model of the
difference type in one of the spectral parameters, construct an extension of
the R-operator for a system of two spins satisfying the Yang-Baxter equation,
and find the local charges. We also construct a twisted monodromy operator,
which leads to the one-dimensional Hubbard model.
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Vector Bosons in the Randall-Sundrum 2 and Lykken-Randall models and
unparticles: Unparticle behavior is shown to be realized in the Randall-Sundrum 2 (RS 2)
and the Lykken-Randall (LR) brane scenarios when brane-localized Standard Model
currents are coupled to a massive vector field living in the five-dimensional
warped background of the RS 2 model. By the AdS/CFT dictionary these
backgrounds exhibit certain properties of the unparticle CFT at large N_c and
strong 't Hooft coupling. Within the RS 2 model we also examine and contrast in
detail the scalar and vector position-space correlators at intermediate and
large distances. Unitarity of brane-to-brane scattering amplitudes is seen to
imply a necessary and sufficient condition on the positivity of the bulk mass,
which leads to the well-known unitarity bound on vector operators in a CFT.
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4d/5d Correspondence for the Black Hole Potential and its Critical
Points: We express the d=4, N=2 black hole effective potential for cubic holomorphic
F functions and generic dyonic charges in terms of d=5 real special geometry
data. The 4d critical points are computed from the 5d ones, and their relation
is elucidated. For symmetric spaces, we identify the BPS and non-BPS classes of
attractors and the respective entropies. These are related by simple formulae,
interpolating between four and five dimensions, depending on the volume modulus
and on the 4d magnetic (or electric) charges, and holding true also for generic
field configurations and for non-symmetric cubic geometries.
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Functional Renormalization Group Approach for Tensorial Group Field
Theory: A Rank-6 Model with Closure Constraint: We develop the functional renormalization group formalism for a tensorial
group field theory with closure constraint, in the case of an Abelian just
renormalizable model with quartic interactions. The method allows us to obtain
a closed but non-autonomous system of differential equations which describe the
renormalization group flow of the couplings beyond perturbation theory. The
explicit dependence of the beta functions on the running scale is due to the
existence of an external scale in the model, the radius of the unit circle. We
study the occurrence of fixed points and their critical properties in two
different approximate regimes, corresponding to the deep UV and deep IR.
Besides confirming the asymptotic freedom of the model, we find also a
non-trivial fixed point, with one relevant direction. Our results are
qualitatively similar to those found previously for a rank-3 model without
closure constraint, and it is thus tempting to speculate that the presence of a
Wilson-Fisher-like fixed point is a general feature of asymptotically free
tensorial group field theories.
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Eternal Inflation: The Inside Story: Motivated by the lessons of black hole complementarity, we develop a causal
patch description of eternal inflation. We argue that an observer cannot
ascribe a semiclassical geometry to regions outside his horizon, because the
large-scale metric is governed by the fluctuations of quantum fields. In order
to identify what is within the horizon, it is necessary to understand the late
time asymptotics. Any given worldline will eventually exit from eternal
inflation into a terminal vacuum. If the cosmological constant is negative, the
universe crunches. If it is zero, then we find that the observer's fate depends
on the mechanism of eternal inflation. Worldlines emerging from an eternal
inflation phase driven by thermal fluctuations end in a singularity. By
contrast, if eternal inflation ends by bubble nucleation, the observer can
emerge into an asymptotic, locally flat region. As evidence that bubble
collisions preserve this property, we present an exact solution describing the
collision of two bubbles.
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Particle production in a Robertson-Walker space with a de Sitter phase
of finite extension: We investigate the phenomenon of particle production in a
Friedmann-Robertson-Walker universe which contains a phase of de Sitter
expansion for a finite interval, outside which it reduces to the flat Minkowski
spacetime. We compute the particle number density for a massive scalar and a
spinorial field and point out differences between the two cases. We find that
the resulting particle density approaches a constant value at the scale of the
Hubble time and that for a certain choice of the parameters the spectrum is
precisely thermal for the spinorial field, and almost thermal for the scalar
field.
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Finiteness and Unitarity of Lorentz-Covariant Green-Schwarz Superstring
Amplitudes: In two recent papers, a new method was developed for calculating
ten-dimensional superstring amplitudes with an arbitrary number of loops and
external massless particles, and for expressing them in manifestly
Lorentz-invariant form. By explicitly checking for divergences when the Riemann
surface degenerates, these amplitudes are proven to be finite. By choosing
light-cone moduli for the surface and comparing with the light-cone
Green-Schwarz formalism, these amplitudes are proven to be unitary.
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Elliptic fibrations for SU(5) x U(1) x U(1) F-theory vacua: Elliptic Calabi-Yau fibrations with Mordell-Weil group of rank two are
constructed. Such geometries are the basis for F-theory compactifications with
two abelian gauge groups in addition to non-abelian gauge symmetry. We present
the elliptic fibre both as a Bl^2P^2[3]-fibration and in the birationally
equivalent Weierstrass form. The spectrum of charged singlets and their Yukawa
interactions are worked out in generality. This framework can be combined with
the toric construction of tops to implement additional non-abelian gauge
groups. We utilise the classification of tops to construct SU(5) x U(1) x U(1)
gauge symmetries systematically and study the resulting geometries, presenting
the defining equations, the matter curves and their charges, the Yukawa
couplings and explaining the process in detail for an example. Brane
recombination relates these geometries to a Bl^1P^2[3]-fibration with a
corresponding class of SU(5) x U(1) models. We also present the SU(5) tops
based on the elliptic fibre Bl^1P_[1,1,2][4], corresponding to another class of
SU(5) x U(1) models.
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Massive type IIA string theory cannot be strongly coupled: Understanding the strong coupling limit of massive type IIA string theory is
a longstanding problem. We argue that perhaps this problem does not exist;
namely, there may be no strongly coupled solutions of the massive theory. We
show explicitly that massive type IIA string theory can never be strongly
coupled in a weakly curved region of space-time. We illustrate our general
claim with two classes of massive solutions in AdS4xCP3: one, previously known,
with N = 1 supersymmetry, and a new one with N = 2 supersymmetry. Both
solutions are dual to d = 3 Chern-Simons-matter theories. In both these massive
examples, as the rank N of the gauge group is increased, the dilaton initially
increases in the same way as in the corresponding massless case; before it can
reach the M-theory regime, however, it enters a second regime, in which the
dilaton decreases even as N increases. In the N = 2 case, we find
supersymmetry-preserving gauge-invariant monopole operators whose mass is
independent of N. This predicts the existence of branes which stay light even
when the dilaton decreases. We show that, on the gravity side, these states
originate from D2-D0 bound states wrapping the vanishing two-cycle of a
conifold singularity that develops at large N.
