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Computing the θ-exact Seiberg-Witten map for arbitrary gauge groups: We discuss how to obtain \theta-exact Seiberg-Witten maps by expanding in the
gauge coupling constant or, equivalently, in the number of ordinary gauge
fields. We do so for arbitrary compact gauge groups in arbitrary unitary
representations. For gauge and matter fields, we fully work out \theta-exact
non-hybrid Seiberg-Witten maps up to order three in the number of ordinary
gauge fields. | Generalized Thirring Models: The Thirring model and various generalizations of it are analyzed in detail.
The four-Fermi interaction modifies the equation of state. Chemical potentials
and twisted boundary conditions both result in complex fermionic determinants
which are analyzed. The non-minimal coupling to gravity does deform the
conformal algebra which in particular contains the minimal models. We compute
the central charges, conformal weights and finite size effects. For the gauged
model we derive the partition functions and the explicit expression for the
chiral condensate at finite temperature and curvature. The Bosonization in
compact curved space-times is also investigated. |
q-Translations on quantum spaces: Attention is focused on quantum spaces of particular importance in physics,
i.e. two-dimensional quantum plane, q-deformed Euclidean space in three or four
dimensions, and q-deformed Minkowski space. Each of these quantum spaces can be
combined with its symmetry algebra to form a Hopf algebra. The Hopf structures
on quantum space coordinates imply their translation. This article is devoted
to the question how to calculate translations on the quantum spaces under
consideration. | On the smoothness of multi center coplanar black hole and membrane
horizons: We study the differentiability of the metric and other fields at any of the
horizons of multi center Reissner-Nordstrom black hole solutions in $d \ge 5$
and of multi center $M2$ brane solutions. The centers are distributed in a
plane in transverse space, hence termed coplanar. We construct the Gaussian
null co-ordinate system for the neighborhood of a horizon by solving the
geodesic equations in expansions of (appropriate powers of) the affine
parameter. Organizing the harmonic functions that appear in the solution in
terms of what can be called generalized Gegenbauer polynomials is key to
obtaining the solution to the geodesic equations in a compact and manageable
form. We then compute the metric and other fields in the Gaussian null
co-ordinate system and find that the differentiability of the coplanar solution
is \emph{identical to} the differentiability of the collinear solution (centers
distributed on a line in transverse space). The results of this paper thus run
counter to a suggestion in the literature that posits reduction in the degree
of smoothness to accompany reduction in symmetries. We end the paper with a
conjecture on the degree of smoothness of the most general multi center
solution, the one with centers distributed arbitrarily and hence possessing no
transverse spatial isometries. |
11D supergravity at ${\cal O}(l^3)$: We compute certain spinorial cohomology groups controlling possible
supersymmetric deformations of eleven-dimensional supergravity up to order
$l^3$ in the Planck length. At ${\cal O}(l)$ and ${\cal O}(l^2)$ the spinorial
cohomology groups are trivial and therefore the theory cannot be deformed
supersymmetrically. At ${\cal O}(l^3)$ the corresponding spinorial cohomology
group is generated by a nontrivial element. On an eleven-dimensional manifold
$M$ such that $p_1(M)\neq 0$, this element corresponds to a supersymmetric
deformation of the theory, which can only be redefined away at the cost of
shifting the quantization condition of the four-form field strength. | $SO(2)$ gauged Skyrmions in $4+1$ dimensions: We study the simplest $SO(2)$ gauged $O(5)$ Skyrme models in $4+1$ (flat)
dimensions. In the gauge decoupled limit, the model supports topologically
stable solitons (Skyrmions) and after gauging, the static energy of the
solutions is bounded from below by a "baryon number". The studied model
features both Maxwell and Maxwell--Chern-Simons dynamics. The considered
configurations are subject to bi-azimuthal symmetry in the ${\mathbb R}^4$
subspace resulting in a two dimensional subsystem, as well as subject to an
enhanced symmetry relating the two planes in the ${\mathbb R}^4$ subspace,
which results in a one dimensional subsystem. Numerical solutions are
constructed in both cases. In the purely magnetic case, fully bi-azimuthal
solutions were given, while electrically charged and spinning solutions were
constructed only in the radial (enhanced symmetric) case, both in the presence
of a Chern-Simons term, and in its absence. We find that, in contrast with the
analogous models in $2+1$ dimensions, the presence of the Chern-Simons term in
the model under study here results only in quantitative effects. |
Chiral Bosons Through Linear Constraints: We study in detail the quantization of a model which apparently describes
chiral bosons. The model is based on the idea that the chiral condition could
be implemented through a linear constraint. We show that the space of states is
of indefinite metric. We cure this disease by introducing ghost fields in such
a way that a BRST symmetry is generated. A quartet algebra is seen to emerge.
The quartet mechanism, then, forces all physical states, but the vacuum, to
have zero norm. | $W_{1+\infty}$ as a Discretization of Virasoro Algebra: It is shown that the $W_{1+\infty}$ algebra is nothing but the simplest
subalgebra of a $q$-discretized \vi\ algebra, in the language of the KP
hierarchy explicitly. |
On the space of quantum fields in massive two-dimensional theories: For a large class of integrable quantum field theories we show that the
S-matrix determines a space of fields which decomposes into subspaces labeled,
besides the charge and spin indices, by an integer k. For scalar fields k is
non-negative and is naturally identified as an off-critical extension of the
conformal level. To each particle we associate an operator acting in the space
of fields whose eigenvectors are primary (k=0) fields of the massive theory. We
discuss how the existing results for models as different as Z_n, sine-Gordon or
Ising with magnetic field fit into this classification. | Quantum Gravity at the Planck Length: I describe our understanding of physics near the Planck length, in particular
the great progress in the last four years in string theory. These are lectures
presented at the 1998 SLAC Summer Institute. |
Two Loop Renormalization of Massive (p,q) Supersymmetric Sigma Models: We calculate the beta-functions of the general massive (p,q) supersymmetric
sigma model to two loop order using (1,0) superfields. The conditions for
finiteness are discussed in relation to (p,q) supersymmetry. We also calculate
the effective potential using component fields to one loop order and consider
the possibility of perturbative breaking of supersymmetry. The effect of one
loop finite local counter terms and the ultra-violet behaviour of the off-shell
(p,q) models to all orders in perturbation theory are also addressed. | Solitons, Links and Knots: Using numerical simulations of the full nonlinear equations of motion we
investigate topological solitons of a modified O(3) sigma model in three space
dimensions, in which the solitons are stabilized by the Hopf charge. We find
that for solitons up to charge five the solutions have the structure of closed
strings, which become increasingly twisted as the charge increases. However,
for higher charge the solutions are more exotic and comprise linked loops and
knots. We discuss the structure and formation of these solitons and demonstrate
that the key property responsible for producing such a rich variety of solitons
is that of string reconnection. |
Transgression forms as unifying principle in field theory: In this work I consider extensions of Chern-Simons gravities and
supergravities associated to the use of Transgression forms as actions, instead
of Chern-Simons forms.
It is noted that Transgression Forms yields a essencially unique prescription
of boundary terms which allows: (i) to make Chern-Simons theories truly gauge
invariant, instead of just quasi-invariant,
(ii) to have a well defined action principle, so that the action is an
extremum when the field equations hold,
(iii) to compute covariant finite conserved charges in agreement with those
obtained using hamiltonian methods,
(iv) to regularize the action so that the euclidean action is finite and the
black hole thermodynamics derived from this action agrees with the one obtained
by hamiltonian methods.