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Covariance of the selfdual vector model: The Poisson algebra between the fields involved in the vectorial selfdual
action is obtained by means of the reduced action. The conserved charges
associated with the invariance under the inhomogeneous Lorentz group are
obtained and its action on the fields. The covariance of the theory is proved
using the Schwinger-Dirac algebra. The spin of the excitations is discussed.
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Non-planar operator mixing by Brauer representations: We study the action of the dilatation operator on the basis of local
operators constructed from the elements of the walled Brauer algebra, with
non-planar corrections fully taken into account. We will see that the operator
mixing can be neatly expressed in terms of the irreducible representations of
the algebra. In particular we focus on a role of the integer that determines
the number of boxes in the representations.
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The Mass Spectrum of N=1 SYM(2+1) at Strong Coupling: We consider supersymmetric Yang-Mills theory on R x S^1 x S^1. In particular,
we choose one of the compact directions to be light-like and another to be
space-like. Since the SDLCQ regularization explicitly preserves supersymmetry,
this theory is totally finite, and thus we can solve for bound state wave
functions and masses numerically without renormalizing. We present the masses
as functions of the longitudinal and transverse resolutions and show that the
masses converge rapidly in both resolutions. We also study the behavior of the
spectrum as a function of the coupling and find that at strong coupling there
is a stable, well defined spectrum which we present. We also find several
unphysical states that decouple at large transverse resolution. There are two
sets of massless states; one set is massless only at zero coupling and the
other is massless at all couplings. Together these sets of massless states are
in one-to-one correspondence with the full spectrum of the dimensionally
reduced theory.
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On Marginal Deformations in Superstring Field Theory: We use level truncated superstring field theory to obtain the effective
potential for the Wilson line marginal deformation parameter which corresponds
to the constant vacuum expectation value of the U(1) gauge field on the D-brane
in a particular direction. We present results for both the BPS and the non-BPS
D-brane. In the case of non-BPS D-brane the effective potential has branches
corresponding to the extrema of the tachyon potential. In the branch with
vanishing tachyon vev (M-branch), the effective potential becomes flatter as
the level of the approximation is increased. The branch which corresponds to
the stable vacuum after the tachyon has condensed (V-branch) exists only for a
finite range of values of marginal deformation parameter. We use our results to
find the mass of the gauge field in the stable tachyonic vacuum. We find this
mass to be of a non-zero value which seems to stabilize as the level
approximation is improved.
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Remarks on string solitons: We consider generalized self-duality equations for U(2r) Yang-Mills theory on
R^8 with quaternionic structure. We employ the extended ADHM method in eight
dimensions to construct exact soliton solutions of the low-energy effective
theory of the heterotic string.
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Phase transition and entropic force of de Sitter black hole in massive
gravity: It is well known that de Sitter(dS) black holes generally have a black hole
horizon and a cosmological horizon, both of which have Hawking radiation. But
the radiation temperature of the two horizons is generally different, so dS
black holes do not meet the requirements of thermal equilibrium stability,
which brings certain difficulties to the study of the thermodynamic
characteristics of black holes. In this paper, dS black hole is regarded as a
thermodynamic system, and the effective thermodynamic quantities of the system
are obtained. The influence of various state parameters on the effective
thermodynamic quantities in the massive gravity space-time is discussed. The
condition of the phase transition of the de Sitter black hole in massive
gravity space-time is given. We consider that the total entropy of the dS black
hole is the sum of the corresponding entropy of the two horizons plus an extra
term from the correlation of the two horizons. By comparing the entropic force
of interaction between black hole horizon and the cosmological horizon with
Lennard-Jones force between two particles, we find that the change rule of
entropic force between the two system is surprisingly the same. The research
will help us to explore the real reason of accelerating expansion of the
universe.
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Free strings in non-critical dimensions: The paper containes a classification of consistent free string models in
physical dimensions and a brief discussion of recent results concerning
relations between various models.
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The symmetry algebra of the N-dimensional anisotropic quantum harmonic
oscillator with rational ratios of frequencies and the Nilsson model: The symmetry algebra of the N-dimensional anisotropic quantum harmonic
oscillator with rational ratios of frequencies is constructed by a method of
general applicability to quantum superintegrable systems. The special case of
the 3-dim oscillator is studied in more detail, because of its relevance in the
description of superdeformed nuclei and nuclear and atomic clusters. In this
case the symmetry algebra turns out to be a nonlinear extension of the u(3)
algebra. A generalized angular momentum operator useful for labeling the
degenerate states is constructed, clarifying the connection of the present
formalism to the Nilsson model in nuclear physics.
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Split attractor flows and the spectrum of BPS D-branes on the Quintic: We investigate the spectrum of type IIA BPS D-branes on the quintic from a
four dimensional supergravity perspective and the associated split attractor
flow picture. We obtain some very concrete properties of the (quantum
corrected) spectrum, mainly based on an extensive numerical analysis, and to a
lesser extent on exact results in the large radius approximation. We predict
the presence and absence of some charges in the BPS spectrum in various regions
of moduli space, including the precise location of the lines of marginal
stability and the corresponding decay products. We explain how the generic
appearance of multiple basins of attraction is due to the presence of conifold
singularities and give some specific examples of this phenomenon. Some
interesting space-time features of these states are also uncovered, such as a
nontrivial, moduli independent lower bound on the area of the core of arbitrary
BPS solutions, whether they are black holes, empty holes, or more complicated
composites.
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Jet fragmentation and gauge/string duality: We consider an analog of e^+e^- annihilation in gauge theories which have a
dual string description in asymptotically AdS_5 space and discuss the nature of
jet fragmentation. We construct the timelike anomalous dimension which governs
the scale dependence of the fragmentation function. In the limit of infinite 't
Hooft coupling, the average multiplicity rises linearly with the energy and the
inclusive spectrum is peaked at the kinematical boundary.
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Dolan-Grady Relations and Noncommutative Quasi-Exactly Solvable Systems: We investigate a U(1) gauge invariant quantum mechanical system on a 2D
noncommutative space with coordinates generating a generalized deformed
oscillator algebra. The Hamiltonian is taken as a quadratic form in gauge
covariant derivatives obeying the nonlinear Dolan-Grady relations. This
restricts the structure function of the deformed oscillator algebra to a
quadratic polynomial. The cases when the coordinates form the su(2) and sl(2,R)
algebras are investigated in detail. Reducing the Hamiltonian to 1D
finite-difference quasi-exactly solvable operators, we demonstrate partial
algebraization of the spectrum of the corresponding systems on the fuzzy sphere
and noncommutative hyperbolic plane. A completely covariant method based on the
notion of intrinsic algebra is proposed to deal with the spectral problem of
such systems.
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On the quantization of folded strings in non-critical dimensions: Classical rotating closed string are folded strings. At the folding points
the scalar curvature associated with the induced metric diverges. As a
consequence one cannot properly quantize the fluctuations around the classical
solution since there is no complete set of normalizable eigenmodes. Furthermore
in the non-critical effective string action of Polchinski and Strominger, there
is a divergence associated with the folds. We overcome this obstacle by putting
a massive particle at each folding point which can be used as a regulator.
Using this method we compute the spectrum of quantum fluctuations around the
rotating string and the intercept of the leading Regge trajectory. The results
we find are that the intercepts are $a=1$ and $a=2$ for the open and closed
string respectively, independent of the target space dimension. We argue that
in generic theories with an effective string description, one can expect
corrections from finite masses associated with either the endpoints of an open
string or the folding points on a closed string. We compute explicitly the
corrections in the presence of these masses.
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Phantom Field from Conformal Invariance: We establish a correspondence between a conformally invariant complex scalar
field action (with a conformal self-interaction potential) and the action of a
phantom scalar field minimally coupled to gravity (with a cosmological
constant). In this correspondence, the module of the complex scalar field is
used to relate conformally the metrics of both systems while its phase is
identified with the phantom scalar field. At the level of the equations, the
correspondence allows to map solution of the conformally non-linear
Klein-Gordon equation with vanishing energy-momentum tensor to solution of a
phantom scalar field minimally coupled to gravity with cosmological constant
satisfying a massless Klein-Gordon equation. The converse is also valid with
the advantage that it offers more possibilities owing to the freedom of
rewriting a metric as the conformal transformation of another metric. Finally,
we provide some examples of this correspondence.
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Secondary Fields in D>2 Conformal Theories: We consider the secondary fields in $D$-dimensional space, $D\ge3$, generated
by the non-abelian current and energy-momentum tensor. These fields appear in
the operator product expansions $j^{a}_\mu(x)\phi(0)$ and
$T_{\mu\nu}(x)\phi(0)$. The secondary fields underlie the construction proposed
herein (see [1,2] for more details) and aimed at the derivation of exact
solutions of conformal models in $D\ge3$. In the case of D=2 this construction
leads to the known [5] exactly solvable models based on the
infinite-dimensional conformal symmetry. It is shown that for $D\ge3$ the
existence of the secondary fields is governed by the existence of anomalous
operator contributions (the scalar fields $R_j$ and $R_T$ of dimensions $d_j =
d_T = D-2$) into the operator product expansions $j^{a}_\mu j^{b}_\nu$ and
$T_{\mu\nu} T_{\rho\sigma}$. The coupling constant between the field $R_j$ and
the fundamental field is found. The fields $R_j$ and $R_T$ are shown to beget
two infinite sets of secondary tensor fields of canonical dimensions $D-2+s$,
where $s$ is the tensor rank. The current and the energy-momentum tensor belong
to those families, their Green functions being expressed through the Green
functions of the fields $R_j$ and $R_T$ correspondingly. We demonstrate that
the Ward identities give rise to the closed set of equations for the Green
functions of the fields $R_j$ and $R_T$.
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Environment-Induced Decoherence in Noncommutative Quantum Mechanics: We address the question of the appearence of ordinary quantum mechanics in
the context of noncommutative quantum mechanics. We obtain the noncommutative
extension of the Hu-Paz-Zhang master equation for a Brownian particle linearly
coupled to a bath of harmonic oscillators. We consider the particular case of
an Ohmic regime.
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Paths with singularities in functional integrals of quantum field theory: In the toy model ($ \phi^{4}$-interacting quantum field theory in
one-dimensional "Euclidean" space-time) we prove that the functional integrals
of the free field theory evaluated over the space of continuous functions are
equal to the functional integrals of the interacting field theory evaluated
over a set of spaces containing the spaces of discontinuous functions.
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The KLT relations in unimodular gravity: With this article, we initiate a systematic study of some of the symmetry
properties of unimodular gravity, building on much of the known structure of
general relativity, and utilising the powerful technology developed in that
context. In particular, we show, up to four-points and tree-level, that the KLT
relations of perturbative gravity hold for tracefree or unimodular gravity.
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Towards Kaluza-Klein Dark Matter on Nilmanifolds: We present a first study of the field spectrum on a class of
negatively-curved compact spaces: nilmanifolds or twisted tori. This is a case
where analytical results can be obtained, allowing to check numerical methods.
We focus on the Kaluza-Klein expansion of a scalar field. The results are then
applied to a toy model where a natural Dark Matter candidate arises as a stable
massive state of the bulk scalar.
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Supersymmetric Classical Mechanics: Free Case: We present a review work on Supersymmetric Classical Mechanics in the context
of a Lagrangian formalism, with $N=1-$supersymmetry. We show that the N=1
supersymmetry does not allow the introduction of a potential energy term
depending on a single commuting supercoordinate, $\phi (t;\Theta)$.
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Classical space from quantum condensates: We review the boson transformation method to deal with spontaneous symmetry
breaking in quantum field theory, focussing on how it describes the emergence
of extended and classical objects in such quantum context. We then apply the
method to the emergence of space itself, as an extended and classical object
resulting from the evaporation of a quantum black hole. In particular, we show
how classical torsion and curvature tensors can emerge as effects of an
inhomogeneous Nambu-Goldstone boson condensation in vacuum, in E(3) invariant
spinor models with symmetry breaking.
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New G_2 metric, D6-branes and Lattice Universe: We construct a new (singular) cohomogeneity-three metric of G_2 holonomy. The
solution can be viewed as a triple intersection of smeared Taub-NUTs. The
metric comprises three non-compact radial-type coordinates, with the principal
orbits being a T^3 bundle over S^1. We consider an M-theory vacuum
(Minkowski)_4\times M_7 where M_7 is the G_2 manifold. Upon reduction on a
circle in the T^3, we obtain the intersection of a D6-brane, a Taub-NUT and a
6-brane with R-R 2-form flux. Reducing the solution instead on the base space
S^1, we obtain three intersecting 6-branes all carrying R-R 2-form flux. These
two configurations can be viewed as a classical flop in the type IIA string
theory. After reducing on the full principal orbits and the spatial
world-volume, we obtain a four-dimensional metric describing a lattice
universe, in which the three non-compact coordinates of the G_2 manifold are
identified with the spatial coordinates of our universe.