In addition a class of models for extended objects or branes with or without
supersymmetry is introduced and studied. The actions for those models and the
space-time in which they propagate is given by the sum of integrals of
transgression forms for ordinary gauge groups, space-time groups orr the
supersymmetric extensions of space-time groups. This brane models are generally
covariant, background independent and true gauge systems. | D-Brane Monodromies, Derived Categories and Boundary Linear Sigma Models: An important subclass of D-branes on a Calabi-Yau manifold, X, are in 1-1
correspondence with objects in D(X), the derived category of coherent sheaves
on X. We study the action of the monodromies in Kaehler moduli space on these
D-branes. We refine and extend a conjecture of Kontsevich about the form of one
of the generators of these monodromies (the monodromy about the "conifold"
locus) and show that one can do quite explicit calculations of the monodromy
action in many examples. As one application, we verify a prediction of Mayr
about the action of the monodromy about the Landau-Ginsburg locus of the
quintic. Prompted by the result of this calculation, we propose a modification
of the derived category which implements the physical requirement that the
shift-by-6 functor should be the identity. Boundary Linear sigma-Models prove
to be a very nice physical model of many of these derived category ideas, and
we explain the correspondence between these two approaches |
Fermionic determinant as an overlap between bosonic vacua: We find a representation for the determinant of a Dirac operator in an even
number $D= 2 n$ of Euclidean dimensions as an overlap between two different
vacua, each one corresponding to a bosonic theory with a quadratic action in $2
n + 1$ dimensions, with identical kinetic terms, but differing in their mass
terms. This resembles the overlap representation of a fermionic determinant
(although bosonic fields are used here). This representation may find
applications to lattice field theory, as an alternative to other bosonized
representations for Dirac determinants already proposed. | Synthetic versus Dirac monopoles: In some recent experiments the distinction between synthetic magnetic
monopoles and Dirac monopoles has been blurred. A case in point is the work in
a letter by Ray {\it et al.} [arXiv:1408.3133] in which a beautiful experiment
is reported but claims with regard to Dirac monopoles are misleading. |
Fast-Roll Inflation: We show that in the simplest theories of spontaneous symmetry breaking one
can have a stage of a fast-roll inflation. In this regime the standard
slow-roll condition |m^2| << H^2 is violated. Nevertheless, this stage can be
rather long if |m| is sufficiently small. Fast-roll inflation can be useful for
generating proper initial conditions for the subsequent stage of slow-roll
inflation in the very early universe. It may also be responsible for the
present stage of accelerated expansion of the universe. We also make two
observations of a more general nature. First of all, the universe after a long
stage of inflation (either slow-roll or fast-roll) cannot reach anti-de Sitter
regime even if the cosmological constant is negative. Secondly, the theories
with the potentials with a "stable" minimum at V(\phi)<0 in the cosmological
background exhibit the same instability as the theories with potentials
unbounded from below. This instability leads to the development of singularity
with the properties practically independent of V(\phi). However, the
development of the instability in some cases may be so slow that the theories
with the potentials unbounded from below can describe the present stage of
cosmic acceleration even if this acceleration occurs due to the fast-roll
inflation. | Black holes Entangled by Radiation: We construct three models to describe the scenario where two eternal black
holes are separated by a flat space, and can eventually be entangled by
exchanging radiations. In the doubly holographic setup, we compute the
entanglement entropy and the mutual information among the subsystems and obtain
the dynamic phase structure of the entanglement. The formation of entanglement
between the two black holes is delayed by the space where the radiations must
travel through. Finally, if the two black holes exchange sufficient Hawking
modes, the final state is characterized by a connected entanglement wedge;
otherwise, the final entanglement wedge contains two separated islands. In the
former case, the entanglement wedge of the two black holes forms at the time
scale of the size of the flat space between them. While in both cases,
unitarity of the evolution is preserved. When the sizes of two black holes are
not equal, we observe a loss of entanglement between the smaller black hole and
the radiation at late times. In the field theory side, we consider two
Sachdev-Ye-Kitaev (SYK) clusters coupled to a Majorana chain, which resemble
two black holes connected by a radiation region. We numerically compute the
same entanglement measures, and obtain similar phase structures as the bulk
results. In general, a time delay of the entanglement between the two SYK
clusters is found in cases with a long Majorana chain. In particular, when the
two SYK clusters are different in size, similar entanglement loss between the
smaller SYK cluster and the Majorana chain is observed. Finally, we investigate
a chain model composed of EPR clusters with particle exchanges between
neighboring clusters, and reproduce the features of entanglement observed in
the other models. |
Matching higher symmetries across Intriligator-Seiberg duality: We study higher symmetries and anomalies of 4d $\mathfrak{so}(2n_c)$ gauge
theory with $2n_f$ flavors. We find that they depend on the parity of $n_c$ and
$n_f$, the global form of the gauge group, and the discrete theta angle. The
contribution from the fermions plays a central role in our analysis.
Furthermore, our conclusion applies to $\mathcal{N}=1$ supersymmetric cases as
well, and we see that higher symmetries and anomalies match across the
Intriligator-Seiberg duality between
$\mathfrak{so}(2n_c)\leftrightarrow\mathfrak{so}(2n_f-2n_c+4)$. | Near Horizon Extreme Magnetized Kerr Geometry: The conjectured magnetized Kerr/CFT correspondence states that the quantum
theory of gravity in the near horizon of extreme Kerr black holes immersed by
the magnetic field, Near Horizon Extreme Magnetized Kerr black holes, is
holographic dual to a two-dimensional chiral conformal field theory. To obtain
Near Horizon Extreme Magnetized Kerr geometry, the extreme limit of the
magnetized Kerr metric is taken so, $ a=M $ and then continued by transforming
the coordinates to have a warped and twisted product of $ \textrm{AdS}_2 \times
\textrm{S}^2 $, and also with the Near Horizon Extreme Kerr metric one.
Consequently, we can obtain also the new Ernst potentials for those geometries.
Finally, the transformed central charge from the extremal non-magnetized one to
the magnetized one in the Ernst-Papapetrou formalism is obtained. |
Islands in Multiverse Models: We consider multiverse models in two-dimensional linear dilaton-gravity
theories as toy models of false vacuum eternal inflation. Coupling conformal
matter we calculate the Von Neumann entropy of subregions. When these are
sufficiently large we find that an island develops covering most of the rest of
the multiverse, leading to a Page-like transition. This resonates with a
description of multiverse models in semiclassical quantum cosmology, where a
measure for local predictions is given by saddle point geometries which
coarse-grain over any structure associated with eternal inflation beyond one's
patch. | The Area Quantum and Snyder Space: We show that in the Snyder space the area of the disc and of the sphere can
be quantized. It is also shown that the area spectrum of the sphere can be
related to the Bekenstein conjecture for the area spectrum of a black hole
horizon. |
The Fate of Unstable Gauge Flux Compactifications: Fluxes are widely used to stabilise extra dimensions, but if they arise
within a non-abelian gauge sector they are often unstable. We seek the fate of
this instability, focussing on the simplest examples: sphere-monopole
compactifications in six dimensions. Without gravity most non-abelian monopoles
are unstable, decaying into the unique stable monopole in the same topological
class. We show that the same is true in Einstein-YM systems, with the geometry
adjusting accordingly: a Mink(d)xS2 geometry supported by an unstable monopole
relaxes to an AdS(d)xS2. For 6D supergravity, the dilaton obstructs this simple
evolution, acquiring a gradient and thus breaking some of the spacetime
symmetries. We argue that it is the 4D symmetries that break, and examine
several endpoint candidates. Oxidising the supergravity system into a
higher-dimensional Einstein-YM monopole, we use the latter to guide us to the
corresponding endpoint. The result is a singular Kasner-like geometry conformal
to Mink(4)xS2. The solution has lower potential energy and is perturbatively
stable, making it a sensible candidate endpoint for the evolution. (Abridged
abstract for arXiv.) | Infrared Behaviour of Massive Scalar Matter coupled to Gravity: In the framework of causal perturbation theory we consider a massive scalar
field coupled to gravity. In the field theoretic approach to quantum gravity
(QG) we start with a massless second rank tensor field. This tensor field is
then quantized in a covariant way in Minkowski space. This article deals with
the adiabatic limit for graviton radiative corrections in a scattering process
of two massive scalar particles. We compute the differential cross-section for
bremsstrahlung processes in which one of the outgoing particles emites a
graviton of low energy, a so called soft graviton. Since the emited graviton
will not be detected we have to integrate over all soft gravitons. |
Boundary states in coset conformal field theories: We construct various boundary states in the coset conformal field theory G/H.
The G/H theory admits the twisted boundary condition if the G theory has an
outer automorphism of the horizontal subalgebra that induces an automorphism of
the H theory. By introducing the notion of the brane identification and the
brane selection rule, we show that the twisted boundary states of the G/H
theory can be constructed from those of the G and the H theories. We apply our
construction to the su(n) diagonal cosets and the su(2)/u(1) parafermion theory
to obtain the twisted boundary states of these theories. | Semiclassical and Quantum Black Holes and their Evaporation, de Sitter
and Anti-de Sitter Regimes, Gravitational and String Phase Transitions: An effective string theory in physically relevant cosmological and black hole
space times is reviewed. Explicit computations of the quantum string entropy,
partition function and quantum string emission by black holes (Schwarzschild,
rotating, charged, asymptotically flat, de Sitter dS and AdS space times) in
the framework of effective string theory in curved backgrounds provide an
amount of new quantum gravity results as: (i) gravitational phase transitions
appear with a distinctive universal feature: a square root branch point
singularity in any space time dimensions. This is of the type of the de Vega -
Sanchez transition for the thermal self-gravitating gas of point particles.
(ii) There are no phase transitions in AdS alone. (iii) For $dS$ background,
upper bounds of the Hubble constant H are found, dictated by the quantum string
phase transition.(iv) The Hawking temperature and the Hagedorn temperature are
the same concept but in different (semiclassical and quantum) gravity regimes
respectively. (v) The last stage of black hole evaporation is a microscopic
string state with a finite string critical temperature which decays as usual
quantum strings do in non-thermal pure quantum radiation (no information
loss).(vi) New lower string bounds are given for the Kerr-Newman black hole
angular momentum and charge, which are entirely different from the upper
classical bounds. (vii) Semiclassical gravity states undergo a phase transition
into quantum string states of the same system, these states are duals of each
other in the precise sense of the usual classical-quantum (wave-particle)
duality, which is universal irrespective of any symmetry or isommetry of the
space-time and of the number or the kind of space-time dimensions. |
Quantization of Integrable Systems and a 2d/4d Duality: We present a new duality between the F-terms of supersymmetric field theories
defined in two- and four-dimensions respectively. The duality relates N=2
supersymmetric gauge theories in four dimensions, deformed by an
Omega-background in one plane, to N=(2,2) gauged linear sigma-models in two
dimensions. On the four dimensional side, our main example is N=2 SQCD with
gauge group SU(L) and 2L fundamental flavours. Using ideas of Nekrasov and
Shatashvili, we argue that the Coulomb branch of this theory provides a
quantization of the classical Heisenberg SL(2) spin chain. Agreement with the
standard quantization via the Algebraic Bethe Ansatz implies the existence of
an isomorphism between the chiral ring of the 4d theory and that of a certain
two-dimensional theory. The latter can be understood as the worldvolume theory
on a surface operator/vortex string probing the Higgs branch of the same 4d
theory. We check the proposed duality by explicit calculation at low orders in
the instanton expansion. One striking consequence is that the Seiberg-Witten
solution of the 4d theory is captured by a one-loop computation in two
dimensions. The duality also has interesting connections with the AGT
conjecture, matrix models and topological string theory where it corresponds to
a refined version of the geometric transition. | Deformation Quantization of Classical Fields: We study the deformation quantization of scalar and abelian gauge classical
free fields. Stratonovich-Weyl quantizer, star-products and Wigner functionals
are obtained in field and oscillator variables. Abelian gauge theory is
particularly intriguing since Wigner functional is factorized into a physical
part and other one containing the constraints only. Some effects of non-trivial
topology within deformation quantization formalism are also considered. |
Translation Invariance, Commutation Relations and Ultraviolet/Infrared
Mixing: We show that the Ultraviolet/Infrared mixing of noncommutative field theories
with the Gronewold-Moyal product, whereby some (but not all) ultraviolet
divergences become infrared, is a generic feature of translationally invariant
associative products. We find, with an explicit calculation that the phase
appearing in the nonplanar diagrams is the one given by the commutator of the
coordinates, the semiclassical Poisson structure of the non commutative
spacetime. We do this with an explicit calculation for represented generic
products. | On consistency of the closed bosonic string with different left-right
ordering constants: Closed bosonic string with different normal ordering constants $a \ne \bar a$
for the right and the left moving sectors is considered. One immediate
consequence of this choice is absence of tachyon in the physical state
spectrum. Selfconsistency of the resulting model in the "old covariant
quantization" (OCQ) framework is studyed. The model is manifestly Poincare
invariant, it has non trivial massless sector and is ghost free for $D=26, ~
a=1, ~\bar a=0$. A possibility to obtain the light-cone formulation for the
model is also discussed. |
Noncommutative vector bundles over fuzzy CP^N and their covariant
derivatives: We generalise the construction of fuzzy CP^N in a manner that allows us to
access all noncommutative equivariant complex vector bundles over this space.