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Regular Black Holes and Confinement: Properties of the rotating Kerr-Newman black hole solution allow to relate it
with spinning particles. Singularity of black hole (BH) can be regularized by a
metric deformation. In this case, as a consequence of the Einstein equations, a
material source appears in the form of a relativistically rotating
superconducting disk which replaces the former singular region. We show a
relation of the BH regularization with confinement formation. By
regularization, a phase transition occurs near the core of a charged black hole
solution: from external electrovacuum to an internal superconducting state of
matter. We discuss two models of such a kind, which demonstrate the appearance
of a baglike structure and a mechanism of confinement based on dual Dirac's
electrodynamics. First one is an approximate solution based on a supersymmetric
charged domain wall, and second is an exact solution based on nonlinear
electrodynamics.
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Holographic bulk viscosity: GPR vs EO: Recently Eling and Oz (EO) proposed a formula for the holographic bulk
viscosity, in arXiv:1103.1657, derived from the null horizon focusing equation.
This formula seems different from that obtained earlier by Gubser, Pufu and
Rocha (GPR) in arXiv:0806.0407 calculated from the IR limit of the two-point
function of the trace of the stress tensor. The two were shown to agree only
for some simple scaling cases. We point out that the two formulae agree in two
non-trivial holographic theories describing RG flows. The first is the strongly
coupled N=2* gauge theory plasma. The second is the semi-phenomenological model
of Improved Holographic QCD.
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Next-to-MHV Yang-Mills kinematic algebra: Kinematic numerators of Yang-Mills scattering amplitudes possess a rich Lie
algebraic structure that suggest the existence of a hidden infinite-dimensional
kinematic algebra. Explicitly realizing such a kinematic algebra is a
longstanding open problem that only has had partial success for simple helicity
sectors. In past work, we introduced a framework using tensor currents and
fusion rules to generate BCJ numerators of a special subsector of NMHV
amplitudes in Yang-Mills theory. Here we enlarge the scope and explicitly
realize a kinematic algebra for all NMHV amplitudes. Master numerators are
obtained directly from the algebraic rules and through commutators and
kinematic Jacobi identities other numerators can be generated. Inspecting the
output of the algebra, we conjecture a closed-form expression for the master
BCJ numerator up to any multiplicity. We also introduce a new method, based on
group algebra of the permutation group, to solve for the generalized gauge
freedom of BCJ numerators. It uses the recently introduced binary BCJ relations
to provide a complete set of NMHV kinematic numerators that consist of pure
gauge.
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SUPERTRACES IN STRING THEORY: We demonstrate that the spectrum of any consistent string theory in $D$
dimensions must satisfy a number of supertrace constraints: $ Str~M^{2n}=0 $
for $0 \leq n < D/2-1$, integer $n$. These results hold for a large class of
string theories, including critical heterotic strings. For strings lacking
spacetime supersymmetry, these supertrace constraints will be satisfied as a
consequence of a hidden ``misaligned supersymmetry'' in the string spectrum.
[Talk given by R.C.M. at Strings '95; to appear in Proceedings]
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Phase structure of matrix quantum mechanics at finite temperature: We study matrix quantum mechanics at finite temperature by Monte Carlo
simulation. The model is obtained by dimensionally reducing 10d U(N) pure
Yang-Mills theory to 1d. Following Aharony et al., one can view the same model
as describing the high temperature regime of (1+1)d U(N) super Yang-Mills
theory on a circle. In this interpretation an analog of the deconfinement
transition was conjectured to be a continuation of the black-hole/black-string
transition in the dual gravity theory. Our detailed analysis in the critical
regime up to N=32 suggests the existence of the non-uniform phase, in which the
eigenvalue distribution of the holonomy matrix is non-uniform but gapless. The
transition to the gapped phase is of second order. The internal energy is
constant (giving the ground state energy) in the uniform phase, and rises
quadratically in the non-uniform phase, which implies that the transition
between these two phases is of third order.
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No Contact Terms for the Magnetic Field in Lorentz- and CPT-Violating
Electrodynamics: In a Lorentz- and CPT-violating modification of electrodynamics, the fields
of a moving charge are known to have unusual singularities. This raises the
question of whether the singular behavior may include $\delta$-function contact
terms, similar to those that appear in the fields of idealized dipoles.
However, by calculating the magnetic field of an infinite straight wire in this
theory, we demonstrate that there are no such contact terms in the magnetic
field of a moving point charge
|
Holographic S-fold theories at one loop: A common feature of tree-level holography is that a correlator in one theory
can serve as a generating function for correlators in another theory with less
continuous symmetry. This is the case for a family of 4d CFTs with eight
supercharges which have protected operators dual to gluons in the bulk. The
most recent additions to this family were defined using S-folds which combine a
spatial identification with an action of the S-duality group in type IIB string
theory. Differences between these CFTs which have a dynamical origin first
become manifest at one loop. To explore this phenomenon at the level of
anomalous dimensions, we use the AdS unitarity method to bootstrap a one-loop
double discontinuity. Compared to previous studies, the subsequent analysis is
performed without any assumption about which special functions are allowed.
Instead, the Casimir singular and Casimir regular terms are extracted
iteratively in order to move from one Regge trajectory to the next. Our results
show that anomalous dimensions in the presence of an S-fold are no longer
rational functions of the spin.
|
QCD Vacuum Properties in a Magnetic Field from AdS/CFT: Chiral
Condensate and Goldstone Mass: Chiral condensate and $\eta^\prime$ meson mass spectrum are studied under the
influence of an external Abelian magnetic field. We work within the D3/D7
Karch--Katz model of flavoured AdS/CFT with supersymmetry broken by the
Constable--Myers deformation of the metric. It is shown that this setting
yields a quadratic dependence of condensate on field, rather than the
non-analytic (linear in field) dependence, typical for chiral perturbation
theory in the exact chiral limit. We argue that the analytic (quadratic) result
must be put into correspondence with the leading-order in the $1/N_c$
decomposition for the condensate, whereas the existing chiral perturbation
theory result, which is linear in field strength, is $1/N_c$ suppressed.
|
Symmetry Resolved Entanglement of Excited States in Quantum Field Theory
I: Free Theories, Twist Fields and Qubits: The excess entanglement resulting from exciting a finite number of
quasiparticles above the ground state of a free integrable quantum field theory
has been investigated quite extensively in the literature. It has been found
that it takes a very simple form, depending only on the number of excitations
and their statistics. There is now mounting evidence that such formulae also
apply to interacting and even higher-dimensional quantum theories. In this
paper we study the entanglement content of such zero-density excited states
focusing on the symmetry resolved entanglement, that is on 1+1D quantum field
theories that possess an internal symmetry. The ratio of charged moments
between the excited and grounds states, from which the symmetry resolved
entanglement entropy can be obtained, takes a very simple and universal form,
which in addition to the number and statistics of the excitations, now depends
also on the symmetry charge. Using form factor techniques, we obtain both the
ratio of moments and the symmetry resolved entanglement entropies in complex
free theories which possess $U(1)$ symmetry. The same formulae are found for
simple qubit states.
|
The Exact SL(K+3,C) Symmetry of String Scattering Amplitudes: We discover that the 26D open bosonic string scattering amplitudes (SSA) of
three tachyons and one arbitrary string state can be expressed in terms of the
D-type Lauricella functions with associated SL(K+3,C) symmetry. As a result,
SSA and symmetries or relations among SSA of different string states at various
limits calculated previously can be rederived. These include the linear
relations conjectured by Gross [1-3] and proved in [4-9] in the hard scattering
limit, the recurrence relations in the Regge scattering limit [14-16] and the
extended recurrence relations in the nonrelativistic scattering limit [19]
discovered recently. Finally, as an application, we calculate a new recurrence
relation of SSA which is valid for all energies.
|
Dual approaches for defects condensation: We review two methods used to approach the condensation of defects
phenomenon. Analyzing in details their structure, we show that in the limit
where the defects proliferate until occupy the whole space these two methods
are dual equivalent prescriptions to obtain an effective theory for the phase
where the defects (like monopoles or vortices) are completely condensed,
starting from the fundamental theory defined in the normal phase where the
defects are diluted.
|
The Transfer of Entanglement: The Case for Firewalls: Black hole complementarity requires that the interior of a black hole be
represented by the same degrees of freedom that describe its exterior.
Entanglement plays a crucial role in the reconstruction of the interior degrees
of freedom. This connection is manifest in "two-sided" eternal black holes. But
for real black holes which are formed from collapse there are no second sides.
The sense in which horizon entropy is entanglement entropy is much more subtle
for one-sided black holes. It involves entanglement between different parts of
the near-horizon system. As a one-sided black hole evaporates the entanglement
that accounts for its interior degrees of freedom disappears, and is gradually
replaced by entanglement with the outgoing Hawking radiation. A principle of
"transfer of entanglement" can be formulated. According to the argument of
Almheiri, Marolf, Polchinski and Sully, it is when the transfer of entanglement
is completed at the Page time, that a firewall replaces the horizon.
Alternatives to firewalls may suffer contradictions which are similar to those
of time travel. The firewall hypothesis would be similar to Hawking's
chronology protection conjecture.
|
Cosmology of the Lifshitz universe: We study the ultraviolet complete non-relativistic theory recently proposed
by Horava. After introducing a Lifshitz scalar for a general background, we
analyze the cosmology of the model in Lorentzian and Euclidean signature.
Vacuum solutions are found and it is argued the existence of non-singular
bouncing profiles. We find a general qualitative agreement with both the
picture of Causal Dynamical Triangulations and Quantum Einstein Gravity.
However, inflation driven by a Lifshitz scalar field on a classical background
might not produce a scale-invariant spectrum when the principle of detailed
balance is assumed.
|
Reflections on Parity Breaking: Parity and CP symmetries are broken in the world around us. Nonetheless,
parity (or CP) may be a gauge symmetry which is higgsed in our universe. This
is assumed in many scenarios for physics beyond the Standard Model, including
the classic Nelson--Barr proposal for the Strong CP problem. Gauged parity can
only arise in quantum gravity, where it corresponds to a path integral over
both orientable and non-orientable spacetime manifolds. We show that
spontaneous breaking of gauged parity leads to exactly stable domain walls, and
describe the implications for the cosmology of models with gauged parity. These
domain walls carry an unusual sort of charge, which superficially has features
in common with both gauge charges and global charges. We show that these
unusual charges are consistent with the expected absence of global symmetries
in quantum gravity when there exists a complete spectrum of dynamical objects
required by the Swampland Cobordism Conjecture, including end-of-the-world
branes.
|
Phantom Energy with Variable G and Lambda: We have investigated a cosmological model of a phantom energy with a variable
cosmological constant ($\Lambda$) depending on the energy density ($\rho$) as
$\Lambda\propto \rho^{-\alpha}$, $\alpha=\rm const.$ and a variable
gravitational constant ($G$). The model requires $\alpha<0$ and a negative
gravitational constant. A negative gravitational constant may forbid
\emph{black holes} to form a particle horizon in a background of phantom
energy. This implies that black holes are naked, and consequently the
\emph{Cosmic Censorship} theorem is violated. The cosmological constant evolves
with time as, $\Lambda\propto t^{-2}$. For $\omega>-1$ and $\alpha<-1$ the
cosmological constant, $\Lambda<0$, $G>0$ and $\rho$ decrease with cosmic
expansion. For ordinary matter (or dark matter), i.e., $\omega>-1$ we have
$-1<\alpha<0$ and $\beta>0$ so that $G>0$ increases with time and $\rho$
decreases with time. Cosmic acceleration with dust particles is granted
provided $-{2/3}<\alpha <0$ and $\Lambda>0$.
|
Exact Electric-Magnetic Duality in N=2 Supersymmetric QCD Theories: We analyze the Coulomb phase of theories of $N=2$ SQCD with $SU(N_c)$ gauge
groups which are conjectured to have exact electric-magnetic duality. We
discuss the duality transformation of the particle spectrum, emphasizing the
differences between the general case and the $SU(2)$ case. Some difficulties
associated with the definition of the duality transformation for a general
gauge group are discussed. We compute the classical monopole spectrum of these
theories, and when it is possible we use it to check the consistency of the
duality. Generally these theories may have phase transitions between strong and
weak coupling, which prevent the semi-classical computation from being useful
for checking the duality.
|
Spontaneously Broken N=2 Supergravity Without Light Mirror Fermions: We present a spontaneously broken N=2 supergravity model that reduces in the
flat limit to a globally supersymmetric N=2 system with explicit soft
supersymmetry breaking terms. These soft terms generate a mass O(100 GeV) for
mirror quarks and leptons, while leaving the physical fermions light, thereby
overcoming one of the major obstacles towards the construction of a realistic
N=2 model of elementary interactions.
|
Efficient Algorithm for Generating Homotopy Inequivalent Calabi-Yaus: We present an algorithm for efficiently exploring inequivalent Calabi-Yau
threefold hypersurfaces in toric varieties. A direct enumeration of fine,
regular, star triangulations (FRSTs) of polytopes in the Kreuzer-Skarke
database is foreseeably impossible due to the large count of distinct FRSTs.