We give a simplified construction of polarization tensors on S^2 that
generalizes to complex projective space, identify Laplacians and natural
noncommutative covariant derivative operators that map between the modules that
describe noncommuative sections. In the process we find a natural
generalization of the Schwinger-Jordan construction to su(n) and identify
composite oscillators that obey a Heisenberg algebra on an appropriate Fock
space. | Neumann-Rosochatius system for strings in ABJ Model: Neumann-Rosochatius system is a well known one dimensional integrable system.
We study the rotating and pulsating string in $AdS_4 \times \mathbb{CP}^3$ with
a $B_{\rm{NS}}$ holonomy turned on over $\mathbb{CP}^1 \subset \mathbb{CP}^3$,
or the so called Aharony-Bergman-Jafferis (ABJ) background. We observe that the
string equations of motion in both cases are integrable and the Lagrangians
reduce to a form similar to that of deformed Neuman-Rosochatius system. We find
out the scaling relations among various conserved charges and comment on the
finite size effect for the dyonic giant magnons on $R_{t}\times
\mathbb{CP}^{3}$ with two angular momenta. For the pulsating string we derive
the energy as function of oscillation number and angular momenta along
$\mathbb{CP}^{3}$. |
Superstring Scattering from O-planes: We write the vertex operators of massless NS-NS and RR states of Type II
superstring theory in the presence of Orientifold p-planes. They include the
usual vertex operators of Type II theory and their images. We then calculate
the two-point functions of these vertex operators at the projective plane PR_2
level. We show that the result can be written in the Veneziano-type formulae,
with the same kinematic factor that appears in the D_p-branes amplitudes. While
the scattering amplitudes with the usual vertex operators are not gauge
invariant, the above amplitudes are invariant. From the amplitude describing
scattering of two NS-NS states off the O-plane, we find the low energy
effective action of O-planes. The result shows a relative factor 2^{p-6}
between couplings to O-planes and to D-branes at (\alpha')^2 order. | Dimensional Reduction Applied to Non-Supersymmetric Theories: We consider regularisation of a Yang-Mills theory by Dimensional Reduction
(DRED). In particular, the anomalous dimensions of fermion masses and gauge
coupling are computed to four-loop order. We put special emphasis on the
treatment of evanescent couplings which appear when DRED is applied to
non-supersymmetric theories. We highlight the importance of distinguishing
between the evanescent and the real couplings. Considering the special case of
a Super-Yang-Mills theory, we find that Dimensional Reduction is sufficient to
preserve Supersymmetry in our calculations. |
RG Flows with Global Symmetry Breaking and Bounds from Chaos: We discuss general aspects of renormalization group (RG) flows between two
conformal fixed points in 4d with a broken continuous global symmetry in the
UV. Every such RG flow can be described in terms of the dynamics of
Nambu-Goldstone bosons of broken conformal and global symmetries. We derive the
low-energy effective action that describes this class of RG flows from basic
symmetry principles. We view the theory of Nambu-Goldstone bosons as a theory
in anti-de Sitter space with the flat space limit. This enables an equivalent
CFT$_3$ formulation of these 4d RG flows in terms of spectral deformations of a
generalized free CFT$_3$. We utilize this dual description to impose further
constraints on the low energy effective action associated with unitary RG flows
in 4d by invoking the chaos bound in 3d. This approach naturally provides a set
of independent monotonically decreasing $C$-functions for 4d RG flows with
global symmetry breaking by explicitly relating 4d $C$-functions with certain
out-of-time-order correlators that diagnose chaos in 3d. We also comment on a
more general connection between RG and chaos in QFT. | Bounded solutions of fermions in the background of mixed vector-scalar
Pöschl-Teller-like potentials: The problem of a fermion subject to a convenient mixing of vector and scalar
potentials in a two-dimensional space-time is mapped into a Sturm-Liouville
problem. For a specific case which gives rise to an exactly solvable effective
modified P\"{o}schl-Teller potential in the Sturm-Liouville problem,
bound-state solutions are found. The behaviour of the upper and lower
components of the Dirac spinor is discussed in detail and some unusual results
are revealed. The Dirac delta potential as a limit of the modified P%
\"{o}schl-Teller potential is also discussed. The problem is also shown to be
mapped into that of massless fermions subject to classical topological scalar
and pseudoscalar potentials. |
A Tree Theorem for Inflation: It is shown that the generating function for tree graphs in the "in-in"
formalism may be calculated by solving the classical equations of motion
subject to certain constraints. This theorem is illustrated by application to
the evolution of a single inflaton field in a Robertson--Walker background. | Symmetry breaking in holographic theories with Lifshitz scaling: We study holographically Lifshitz-scaling theories with broken symmetries. In
order to do this, we set up a bulk action with a complex scalar and a massless
vector on a background which consists in a Lifshitz metric and a massive
vector. We first study separately the complex scalar and the massless vector,
finding a similar pattern in the two-point functions that we can compute
analytically. By coupling the probe complex scalar to the background massive
vector we can construct probe actions that are more general than the usual
Klein--Gordon action. Some of these actions have Galilean boost symmetry.
Finally, in the presence of a symmetry breaking scalar profile in the bulk, we
reproduce the expected Ward identities of a Lifshitz-scaling theory with a
broken global continuous symmetry. In the spontaneous case, the latter imply
the presence of a gapless mode, the Goldstone boson, which will have dispersion
relations dictated by the Lifshitz scaling. |
D-dimensional massless particle with extended gauge invariance: We propose the model of $D-$dimensional massless particle whose Lagrangian is
given by the $N-$th extrinsic curvature of world-line. The system has $N+1$
gauge degrees of freedom constituting $W-$like algebra; the classical
trajectories of the model are space-like curves which obey the conditions
$k_{N+a}=k_{N-a}$, $k_{2N}=0$, $a=1,...,N-1$, $N\leq[(D-2)/2]$, while the first
$N$ curvatures $k_i$ remain arbitrary. We show that the model admits consistent
formulation on the anti-De Sitter space. The solutions of the system are the
massless irreducible representations of Poincar\'e group with $N$ nonzero
helicities, which are equal to each other. | The Non-Compact Weyl Equation: A non-compact version of the Weyl equation is proposed, based on the infinite
dimensional spin zero representation of the sl_2 algebra. Solutions of the
aforementioned equation are obtained in terms of the Kummer functions. In this
context, we discuss the ADHMN approach in order to construct the corresponding
non-compact BPS monopoles. |
Holographic Entanglement Entropy: An Overview: In this article, we review recent progresses on the holographic
understandings of the entanglement entropy in the AdS/CFT correspondence. After
reviewing the general idea of holographic entanglement entropy, we will explain
its applications to confinement/deconfinement phase transitions, black hole
entropy and covariant formulation of holography. | The a-theorem and conformal symmetry breaking in holographic RG flows: We study holographic models describing an RG flow between two fixed points
driven by a relevant scalar operator. We show how to introduce a spurion field
to restore Weyl invariance and compute the anomalous contribution to the
generating functional in even dimensional theories. We find that the
coefficient of the anomalous term is proportional to the difference of the
conformal anomalies of the UV and IR fixed points, as expected from anomaly
matching arguments in field theory. For any even dimensions the coefficient is
positive as implied by the holographic a-theorem. For flows corresponding to
spontaneous breaking of conformal invariance, we also compute the two-point
functions of the energy-momentum tensor and the scalar operator and identify
the dilaton mode. Surprisingly we find that in the simplest models with just
one scalar field there is no dilaton pole in the two-point function of the
scalar operator but a stronger singularity. We discuss the possible
implications. |
Hamiltonian Analysis of the Effective Action for Hard Thermal Loops in
QCD: The effective action for hard thermal loops in QCD is related to a gauged
WZNW theory. Some of the technical issues of this approach are clarified and
the Hamiltonian formulation is presented. The two-point correlation function
for the induced current in QCD is obtained; some simplifications of the
dynamics of the longitudinal modes are also pointed out. | Galilean anti-de-Sitter spacetime in Romans theory: The Romans type IIA theory is the only known example of 10-dimensional
maximal supergravity where (tensor) fields are explicitly massive. We provide
an example of a non-relativistic anti-de Sitter $NRadS_4\times S^6$ background
as a solution in massive type IIA. A compactification of which on $S^6$ gives
immediately the prototype NRadS background in D=4 which is proposed to be dual
to `cold atoms' or unitary fermions on a wire. |
Boundary condition for D-brane from Wilson loop, and gravitational
interpretation of eigenvalue in matrix model in AdS/CFT correspondence: We study the supersymmetric Wilson loops in the four-dimensional N=4 super
Yang-Mills theory in the context of AdS/CFT correspondence. In the gauge theory
side, it is known that the expectation value of the Wilson loops of circular
shape with winding number k is calculable by using a Gaussian matrix model. On
the other hand, in the gravity side, it has been conjectured that the
expectation value of the Wilson loop is given by the classical value of the
action for a probe D3-brane with k electric fluxes. Given such correspondence,
we pursue the interpretation of the matrix model eigenvalue density, or more
precisely the resolvent, from the viewpoint of the probe D3-brane in the
gravity side. We see that in the gravity side, the position of an eigenvalue
appears as an integrated flux on the D3-brane. In the course of our analysis,
we also clarify the boundary condition on the D3-brane in terms of the Wilson
loop. | Metastability of Spherical Membranes in Supermembrane and Matrix Theory: Motivated by recent work we study rotating ellipsoidal membranes in the
framework of the light-cone supermembrane theory. We investigate stability
properties of these classical solutions which are important for the
quantization of super membranes. We find the stability modes for all sectors of
small multipole deformations. We exhibit an isomorphism of the linearized
membrane equation with that of the SU(N) matrix model for every value of $N$.