Moreover, such an enumeration is needlessly redundant because many such
triangulations have the same restrictions to 2-faces and hence, by Wall's
theorem, lead to equivalent Calabi-Yau threefolds. We show that this redundancy
can be circumvented by finding a height vector in the strict interior of the
intersection of the secondary cones associated with each 2-face triangulation.
We demonstrate that such triangulations are generated with orders of magnitude
fewer operations than the naive approach of generating all FRSTs and selecting
only those differing on 2-faces. Similar methods are also presented to directly
generate (the support of) the secondary subfan of all fine triangulations,
relevant for random sampling of FRSTs.
|
Expressing entropy globally in terms of (4D) field-correlations: We express the entropy of a scalar field phi directly in terms of its
spacetime correlation function W(x,y) = <phi(x) phi(y)>, assuming that the
higher correlators are of "Gaussian" form. The resulting formula associates an
entropy S(R) to any spacetime region R; and when R is globally hyperbolic with
Cauchy surface Sigma, S(R) can be interpreted as the entropy of the reduced
density-matrix belonging to Sigma. One acquires in particular a new expression
for the entropy of entanglement across an event-horizon. Thanks to its
spacetime character, this expression makes sense in a causal set as well as in
a continuum spacetime.
|
Variable Fine Structure Constant from Maximal-Acceleration Phase Space
Relativity: We presented a new physical model that links the maximum speed of light with
the minimal Planck scale into a maximal-acceleration Relativity principle in
the spacetime tangent bundle and in phase spaces (cotangent bundle). The
maximal proper-acceleration bound is a = c^2/ \Lambda in full agreement with
the old predictions of Caianiello, the Finslerian geometry point of view of
Brandt and more recent results in the literature. Inspired by the
maximal-acceleration corrections to the Lamb shifts of one-electron atoms by
Lambiase, Papini and Scarpetta, we derive the exact integral equation that
governs the Renormalization-Group-like scaling dependence of the fractional
change of the fine structure constant as a function of the cosmological
redshift factor and a cutoff scale L_c, where the maximal acceleration
relativistic effects are dominant. A particular physical model exists dominated
entirely by the vacuum energy, when the cutoff scale is the Planck scale, with
\Omega_\Lambda \sim 1 . The implications of this extreme case scenario are
studied.
|
Zero-energy modes, fractional fermion numbers and the index theorem in a
vortex-Dirac fermion system: Physics of topological materials have attracted much attention from both
physicists and mathematicians recently. The index and the fermion number of
Dirac fermions play an important role in topological insulators and topological
superconductors. A zero-energy mode exists when Dirac fermions couple to
objects with soliton-like structure such as kinks, vortices, monopoles, strings
and branes. We discuss a system of Dirac fermions interacting with a vortex and
a kink. This kind of systems will be realized on the surface of topological
insulators where Dirac fermions exist. The fermion number is fractionalized and
this is related to the presence of fermion zero-energy excitation modes. A
zero-energy mode can be regarded as a Majorana fermion mode when the chemical
potential vanishes. Our discussion includes the case where there is a half-flux
quantum vortex associated with a kink in a magnetic field in a bilayer
superconductor. A normalizable wave function of fermion zero-energy mode does
not exist in the core of the half-flux quantum vortex. The index of Dirac
operator and the fermion number have additional contributions when a soliton
scalar field has a singularity.
|
Twisted Poincare Invariance, Noncommutative Gauge Theories and UV-IR
Mixing: In the absence of gauge fields, quantum field theories on the
Groenewold-Moyal (GM) plane are invariant under a twisted action of the
Poincare group if they are formulated following [1, 2, 3, 4, 5, 6]. In that
formulation, such theories also have no UV-IR mixing [7]. Here we investigate
UV-IR mixing in gauge theories with matter following the approach of [3, 4]. We
prove that there is UV-IR mixing in the one-loop diagram of the S-matrix
involving a coupling between gauge and matter fields on the GM plane, the gauge
field being nonabelian. There is no UV-IR mixing if it is abelian.
|
Coupled dark energy: Towards a general description of the dynamics: In dark energy models of scalar-field coupled to a barotropic perfect fluid,
the existence of cosmological scaling solutions restricts the Lagrangian of the
field $\vp$ to $p=X g(Xe^{\lambda \vp})$, where $X=-g^{\mu\nu} \partial_\mu \vp
\partial_\nu \vp /2$, $\lambda$ is a constant and $g$ is an arbitrary function.
We derive general evolution equations in an autonomous form for this Lagrangian
and investigate the stability of fixed points for several different dark energy
models--(i) ordinary (phantom) field, (ii) dilatonic ghost condensate, and
(iii) (phantom) tachyon. We find the existence of scalar-field dominant fixed
points ($\Omega_\vp=1$) with an accelerated expansion in all models
irrespective of the presence of the coupling $Q$ between dark energy and dark
matter. These fixed points are always classically stable for a phantom field,
implying that the universe is eventually dominated by the energy density of a
scalar field if phantom is responsible for dark energy. When the equation of
state $w_\vp$ for the field $\vp$ is larger than -1, we find that scaling
solutions are stable if the scalar-field dominant solution is unstable, and
vice versa. Therefore in this case the final attractor is either a scaling
solution with constant $\Omega_\vp$ satisfying $0<\Omega_\vp<1$ or a
scalar-field dominant solution with $\Omega_\vp=1$.
|
Indications for Gluon Condensation from Nonperturbative Flow Equations: We employ nonperturbative flow equations for the description of the effective
action in Yang-Mills theories. We find that the perturbative vacuum with
vanishing gauge field strength does not correspond to the minimum of the
Euclidean effective action. The true ground state is characterized by a
nonvanishing gluon condensate.