The boundaries of the linearized stability region are at a finite distance and
they appear for finite size perturbations. |
Vortex content of calorons and deconfinement mechanism: We reveal the center vortex content of SU(2) calorons and ensembles of them.
While one part of the vortex connects the constituent dyons of a single
caloron, another part is predominantly spatial and can be related to the twist
that exists in the caloron gauge field. The latter part depends strongly on the
caloron holonomy and degenerates to a plane between the dyons when the
asymptotic Polyakov loop is traceless. Correspondingly, the spatial vortex in
caloron ensembles is percolating in this case. This finding fits perfectly in
the confinement scenario of vortices and shows that calorons are suitable to
facilitate the vortex (de)confinement mechanism. | Asymptotic Four Point Functions: We initiate the study of four-point functions of large BPS operators at any
value of the coupling. We do it by casting it as a sum over exchange of
superconformal primaries and computing the structure constants using
integrability. Along the way, we incorporate the nested Bethe ansatz structure
to the hexagon formalism for the three-point functions and obtain a compact
formula for the asymptotic structure constant of a non-BPS operator in a higher
rank sector. |
The implications of noninertial motion on covariant quantum spin: It is shown that the Pauli-Lubanski spin vector defined in terms of
curvilinear co-ordinates does not satisfy Lorentz invariance for spin-1/2
particles in noninertial motion along a curved trajectory. The possibility of
detecting this violation in muon decay experiments is explored, where the
noninertial contribution to the decay rate becomes large for muon beams with
large momenta and trajectories with radius of curvature approaching the muon's
Compton wavelength scale. A new spacelike spin vector is derived from the
Pauli-Lubanski vector that satisfies Lorentz invariance for both inertial and
noninertial motion. In addition, this spin vector suggests a generalization for
the classification of spin-1/2 particles, and has interesting properties that
are applicable for both massive and massless particles. | BRST cohomology of the sum of two pure spinors: We study the zero mode cohomology of the sum of two pure spinors. The
knowledge of this cohomology allows us to better understand the structure of
the massless vertex operator of the Type IIB pure spinor superstring. |
Tachyon condensation and universality of DBI action: We show that a low-energy action for massless fluctuations around a tachyonic
soliton background representing a codimension one D-brane coincides with the
Dirac-Born-Infeld action. The scalar modes which describe transverse
oscillations of the D-brane are translational collective coordinates of the
soliton. The appearance of the DBI action is a universal feature independent of
details of a tachyon effective action, provided it has the structure implied by
the open string sigma model partition function. | UV caps, IR modification of gravity, and recovery of 4D gravity in
regularized braneworlds: In the context of six-dimensional conical braneworlds we consider a simple
and explicit model that incorporates long distance modification of gravity and
regularization of codimension-2 singularities. To resolve the conical
singularities we replace the codimension-2 branes with ring-like codimension-1
branes, filling in the interiors with regular caps. The six-dimensional Planck
scale in the cap is assumed to be much greater than the bulk Planck scale,
which gives rise to the effect analogous to brane-induced gravity. Weak gravity
on the regularized brane is studied in the case of a sharp conical bulk. We
show by a linear analysis that gravity at short distances is effectively
described by the four-dimensional Brans-Dicke theory, while the higher
dimensional nature of gravity emerges at long distances. The linear analysis
breaks down at some intermediate scale, below which four-dimensional Einstein
gravity is shown to be recovered thanks to the second-order effects of the
brane bending. |
On the Rotating Charged BTZ Metric: It is shown that the charged non-diagonal BTZ (2+1)-spacetime is not a
solution of the Einstein-Maxwell field equations with cosmological constant. | Correlators of chiral primaries and 1/8 BPS Wilson loops from
perturbation theory: We study at perturbative level the correlation functions of a general class
of 1/8 BPS Wilson loops and chiral primaries in N = 4 Super Yang-Mills theory.
The contours and the location of operator insertions share a sphere S^2
embedded into spacetime and the system preserves at least two supercharges. We
perform explicit two-loop computations, for some particular but still rather
general configuration, that confirm the elegant results expected from
localization procedure. We find notably full consistency with the multi-matrix
model averages, obtained from 2D Yang-Mills theory on the sphere, when
interacting diagrams do not cancel and contribute non-trivially to the final
answer. |
Rotating stealth black holes with a cohomogeneity-1 metric: In five dimensions we consider a general shift symmetric and parity
preserving scalar tensor action that contains up to second order covariant
derivatives of the scalar field. A rotating stealth black hole solution is
constructed where the metric is given by the Myers-Perry spacetime with equal
momenta and the scalar field is identified with the Hamilton-Jacobi potential.
This nontrivial scalar field has an extra hair associated with the rest mass of
the test particle, and the solution does not require any fine tuning of the
coupling functions of the theory. Interestingly enough, we show that the
disformal transformation, generated by this scalar field, and with a constant
degree of disformality, leaves invariant (up to diffeomorphisms) the
Myers-Perry metric with equal momenta. This means that the hair of the scalar
field, along with the constant disformality parameter, can be consistently
absorbed into further redefinitions of the mass and of the single angular
parameter of the disformed metric. These results are extended in higher odd
dimensions with a Myers-Perry metric for which all the momenta are equal. The
key of the invariance under disformal transformation of the metric is mainly
the cohomogeneity-1 character of the Myers-Perry metric with equal momenta.
Starting from this observation, we consider a general class of cohomogeneity-1
metrics in arbitrary dimension, and we list the conditions ensuring that this
class of metrics remain invariant (up to diffeomorphisms) under a disformal
transformation with a constant degree of disformality and with a scalar field
with constant kinetic term. The extension to the Kerr-(A)dS case is also
considered where it is shown that rotating stealth solutions may exist provided
some fine tuning of the coupling functions of the scalar tensor theory. | Duality rotations in supersymmetric nonlinear electrodynamics revisited: We revisit the U(1) duality-invariant nonlinear models for N=1 and N=2 vector
multiplets coupled to off-shell supergravities. For such theories we develop
new formulations which make use of auxiliary chiral superfields (spinor in the
N=1 case and scalar for N=2) and are characterized by the remarkable property
that U(1) duality invariance is equivalent to the manifest U(1) invariance of
the self-interaction. Our construction is inspired by the non-supersymmetric
approach that was proposed by Ivanov and Zupnik a decade ago and recently
re-discovered in the form of twisted self-duality. |
N=4 Super NLS-mKdV Hierarchies: N=2 extension of affine algebra $\hat{sl(2)\oplus u(1)}$ possesses a hidden
global N=4 supersymmetry and provides a second hamiltonian structure for a new
N=4 supersymmetric integrable hierarchy defined on N=2 affine supercurrents.
This system is an N=4 extension of at once two hierarchies, N=2 NLS and N=2
mKdV ones. It is related to N=4 KdV hierarchy via a generalized
Sugawara-Feigin-Fuks construction which relates N=2 $\hat{sl(2)\oplus u(1)}$
algebra to ``small'' N=4 SCA. We also find the underlying affine hierarchy for
another integrable system with the N=4 SCA second hamiltonian structure,
``quasi'' N=4 KdV hierarchy. It respects only N=2 supersymmetry. For both new
hierarchies we construct scalar Lax formulations. We speculate that any N=2
affine algebra admitting a quaternionic structure possesses N=4 supersymmetry
and so can be used to produce N=4 supersymmetric hierarchies. This suggests a
way of classifying all such hierarchies. | A remarkably simple theory of 3d massive gravity: We propose and study a new action for three-dimensional massive gravity. This
action takes a very simple form when written in terms of connection and triad
variables, but the connection can also be integrated out to obtain a triad
formulation. The quadratic action for the perturbations around a Minkowski
background reproduces the action of self-dual massive gravity, in agreement
with the expectation that the theory propagates a massive graviton. We confirm
this result at the non-linear level with a Hamiltonian analysis, and show that
this new theory does indeed possess a single massive degree of freedom. The
action depends on four coupling constants, and we identify the various massive
and topological (or massless) limits in the space of parameters. This richness,
along with the simplicity of the action, opens a very interesting new window
onto massive gravity. |
Canonical equivalence in anisotropic models for higher order theory of
gravity: We show that as in the case of isotropic models, the `Dirac Algorithm' and
`Modified Horowitz' Formalism' lead to identical phase-space structure of the
Hamiltonian for the gravitational action with curvature squared terms, in
anisotropic space-time, viz, Bianchi-I, Bianchi-III and Kantowski-Sachs models
too. | On Cosmic No-hair in Bimetric Gravity and the Higuchi Bound: We study the cosmic no-hair in the presence of spin-2 matter, i.e. in
bimetric gravity. We obtain stable de Sitter solutions with the cosmological
constant in the physical sector and find an evidence that the cosmic no-hair is
correct. In the presence of the other cosmological constant, there are two
branches of de Sitter solutions. Under anisotropic perturbations, one of them
is always stable and there is no violation of the cosmic no-hair at the linear
level. The stability of the other branch depends on parameters and the cosmic
no-hair can be violated in general. Remarkably, the bifurcation point of two
branches exactly coincides with the Higuchi bound. It turns out that there
exists a de Sitter solution for which the cosmic no-hair holds at the linear
level and the effective mass for the anisotropic perturbations is above the
Higuchi bound. |
Compactified rotating branes in the matrix model, and excitation
spectrum towards one loop: We study compactified brane solutions of type R^4 x K in the IIB matrix
model, and obtain explicitly the bosonic and fermionic fluctuation spectrum
required to compute the one-loop effective action. We verify that the one-loop
contributions are UV finite for R^4 x T^2, and supersymmetric for R^3 x S^1.