|
Emergent Strings from Infinite Distance Limits: As a refinement of the Swampland Distance Conjecture, we propose that a
quantum gravitational theory in an infinite distance limit of its moduli space
either decompactifies, or reduces to an asymptotically tensionless, weakly
coupled string theory. We support our claim by classifying, as special cases,
the behaviour of M-Theory and Type IIA string theory compactifications on
Calabi-Yau three-folds at infinite distances in Kahler moduli space. The
analysis comprises three parts: We first classify the possible infinite
distance limits in the classical Kahler moduli space of a Calabi-Yau
three-fold. Each such limit at finite volume is characterized by a universal
fibration structure, for which the generic fiber shrinking in the limit is
either an elliptic curve, a K3 surface, or an Abelian surface. In the second
part we focus on M-Theory and investigate the nature of the towers of
asymptotically massless states that arise from branes wrapped on the shrinking
fibers. Depending on which of the three classes of fibrations are considered,
we obtain decompactification to F-Theory, or a theory with a unique
asymptotically tensionless, weakly coupled heterotic or Type II string,
respectively. The latter probes a dual D-manifold which is in general
non-geometric. In addition to the intrinsic string excitations, towers of
states from M2-branes along non-contractible curves become light and correspond
to further wrapping and winding modes of the tensionless heterotic or Type II
string. In the third part of the analysis, we consider Type IIA string theory
on Calabi-Yau three-folds and show that quantum effects obstruct taking finite
volume infinite distance limits in the Kahler moduli space. The only possible
infinite distance limit which is not a decompactification limit involves
K3-fibrations with string scale fiber volume and gives rise to an emergent
tensionless heterotic string.
|
Rigid invariance as derived from BRS invariance: The abelian Higgs model: Consequences of a symmetry, e.g.\ relations amongst Green functions, are
renormalization scheme independently expressed in terms of a rigid Ward
identity. The corresponding local version yields information on the respective
current. In the case of spontaneous breakdown one has to define the theory via
the BRS invariance and thus to construct rigid and current Ward identity
non-trivially in accordance with it. We performed this construction to all
orders of perturbation theory in the abelian Higgs model as a prelude to the
standard model. A technical tool of interest in itself is the use of a doublet
of external scalar ``background'' fields. The Callan-Symanzik equation has an
interesting form and follows easily once the rigid invariance is established.
|
Semiclassical relativistic strings in S^5 and long coherent operators in
N=4 SYM theory: We consider the low energy effective action corresponding to the 1-loop,
planar, dilatation operator in the scalar sector of N=4 SU(N) SYM theory. For a
general class of non-holomorphic ``long'' operators, of bare dimension L>>1, it
is a sigma model action with 8-dimensional target space and agrees with a limit
of the phase-space string sigma model action describing generic fast-moving
strings in the S^5 part of AdS_5 x S^5. The limit of the string action is taken
in a way that allows for a systematic expansion to higher orders in the
effective coupling $\lambda/L^2$. This extends previous work on rigid rotating
strings in S^5 (dual to operators in the SU(3) sector of the dilatation
operator) to the case when string oscillations or pulsations in S^5 are
allowed. We establish a map between the profile of the leading order string
solution and the structure of the corresponding coherent, ``locally BPS'', SYM
scalar operator. As an application, we explicitly determine the form of the
non-holomorphic operators dual to the pulsating strings. Using action--angle
variables, we also directly compute the energy of pulsating solutions,
simplifying previous treatments.
|
Similarity between the kinematic viscosity of quark-gluon plasma and
liquids at the viscosity minimum: Recently, it has been found that the kinematic viscosity of liquids at the
minimum, $\nu_m$, can be expressed in terms of fundamental physical constants,
giving $\nu_m$ on the order of $10^{-7}~{\rm m^2/s}$. Here, we show that the
kinematic viscosity of quark-gluon plasma (QGP) has a similar value and support
this finding by experimental data and theoretical estimations. The similarity
is striking, given that the dynamic viscosity and the density of QGP are about
16 orders of magnitude larger than in liquids and that the two systems have
disparate interactions and fundamental theories. We discuss the implications of
this result for understanding the QGP including the similarity of flow and
particle dynamics at the viscosity minimum, the associated dynamical crossover
and universality of shear diffusivity.
|
The moduli space of striped black branes: At finite charge density certain holographic models exhibit the spontaneous
breaking of translational invariance resulting in an inhomogeneous phase. We
follow up on recent numerical work, reporting results for a larger class of
cohomogeneity two black branes in AdS, dual to a holographic striped phase. We
construct the continuous moduli space of inhomogeneous black branes as a
function of the temperature. Minimising the free energy we determine the
dominant striped solutions, revealing a growth in the stripe size as the system
is cooled. We discuss the thermodynamic properties of this line of solutions.
|
Equations of Motion as Covariant Gauss Law: The Maxwell-Chern-Simons
Case: Time-independent gauge transformations are implemented in the canonical
formalism by the Gauss law which is not covariant. The covariant form of Gauss
law is conceptually important for studying asymptotic properties of the gauge
fields. For QED in $3+1$ dimensions, we have developed a formalism for treating
the equations of motion (EOM) themselves as constraints, that is, constraints
on states using Peierls' quantization. They generate spacetime dependent gauge
transformations. We extend these results to the Maxwell-Chern-Simons (MCS)
Lagrangian. The surprising result is that the covariant Gauss law commutes with
all observables: the gauge invariance of the Lagrangian gets trivialized upon
quantization. The calculations do not fix a gauge. We also consider a novel
gauge condition on test functions (not on quantum fields) which we name the
"quasi-self-dual gauge" condition. It explicitly shows the mass spectrum of the
theory. In this version, no freedom remains for the gauge transformations: EOM
commute with all observables and are in the center of the algebra of
observables.
|
Three-dimensional Dirac oscillator in a thermal bath: The thermal properties of the three-dimensional Dirac oscillator are
considered. The canonical partition function is determined, and the
high-temperature limit is assessed. The degeneracy of energy levels and their
physical implications on the main thermodynamic functions are analyzed,
revealing that these functions assume values greater than the one-dimensional
case. So that at high temperatures, the limit value of the specific heat is
three times bigger.
|
Quantization of Higher Spin Superfields in the anti-de Sitter Superspace: We describe a Lagrangian quantization of the free massless gauge superfield
theories of higher superspins both in the anti-de Sitter and flat global
superspaces.