The higher Kaluza-Klein modes are shown to have a gap in the presence of flux
on T^2, and potential problems concerning stability are discussed. | SU(5) D-brane realizations, Yukawa couplings and proton stability: We discuss SU(5) Grand Unified Theories in the context of orientifold
compactifications. Specifically, we investigate two and three D-brane stack
realizations of the Georgi-Glashow and the flipped SU(5) model and analyze them
with respect to their Yukawa couplings. As pointed out in arXiv:0909.0271 the
most economical Georgi-Glashow realization based on two stacks generically
suffers from a disastrous large proton decay rate. We show that allowing for an
additional U(1) D-brane stack this as well as other phenomenological problems
can be resolved. We exemplify with globally consistent Georgi-Glashow models
based on RCFT that these D-brane quivers can be indeed embedded in a global
setting. These globally consistent realizations admit rigid O(1) instantons
inducing the perturbatively missing coupling 10105^H. Finally we show that
flipped SU(5) D-brane realizations even with multiple U(1) D-brane stacks are
plagued by severe phenomenological drawbacks which generically cannot be
overcome. |
Braneless Black Holes: It is known that the naive version of D-brane theory is inadequate to explain
the black hole entropy in the limit in which the Schwarzschild radius becomes
larger than all compactification radii. We present evidence that a more
consistent description can be given in terms of strings with rescaled tensions.
We show that the rescaling can be interpreted as a redshift of the tension of a
fundamental string in the gravitational field of the black hole. An interesting
connection is found between the string level number and the Rindler energy.
Using this connection, we reproduce the entropies of Schwarzschild black holes
in arbitrary dimensions in terms of the entropy of a single string at the
Hagedorn temperature. | Anomalies for Nonlocal Dirac Operators: The anomalies of a very general class of non local Dirac operators are
computed using the $\zeta$-function definition of the fermionic determinant and
an asymmetric version of the Wigner transformation. For the axial anomaly all
new terms introduced by the non locality can be brought to the standard minimal
Bardeen's form. Some extensions of the present techniques are also commented. |
Radiation from a D-dimensional collision of shock waves: first order
perturbation theory: We study the spacetime obtained by superimposing two equal Aichelburg-Sexl
shock waves in D dimensions traveling, head-on, in opposite directions.
Considering the collision in a boosted frame, one shock becomes stronger than
the other, and a perturbative framework to compute the metric in the future of
the collision is setup. The geometry is given, in first order perturbation
theory, as an integral solution, in terms of initial data on the null surface
where the strong shock has support. We then extract the radiation emitted in
the collision by using a D-dimensional generalisation of the Landau-Lifschitz
pseudo-tensor and compute the percentage of the initial centre of mass energy
epsilon emitted as gravitational waves. In D=4 we find epsilon=25.0%, in
agreement with the result of D'Eath and Payne. As D increases, this percentage
increases monotonically, reaching 40.0% in D=10. Our result is always within
the bound obtained from apparent horizons by Penrose, in D=4, yielding 29.3%,
and Eardley and Giddings, in D> 4, which also increases monotonically with
dimension, reaching 41.2% in D=10. We also present the wave forms and provide a
physical interpretation for the observed peaks, in terms of the null generators
of the shocks. | Instantons, Twistors, and Emergent Gravity: Motivated by potential applications to holography on space-times of positive
curvature, and by the successful twistor description of scattering amplitudes,
we propose a new dual matrix formulation of N = 4 gauge theory on S(4). The
matrix model is defined by taking the low energy limit of a holomorphic
Chern-Simons theory on CP(3|4), in the presence of a large instanton flux. The
theory comes with a choice of S(4) radius L and a parameter N controlling the
overall size of the matrices. The flat space variant of the 4D effective theory
arises by taking the large N scaling limit of the matrix model, with l_pl^2 ~
L^2 / N held fixed. Its massless spectrum contains both spin one and spin two
excitations, which we identify with gluons and gravitons. As shown in the
companion paper, the matrix model correlation functions of both these
excitations correctly reproduce the corresponding MHV scattering amplitudes. We
present evidence that the scaling limit defines a gravitational theory with a
finite Planck length. In particular we find that in the l_pl -> 0 limit, the
matrix model makes contact with the CSW rules for amplitudes of pure gauge
theory, which are uncontaminated by conformal supergravity. We also propose a
UV completion for the system by embedding the matrix model in the physical
superstring. |
Non-Abelian W-representation for GKM: $W$-representation is a miraculous possibility to define a non-perturbative
(exact) partition function as an exponential action of somehow integrated Ward
identities on unity. It is well known for numerous eigenvalue matrix models
when the relevant operators are of a kind of $W$-operators: for the Hermitian
matrix model with the Virasoro constraints, it is a $W_3$-like operator, and so
on. We extend this statement to the monomial generalized Kontsevich models
(GKM), where the new feature is the appearance of an ordered P-exponential for
the set of non-commuting operators of different gradings. | The Heterotic Green-Schwarz Superstring on an N=(2,0) Super-Worldsheet: By defining the heterotic Green-Schwarz superstring action on an N=(2,0)
super-worldsheet, rather than on an ordinary worldsheet, many problems with the
interacting Green-Schwarz superstring formalism can be solved. In the
light-cone approach, superconformally transforming the light-cone
super-worldsheet onto an N=(2,0) super-Riemann surface allows the elimination
of the non-trivial interaction-point operators that complicate the evaluation
of scattering amplitudes. In the Polyakov approach, the ten-dimensional
heterotic Green-Schwarz covariant action defined on an N=(2,0) super-worldsheet
can be gauge-fixed to a free-field action with non-anomalous N=(2,0)
superconformal invariance, and integrating the exponential of the covariant
action over all punctured N=(2,0) super-Riemann surfaces produces scattering
amplitudes that closely resemble amplitudes obtained using the unitary
light-cone approach. |
Functional Relations in Solvable Lattice Models II: Reported are two applications of the functional relations ($T$-system) among
a commuting family of row-to-row transfer matrices proposed in the previous
paper Part I. For a general simple Lie algebra $X_r$, we determine the
correlation lengths of the associated massive vertex models in the
anti-ferroelectric regime and central charges of the RSOS models in two
critical regimes. The results reproduce known values or even generalize them,
demonstrating the efficiency of the $T$-system. | All-Multiplicity Amplitudes with Massive Scalars: We compute two infinite series of tree-level amplitudes with a massive scalar
pair and an arbitrary number of gluons. We provide results for amplitudes where
all gluons have identical helicity, and amplitudes with one gluon of opposite
helicity. These amplitudes are useful for unitarity-based one-loop calculations
in nonsupersymmetric gauge theories generally, and QCD in particular. |
The black hole and FRW geometries of non-relativistic gravity: We consider the recently proposed non-relativistic Ho\v{r}ava-Lifshitz
four-dimensional theory of gravity. We study a particular limit of the theory
which admits flat Minkowski vacuum and we discuss thoroughly the quadratic
fluctuations around it. We find that there are two propagating polarizations of
the metric. We then explicitly construct a spherically symmetric,
asymptotically flat, black hole solution that represents the analog of the
Schwarzschild solution of GR. We show that this theory has the same Newtonian
and post-Newtonian limits as GR and thus, it passes the classical tests. We
also consider homogeneous and isotropic cosmological solutions and we show that
although the equations are identical with GR cosmology, the couplings are
constrained by the observed primordial abundance of ${}^4{\rm He}$. | Up-type quark masses in SU(5) F-theory models: F-theory SU(5) unification has been proposed as a scenario where the mass of
the top quark is naturally large, as opposed to type II SU(5) models. We
analyze this claim from the viewpoint of local SU(5) F-theory models, by
explicitly computing the 10 x 10 x 5 Yukawa couplings that are developed in the
vicinity of an E6 singularity. Realizing this singularity via T-branes allows
for a non-trivial mass for the top quark, while lighter generations of up-type
quarks still have vanishing Yukawa couplings. Nevertheless, we show that by
taking instanton effects into account non-vanishing Yukawas are induced for all
U-quark families, together with a hierarchical structure at the level of the
superpotential. Finally, by solving for internal wavefunction profiles we
compute physical U-quark Yukawa couplings and show that this F-theory scenario
allows to describe the measured top quark mass, as well as the observed
quotients of U-quark masses. |
Mining Energy from a Black Hole by Strings: We discuss how cosmic strings can be used to mine energy from black holes. A
string attached to the black hole gives rise to an additional channel for the
energy release. It is demonstrated that when a string crosses the event
horizon, its transverse degrees of freedom are thermally excited and thermal
string perturbations propagate along the string to infinity. The internal
metric induced on the 2D worldsheet of the static string crossing the horizon
describes a 2D black hole. For this reason thermal radiation of string
excitations propagating along the string can be interpreted as Hawking
radiation of the 2D black hole. It is shown that the rate of energy emission
through the string channel is of the same order of magnitude as the bulk
radiation of the black hole. Thus, for N strings attached to the black hole the
efficiency of string channels is increased by factor N. We discuss restrictions
on N which exist because of the finite thickness of strings, the gravitational
backreaction and quantum fluctuations. Our conclusion is that the energy
emission rate by strings can be increased as compared to the standard emission
in the bulk by the factor 10^3 for GUT strings and up to the factor 10^{31} for
electroweak strings. | Critical Boundary Sine-Gordon Revisited: We revisit the exact solution of the two space-time dimensional quantum field
theory of a free massless boson with a periodic boundary interaction and
self-dual period. We analyze the model by using a mapping to free fermions with
a boundary mass term originally suggested in ref.[22]. We find that the entire
SL(2,C) family of boundary states of a single boson are boundary sine-Gordon
states and we derive a simple explicit expression for the boundary state in
fermion variables and as a function of sine-Gordon coupling constants. We use
this expression to compute the partition function. We observe that the solution
of the model has a strong-weak coupling generalization of T-duality. We then
examine a class of recently discovered conformal boundary states for compact
bosons with radii which are rational numbers times the self-dual radius. These
have simple expression in fermion variables. We postulate sine-Gordon-like
field theories with discrete gauge symmmetries for which they are the
appropriate boundary states. |
Supersymmetric Black Holes and Freudenthal Duality: We study the effect of Freudenthal duality on supersymmetric extremal black
hole attractors in N = 2, D = 4 ungauged supergravity. Freudenthal duality acts
on the dyonic black hole charges as an anti-involution which keeps the black
hole entropy and the critical points of the effective black hole potential
invariant. We analyze its effect on the recently discovered distinct, mutually
exclusive phases of axionic supersymmetric black holes, related to the
existence of non-trivial involutory constant matrices. In particular, we
consider a supersymmetric D0-D4-D6 black hole and we explicitly Freudenthal-map
it to a supersymmetric D0-D2-D4-D6 black hole. We thus show that the charge
representation space of a supersymmetric D0-D2-D4-D6 black hole also contains
mutually exclusive domains. | M-theory branes and their interactions: In recent years there has been some progress in understanding how one might
model the interactions of branes in M-theory despite not having a fundamental
perturbative description. The goal of this review is to describe different
approaches to M-theory branes and their interactions. This includes: a review
of M-theory branes themselves and their properties; brane interactions; the
self-dual string and its properties; the role of anomalies in learning about
brane systems; the recent work of Basu and Harvey with subsequent developments;
and how these complimentary approaches might fit together. |
Soliton solutions of the classical lattice sine-Gordon system: We study the soliton-type solutions of the system introduced by B. Feigin and
the author in in [EF]. We show that it reduces to a top-like system, and we
study the behaviour of the solutions at the lattice infinity. We compute the
scattering of the solitons and study some periodic solutions of the system. | A differential equation approach for examining the subtraction schemes: We propose a natural differential equation with respect to mass(es) to
analyze the scheme dependence problem. It is shown that the vertex functions
subtracted at an arbitrary Euclidean momentum (MOM) do not satisfy such
differential equations, as extra unphysical mass dependence is introduced which
is shown to lead to the violation of the canonical form of the Slavnov-Taylor
identities, a notorious fact with MOM schemes. By the way, the traditional
advantage of MOM schemes in decoupling issue is shown to be lost in the context
of Callan-Symanzik equations. |
Elko in 1+1 dimensions: The quantum field operator for spin-half Elko describes a massive
self-interacting fermionic dark matter candidate of mass dimension one. It has
been shown that the theory has a built-in violation of the Lorentz symmetry and
a well-defined element of non-locality in the form of a preferred direction.
This note shows that quantum field operators constructed using spin-half and
higher-spin Elko violate Lorentz symmetry from first principle. Subsequently,
we study the kinematics of Elko and its quantum field operator for any spin
along the preferred direction. | The D-branes of SU(n): D-branes that appear to generate all the K-theory charges of string theory on
SU(n) are constructed, and their charges are determined. |
Extending Starobinsky inflationary model in gravity and supergravity: We review some recent trends in the inflationary model building, the
supersymmetry (SUSY) breaking, the gravitino Dark Matter (DM) and the
Primordial Black Holes (PBHs) production in supergravity. The Starobinsky
inflation can be embedded into supergravity when the inflaton belongs to the
massive vector multiplet associated with a (spontaneously broken) $U(1)$ gauge
symmetry. The SUSY and R-symmetry can be also spontaneously broken after
inflation by the (standard) Polonyi mechanism. Polonyi particles and gravitinos
are super heavy and can be copiously produced during inflation via the
Schwinger mechanism sourced by the Universe expansion. The overproduction and
instability problems can be avoided, and the positive cosmological constant
(dark energy) can also be introduced. The observed abundance of the Cold Dark
Matter (CDM) composed of gravitinos can be achieved in our supergravity model
too, thus providing the unifying framework for inflation, supersymmetry
breaking, dark energy and dark matter genesis. Our supergravity approach may
also lead to a formation of primordial non-linear structures like
stellar-mass-type black holes, and may include the SUSY GUTs inspired by
heterotic string compactifications, unifying particle physics with quantum
gravity. | A particle-like description of Planckian black holes: In this paper we abandon the idea that even a "quantum" black hole, of Planck
size, can still be described as a classical, more or less complicated,
geometry. Rather, we consider a genuine quantum mechanical approach where a
Planckian black hole is, by all means, just another "particle", even if with a
distinguishing property: its linear size increases with the energy. The horizon
dynamics is equivalently described in terms of a particle moving in
gravitational potential derived from the horizon equation itself in a
self-consistent manner. The particle turning-points match the radius of the
inner and outer horizons of a charged black hole. This classical model pave the
way towards the wave equation for a truly quantum black hole. We compute the
exact form of the wave function and determine the energy spectrum. Finally, we
describe the classical limit in which the quantum picture correctly approaches
the classical geometric formulation. We find that the quantum-to-classical
transition occurs far above the Planck scale. |
Holographic Renormalisation for the Spin-3 Theory and the (A)dS3/CFT2
correspondence: We compute the two-point correlation functions for the spin-3 theory in three
dimensional (Anti-) de Sitter spacetimes by using holographic renormalisation.
For the AdS case, we find results consistent with the general requirements of
two-dimensional conformal invariance. In the de Sitter case, we find similar
results. We discuss consistency requirements on the three point functions TWW
for our results to be compatible with the asymptotic symmetry algebra for AdS
case and with the de-Sitter central charge found in hep-th/0106113 by analyzing
the stress-tensor. We also discuss why it is very likely that our results are
not compatible with the imaginary central charge previously found for
higher-spin theories in dS(3). | Spectral dimensions from the spectral action: The generalised spectral dimension $D_{ S}(T)$ provides a powerful tool for
comparing different approaches to quantum gravity. In this work, we apply this
formalism to the classical spectral actions obtained within the framework of
almost-commutative geometry. Analysing the propagation of spin-0, spin-1 and
spin-2 fields, we show that a non-trivial spectral dimension arises already at
the classical level. The effective field theory interpretation of the spectral
action yields plateau-structures interpolating between a fixed spin-independent
$D_{ S}(T) = d_S$ for short and $D_{ S}(T) = 4$ for long diffusion times $T$.
Going beyond effective field theory
the spectral dimension is completely dominated by the high-momentum
properties of the spectral action, yielding $D_{ S}(T)=0$ for all spins. Our
results support earlier claims that high-energy bosons do not propagate. |
De Sitter space as BRST invariant coherent state of gravitons: The $S$-matrix formulation indicates that a consistent embedding of de Sitter
state in quantum gravity is possible exclusively as an excited quantum state
constructed on top of a valid $S$-matrix vacuum such as Minkowski. In the
present paper we offer such a construction of de Sitter in the form of a
coherent state of gravitons. Unlike previous realizations of this idea, we
focus on BRST invariance as the guiding principle for physicality. In order to
establish the universal rules of gauge consistency, we study the BRST-invariant
construction of coherent states created by classical and quantum sources in QED
and in linearized gravity. Introduction of $N$ copies of scalar matter coupled
to gravity allows us to take a special double scaling limit, a so-called
species limit, in which our construction of de Sitter becomes exact. In this
limit, the irrelevant quantum gravitational effects vanish whereas the
collective phenomena, such as Gibbons-Hawking radiation, are calculable. | Infinite Symmetry in the Fractional Quantum Hall Effect: We have generalized recent results of Cappelli, Trugenberger and Zemba on the
integer quantum Hall effect constructing explicitly a ${\cal W}_{1+\infty}$ for
the fractional quantum Hall effect such that the negative modes annihilate the
Laughlin wave functions. This generalization has a nice interpretation in
Jain's composite fermion theory. Furthermore, for these models we have
calculated the wave functions of the edge excitations viewing them as area
preserving deformations of an incompressible quantum droplet, and have shown
that the ${\cal W}_{1+\infty}$ is the underlying symmetry of the edge
excitations in the fractional quantum Hall effect. Finally, we have applied
this method to more general wave functions. |
Phases of planar 5-dimensional supersymmetric Chern-Simons theory: In this paper we investigate the large-$N$ behavior of 5-dimensional
$\mathcal{N}=1$ super Yang-Mills with a level $k$ Chern-Simons term and an
adjoint hypermultiplet. As in three-dimensional Chern-Simons theories, one must
choose an integration contour to completely define the theory. Using
localization, we reduce the path integral to a matrix model with a cubic action
and compute its free energy in various scenarios. In the limit of infinite
Yang-Mills coupling and for particular choices of the contours, we find that
the free-energy scales as $N^{5/2}$ for $U(N)$ gauge groups with large values
of the Chern-Simons 't\,Hooft coupling, $\tilde\lambda\equiv N/k$. If we also
set the hypermultiplet mass to zero, then this limit is a superconformal fixed
point and the $N^{5/2}$ behavior parallels other fixed points which have known
supergravity duals. We also demonstrate that $SU(N)$ gauge groups cannot have
this $N^{5/2}$ scaling for their free-energy. At finite Yang-Mills coupling we
establish the existence of a third order phase transition where the theory
crosses over from the Yang-Mills phase to the Chern-Simons phase. The phase
transition exists for any value of $\tilde\lambda$, although the details differ
between small and large values of $\tilde\lambda$. For pure Chern-Simons
theories we present evidence for a chain of phase transitions as
$\tilde\lambda$ is increased.