|
A gauge theory for the 3+1 dimensional incompressible Euler equations: We show that the incompressible Euler equations in three spatial dimensions
can be expressed in terms of an abelian gauge theory with a topological BF
term. A crucial part of the theory is a 3-form field strength, which is dual to
a material invariant local helicity in the fluid. In one version of the theory,
there is an additional 2-form field strength, with the magnetic field
corresponding to fluid vorticity and the electric field identified with the
cross-product of the velocity and the vorticity. In the second version, the
2-form field strength is instead expressed in terms of Clebsch scalars. We
discuss the theory in the presence of the boundary and argue that edge modes
may be present in the dual description of fluid flows with a boundary.
|
Deep inelastic scattering from polarized spin-$1/2$ hadrons at low $x$
from string theory: We study polarized deep inelastic scattering of charged leptons from
spin-$1/2$ hadrons at low values of the Bjorken parameter and large 't Hooft
coupling in terms of the gauge/string theory duality. We calculate the
structure functions from type IIB superstring theory scattering amplitudes. We
discuss the role of the non-Abelian Chern-Simons term and the Pauli term from
the five-dimensional $SU(4)$ gauged supergravity. Furthermore, the
exponentially small-$x$ regime where Regge physics becomes important is
analyzed in detail for the antisymmetric structure functions. In this case the
holographic dual picture of the Pomeron exchange is realized by a Reggeized
gauge field. We compare our results with experimental data of the proton
antisymmetric structure function $g_1$, obtaining a very good level of
agreement.
|
Twisted Covariance as a Non Invariant Restriction of the Fully Covariant
DFR Model: We discuss twisted covariance over the noncommutative spacetime algebra
generated by the relations [q_theta^mu,q_theta^nu]=i theta^{mu nu}, where the
matrix theta is treated as fixed (not a tensor), and we refrain from using the
asymptotic Moyal expansion of the twists. We show that the tensor nature of
theta is only hidden in the formalism: in particular if theta fulfils the DFR
conditions, the twisted Lorentz covariant model of the flat quantum spacetime
may be equivalently described in terms of the DFR model, if we agree to discard
a huge non invariant set of localisation states; it is only this last step
which, if taken as a basic assumption, severely breaks the relativity
principle. We also will show that the above mentioned, relativity breaking, ad
hoc rejection of localisation states is an independent, unnecessary assumption,
as far as some popular approaches to quantum field theory on the quantum
Minkowski spacetime are concerned. The above should raise some concerns about
speculations on possible observable consequences of arbitrary choices of theta
in arbitrarily selected privileged frames.
|
Generating string field theory solutions with matter operators from
$KBc$ algebra: The $KBc$ algebra is a subalgebra that has been used to construct classical
solutions in Witten's open string field theory, such as the tachyon vacuum
solution. The main purpose of this paper is to give various operator sets that
satisfy the $KBc$ algebra. In addition, since those sets can contain matter
operators arbitrarily, we can reproduce the KOS and the Erler-Maccaferri
solutions. Starting with a single D-brane solution on the tachyon vacuum, we
replace the original $KBc$ in it with an appropriate set to generate each of
the above solutions. Thus, it is expected that the $KBc$ algebra, combined with
the single D-brane solution, leads to a more unified description of classical
solutions.
|
Nilpotent Networks and 4D RG Flows: Starting from a general $\mathcal{N} = 2$ SCFT, we study the network of
$\mathcal{N} = 1$ SCFTs obtained from relevant deformations by nilpotent mass
parameters. We also study the case of flipper field deformations where the mass
parameters are promoted to a chiral superfield, with nilpotent vev. Nilpotent
elements of semi-simple algebras admit a partial ordering connected by a
corresponding directed graph. We find strong evidence that the resulting fixed
points are connected by a similar network of 4D RG flows. To illustrate these
general concepts, we also present a full list of nilpotent deformations in the
case of explicit $\mathcal{N} = 2$ SCFTs, including the case of a single
D3-brane probing a $D$- or $E$-type F-theory 7-brane, and 6D $(G,G)$ conformal
matter compactified on a $T^2$, as described by a single M5-brane probing a
$D$- or $E$-type singularity. We also observe a number of numerical
coincidences of independent interest, including a collection of theories with
rational values for their conformal anomalies, as well as a surprisingly nearly
constant value for the ratio $a_{\mathrm{IR}} / c_{\mathrm{IR}}$ for the entire
network of flows associated with a given UV $\mathcal{N} = 2$ SCFT. The
$\texttt{arXiv}$ submission also includes the full dataset of theories which
can be accessed with a companion $\texttt{Mathematica}$ script.
|
Solid Inflation: We develop a cosmological model where primordial inflation is driven by a
'solid', defined as a system of three derivatively coupled scalar fields
obeying certain symmetries and spontaneously breaking a certain subgroup of
these. The symmetry breaking pattern differs drastically from that of standard
inflationary models: time translations are unbroken. This prevents our model
from fitting into the standard effective field theory description of adiabatic
perturbations, with crucial consequences for the dynamics of cosmological
perturbations. Most notably, non-gaussianities in the curvature perturbations
are unusually large, with f_NL ~ 1/(\epsilon.c_s^2), and have a novel shape:
peaked in the squeezed limit, with anisotropic dependence on how the limit is
approached. Other unusual features include the absence of adiabatic fluctuation
modes during inflation---which does not impair their presence and near
scale-invariance after inflation---and a slightly blue tilt for the tensor
modes.
|
L-functions for Meromorphic Modular Forms and Sum Rules in Conformal
Field Theory: We define L-functions for meromorphic modular forms that are regular at
cusps, and use them to: (i) find new relationships between Hurwitz class
numbers and traces of singular moduli, (ii) establish predictions from the
physics of T-reflection, and (iii) express central charges in two-dimensional
conformal field theories (2d CFT) as a literal sum over the states in the CFTs
spectrum. When a modular form has an order-$p$ pole away from cusps, its
$q$-series coefficients grow as $n^{p-1} e^{2 \pi n t}$ for $t \geq
\sqrt{3}/2$. Its L-function must be regularized. We define such L-functions by
a deformed Mellin transform. We study the L-functions of logarithmic
derivatives of modular forms.L-functions of logarithmic derivatives of
Borcherds products reveal a new relationship between Hurwitz class numbers and
traces of singular moduli. If we can write 2d CFT path integrals as infinite
products, our L-functions confirm T-reflection predictions and relate central
charges to regularized sums over the states in a CFTs spectrum. Equating
central charges, which are a proxy for the number of degrees of freedom in a
theory, directly to a sum over states in these CFTs is new and relies on our
regularization of such sums that generally exhibit exponential (Hagedorn)
divergences.
|
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