We also find the expectation values for supersymmetric circular Wilson loops
in these various scenarios and show that the Chern-Simons term leads to
different physical properties for fundamental and anti-fundamental Wilson
loops. Different choices of the integration contours also lead to different
properties for the loops. | Duality, Superconvergence and the Phases of Gauge Theories: Results about the phase structure of certain N=1 supersymmetric gauge
theories, which have been obtained as a consequence of holomorphy and
`electric-magnetic' duality, are shown to be in quantitative agreement with
corresponding consequences of analyticity and superconvergence of the gauge
field propagator. This connection is of interest, because the superconvergence
arguments for confinement are not restricted to theories with supersymmetry.
The method of reduction in the space of coupling parameters is used in order to
define, beyond the matching conditions, an asymptotically free, dual magnetic
theory involving Yukawa couplings. |
Cooling-heating phase transition and critical behavior of the charged
accelerating AdS black hole: We study the cooling-heating phase transition of the charged accelerating
anti-de Sitter black hole in extended phase space, and investigate the critical
behavior of this black hole in extended phase space. By calculating the
thermodynamic quantities and state equation, we found that the charged
accelerating AdS black hole as thermodynamic system is similar to the van der
Waals system. The inversion temperature of this black hole is obtained, and
cooling-heating and isenthalpic curves are plotted in T-P plane. Our results
indicate that the inversion temperature for a given pressure increases with e,
and the acceleration parameter has the opposite effect, which the
cooling-heating curves decreases gradually with the the increases of a. We also
analyse the influence of acceleration parameter on isenthalpic curves, implying
that the phase transition point decreases with the increase of acceleration
factor under constant pressure. | Yangian Symmetry in Five Dimensions: Quantum gravity in AdS$_7 \times$S$^4$ is dual to a 6d superconformal field
theory, known as the 6d $(2,0)$ theory, which is very challenging to describe
because it lacks a conventional Lagrangian description. On the other hand,
certain null reductions of the 6d $(2,0)$ theory give rise to 5d Lagrangian
theories with $SU(1,3)$ spacetime symmetry, $SO(5)$ R-symmetry, and 24
supercharges. This appears to be closely related to the superconformal group of
a 3d superconformal Chern-Simons theory known as the ABJM theory, which is
believed to be integrable in the planar limit, if one exchanges the role of
conformal and R-symmetry. In this note, we construct a representation of the 5d
superconformal group using 6d supertwistors and show that it admits an infinite
dimensional extension known as Yangian symmetry, which opens up the possiblity
that these 5d theories are exactly solvable in the planar limit. |
Secret Symmetries of Type IIB Superstring Theory on AdS3 x S3 x M4: We establish features of so-called Yangian secret symmetries for AdS3 type
IIB superstring backgrounds thus verifying the persistence of such symmetries
to this new instance of the AdS/CFT correspondence. Specifically, we find two a
priori different classes of secret symmetry generators. One class of
generators, anticipated from the previous literature, is more naturally
embedded in the algebra governing the integrable scattering problem. The other
class of generators is more elusive, and somewhat closer in its form to its
higher-dimensional AdS5 counterpart. All of these symmetries respect left-right
crossing. In addition, by considering the interplay between left and right
representations, we gain a new perspective on the AdS5 case. We also study the
RTT-realisation of the Yangian in AdS3 backgrounds thus establishing a new
incarnation of the Beisert-de Leeuw construction. | The universal Vassiliev-Kontsevich invariant for framed oriented links: We give a generalization of the Reshetikhin-Turaev functor for tangles to get
a combinatorial formula for the universal Vassiliev-Kontsevich invariant of
framed oriented links which is coincident with the Kontsevich integral. The
universal Vassiliev-Kontsevich invariant is constructed using the Drinfeld
associator. We prove the uniqueness of the Drinfeld associator. As a corollary
one gets the rationality of the Kontsevich integral. Many properties of the
universal Vassiliev-Kontsevich invariant are established. Connections to
quantum group invariants and to multiple zeta values are discussed. |
Numerical Evaluation of Gauge Invariants for a-gauge Solutions in Open
String Field Theory: We evaluate gauge invariants, action and gauge invariant overlap, for
numerical solutions which satisfy the "a-gauge" condition with various values
of $a$ in cubic open bosonic string field theory. We use the level truncation
approximation and an iterative procedure to construct numerical solutions in
the twist even universal space. The resulting gauge invariants are numerically
stable and almost equal to those of Schnabl's solution for tachyon
condensation. Our result provides further evidence that these numerical and
analytical solutions are gauge equivalent. | The Hubble parameters in the D-brane models: We consider the DBI action for the D-branes with the dynamic embeddings in
the background produced by p-branes. For the D-brane with the special topology
we obtain two Hublle parameters on this brane. The condition for the equality
of these parameters is analyzed. In the special case a mass and a charge of the
background p-branes are derived from this condition. |
Mechanization of scalar field theory in 1+1 dimensions: The `mechanization' is a procedure of replacing a scalar field in 1+1
dimensions with a piece-wise linear function, i.e. a finite graph consisting of
$N$ joints (vertices) and straight segments (edges). As a result, the field
theory is approximated by a sequence of algebraically tractable,
general-purpose collective coordinate mechanical models. We observe the
step-by-step emergence of dynamical objects and associated phenomena as the $N$
increases. Mech-kinks and mech-oscillons -- mechanical analogs of kinks and
oscillons (bions) -- appear in the simplest models, while more intricate
dynamical patterns, such as bouncing phenomenon and bion pair-production,
emerge gradually as decay states of high $N$ mech-oscillons. | Hodge Numbers for CICYs with Symmetries of Order Divisible by 4: We compute the Hodge numbers for the quotients of complete intersection
Calabi-Yau three-folds by groups of orders divisible by 4. We make use of the
polynomial deformation method and the counting of invariant K\"ahler classes.
The quotients studied here have been obtained in the automated classification
of V. Braun. Although the computer search found the freely acting groups, the
Hodge numbers of the quotients were not calculated. The freely acting groups,
$G$, that arise in the classification are either $Z_2$ or contain $Z_4$, $Z_2
\times Z_2$, $Z_3$ or $Z_5$ as a subgroup. The Hodge numbers for the quotients
for which the group $G$ contains $Z_3$ or $Z_5$ have been computed previously.
This paper deals with the remaining cases, for which $G \supseteq Z_4$ or
$G\supseteq Z_2 \times Z_2$. We also compute the Hodge numbers for 99 of the
166 CICY's which have $Z_2$ quotients. |
Electromagnetic Casimir densities for a wedge with a coaxial cylindrical
shell: Vacuum expectation values of the field square and the energy-momentum tensor
for the electromagnetic field are investigated for the geometry of a wedge with
a coaxal cylindrical boundary. All boundaries are assumed to be perfectly
conducting and both regions inside and outside the shell are considered. By
using the generalized Abel-Plana formula, the vacuum expectation values are
presented in the form of the sum of two terms. The first one corresponds to the
geometry of the wedge without the cylindrical shell and the second term is
induced by the presence of the shell. The vacuum energy density induced by the
shell is negative for the interior region and is positive for the exterior
region. The asymptotic behavior of the vacuum expectation values are
investigated in various limiting cases. It is shown that the vacuum forces
acting on the wedge sides due to the presence of the cylindrical boundary are
always attractive. | The coherent states: old geometrical methods in new quantum clothes: A geometric characterization of transition amplitudes between coherent
states, or equivalently, of the hermitian scalar product of holomorphic cross
sections in the associated D - M tilda - module, in terms of the embedding of
the cohe- rent state manifold M-tilda into a projective Hilbert space is
proposed. Cohe- rent state manifolds endowed with a homogeneous kaehler
structure are conside- red. Using the coherent state approach, an effective
method to find the cut loci on symmetric manifolds and generalized symmetric
manifolds M-tilda is proposed. The CW - complex structure of coherent state
manifolds of flag type is discussed. Recent results of Anandan and Aharonov are
commented vis-a-vis of last century constructions in projective geometry.
Calculations with signi- ficance in coherent state approch furnish explicit
proofs of the results announ- ced by Y. C. Wong on conjugate locus in complex
Grassmann manifold. |
Equilibration of Small and Large Subsystems in Field Theories and Matrix
Models: It has been recently shown that small subsystems of finite quantum systems
generically equilibrate. We extend these results to infinite-dimensional
Hilbert spaces of field theories and matrix models. We consider a quench setup,
where initial states are chosen from a microcanonical ensemble of finite energy
in free theory, and then evolve with an arbitrary non-perturbative Hamiltonian.
Given a dynamical assumption on the expectation value of particle number
density, we prove that small subsystems reach equilibrium at the level of
quantum wave-function, and with respect to all observables. The picture that
emerges is that at higher energies, larger subsystems can reach equilibrium.
For bosonic fields on a lattice, in the limit of large number of bosons per
site, all subsystem smaller than half equilibrate. In the Hermitian matrix
model, by contrast, this occurs in the limit of large energy per matrix
element, emphasizing the importance of the $O(N^2)$ energy scale for the fast
scrambling conjecture. Applying our techniques to continuum field theories on
compact spaces, we show that the density matrix of small momentum-space
observables equilibrate. Finally, we discuss the connection with scrambling,
and provide a sufficient condition for a time-independent Hamiltonian to be a
scrambler in terms of the entanglement entropy of its energy eigenstates. | Dynamics of Warped Flux Compactifications: We discuss the four dimensional effective action for type IIB flux
compactifications, and obtain the quadratic terms taking warp effects into
account. The analysis includes both the 4-d zero modes and their KK
excitations, which become light at large warping. We identify an `axial' type
gauge for the supergravity fluctuations, which makes the four dimensional
degrees of freedom manifest. The other key ingredient is the existence of
constraints coming from the ten dimensional equations of motion. Applying these
conditions leads to considerable simplifications, enabling us to obtain the low
energy lagrangian explicitly. In particular, the warped K\"ahler potential for
metric moduli is computed and it is shown that there are no mixings with the KK
fluctuations and the result differs from previous proposals. The four
dimensional potential contains a generalization of the Gukov-Vafa-Witten term,
plus usual mass terms for KK modes. |
Finite-size effect of η-deformed AdS_5 x S^5 at strong coupling: We compute Luscher corrections for a giant magnon in the \eta-deformed
(AdS_5\times S^5)_{\eta} using the su(2|2)_q-invariant S-matrix at strong
coupling and compare with the finite-size effect of the corresponding string
state, derived previously. We find that these two results match and confirm
that the su(2|2)_q-invariant S-matrix is describing world-sheet excitations of
the \eta-deformed background. | Effective Potential for Revolving D-branes: We quantize an open string stretched between D0-branes revolving around each
other. The worldsheet theory is analyzed in a rotating coordinate system in
which the worldsheet fields obey simple boundary conditions, but instead the
worldsheet Lagrangian becomes nonlinear. We quantize the system perturbatively
with respect to the velocity of the D-branes and determine the one-loop
partition function of the open string, from which we extract the short-distance
behavior of the effective potential for the revolving D0-branes. It is compared
with the calculation of the partition function of open strings between
D0-branes moving at a constant relative velocity. |
Non-Gravitating Scalars and Spacetime Compactification: We discuss role of partially gravitating scalar fields, scalar fields whose
energy-momentum tensors vanish for a subset of dimensions, in dynamical
compactification of a given set of dimensions. We show that the resulting
spacetime exhibits a factorizable geometry consisting of usual four-dimensional
spacetime with full Poincare invariance times a manifold of extra dimensions
whose size and shape are determined by the scalar field dynamics. Depending on
the strength of its coupling to the curvature scalar, the vacuum expectation
value (VEV) of the scalar field may or may not vanish. When its VEV is zero the
higher dimensional spacetime is completely flat and there is no
compactification effect at all. On the other hand, when its VEV is nonzero the
extra dimensions get spontaneously compactified. The compactification process
is such that a bulk cosmological constant is utilized for curving the extra
dimensions. | Stability of the Early Universe in Bigravity Theory: We study the stability of a spherically symmetric perturbation around the
flat Friedmann-Lema$\hat{\i}$tre-Robertson-Walker spacetime in the ghost-free
bigravity theory, retaining nonlinearities of the helicity-$0$ mode of the
massive graviton. It has been known that, when the graviton mass is smaller
than the Hubble parameter, homogeneous and isotropic spacetimes suffer from the
Higuchi-type ghost or the gradient instability against the linear perturbation
in the bigravity. Hence, the bigravity theory has no healthy massless limit for
cosmological solutions at linear level. In this paper we show that the
instabilities can be resolved by taking into account nonlinear effects of the
scalar graviton mode for an appropriate parameter space of coupling constants.
The growth history in the bigravity can be restored to the result in general
relativity in the early stage of the Universe, in which the St\"uckelberg
fields are nonlinear and there is neither ghost nor gradient instability.
Therefore, the bigravity theory has the healthy massless limit, and cosmology
based on it is viable even when the graviton mass is smaller than the Hubble
parameter. |
Multi-trace Correlators from Permutations as Moduli Space: We study the $n$-point functions of scalar multi-trace operators in the
$U(N_c)$ gauge theory with adjacent scalars, such as ${\cal N}=4$ super
Yang-Mills, at tree-level by using finite group methods. We derive a set of
formulae of the general $n$-point functions, valid for general $n$ and to all
orders of $1/N_c$. In one formula, the sum over Feynman graphs becomes a
topological partition function on $\Sigma_{0,n}$ with a discrete gauge group,
which resembles closed string interactions. In another formula, a new skeleton
reduction of Feynman graphs generates connected ribbon graphs, which resembles
open string interaction. We define the moduli space ${\cal M}_{g,n}^{\rm
gauge}$ from the space of skeleton-reduced graphs in the connected $n$-point
function of gauge theory. This moduli space is a proper subset of ${\cal
M}_{g,n}$ stratified by the genus, and its top component gives a simple
triangulation of $\Sigma_{g,n}$. | The Off-shell Symmetry Algebra of the Light-cone AdS_5 x S^5 Superstring: We analyze the psu(2,2|4) supersymmetry algebra of a superstring propagating
in the AdS_5 x S^5 background in the uniform light-cone gauge. We consider the
off-shell theory by relaxing the level-matching condition and take the limit of
infinite light-cone momentum, which decompactifies the string world-sheet. We
focus on the psu(2|2)+psu(2|2) subalgebra which leaves the light-cone
Hamiltonian invariant and show that it undergoes extension by a central element
which is expressed in terms of the level-matching operator. This result is in
agreement with the conjectured symmetry algebra of the dynamic S-matrix in the
dual N=4 gauge theory. |
Minimal $\cal N=4$ topologically massive supergravity: Using the superconformal framework, we construct a new off-shell model for
$\cal N=4$ topologically massive supergravity which is minimal in the sense
that it makes use of a single compensating vector multiplet and involves no
free parameter. As such, it provides a counterexample to the common lore that
two compensating multiplets are required within the conformal approach to
supergravity with eight supercharges in diverse dimensions. This theory is an
off-shell $\cal N=4$ supersymmetric extension of chiral gravity. All of its
solutions correspond to non-conformally flat superspaces. Its maximally
supersymmetric solutions include the so-called critical (4,0) anti-de Sitter
superspace introduced in arXiv:1205.4622, and well as warped critical (4,0)
anti-de Sitter superspaces. We also propose a dual formulation for the theory
in which the vector multiplet is replaced with an off-shell hypermultiplet.
Upon elimination of the auxiliary fields belonging to the hypermultiplet and
imposing certain gauge conditions, the dual action reduces to the one
introduced in arXiv:1605.00103. | Recursion Relations for Long-Range Integrable Spin Chains with Open
Boundary Conditions: It is well known that integrable charges for short-range (e.g.
nearest-neighbor) spin chains with periodic boundary conditions can be
recursively generated by a so-called boost operator. In the past, this
iterative construction has been generalized to periodic long-range spin chains
as they appear in the context of the gauge/gravity correspondence. Here we
introduce recursion relations for open long-range spin chain charges converting
a short-range into a long-range integrable model. |
CFTs on curved spaces: We study conformal field theories (CFTs) on curved spaces including both
orientable and unorientable manifolds possibly with boundaries. We first review
conformal transformations on curved manifolds. We then compute the identity
components of conformal groups acting on various metric spaces using a simple
fact; given local coordinate systems be single-valued. Boundary conditions thus
obtained which must be satisfied by conformal Killing vectors (CKVs) correctly
reproduce known conformal groups. As a byproduct, on $\mathbb
S^1_l\times\mathbb H^2_r$, by setting their radii $l=Nr$ with $N\in\mathbb
N^\times$, we find (the identity component of) the conformal group enhances,
whose persistence in higher dimensions is also argued. We also discuss forms of
correlation functions on these spaces using the symmetries. Finally, we study a
$d$-torus $\mathbb T^d$ in detail, and show the identity component of the
conformal group acting on the manifold in general is given by
$\text{Conf}_0(\mathbb T^d)\simeq U(1)^d$ when $d\ge2$. Using the fact, we
suggest some candidates of conformal manifolds of CFTs on $\mathbb T^d$ without
assuming the presence of supersymmetry (SUSY). In order to clarify which parts
of correlation functions are physical, we also discuss renormalization group
(RG) and local counterterms on curved spaces. | Semi-classical BMS$_3$ blocks and flat holography: We present the construction of BMS$_3$ blocks in a two-dimensional field
theory and compare the results with holographic computations involving probe
particles propagating in flat space cosmologies. On the field theory side, we
generalize the monodromy method used in the context of AdS/CFT to theories with
BMS symmetry. On the bulk side we consider geodesic Feynman diagrams, recently
introduced in [arXiv:1712.07131], evaluated in locally flat geometries
generated by backreaction of heavy BMS primary operators. We comment on the
implications of these results for the eigenstate thermalization hypothesis in
flat holography. |
Phases of higher spin black holes: Hawking-Page, transitions between
black holes and a critical point: We study the thermodynamic phase diagram of three-dimensional
$sl(N;\mathbb{R})$ higher spin black holes. By analyzing the semi-classical
partition function we uncover a rich structure that includes Hawking-Page
transitions to the AdS$_3$ vacuum, first order phase transitions among black
hole states, and a second order critical point. Our analysis is explicit for
$N=4$ but we extrapolate some of our conclusions to arbitrary $N$. In
particular, we argue that even $N$ is stable in the ensemble under
consideration but odd $N$ is not. | Construction of a Wilson action for the Wess-Zumino model: We construct a Wilson action for the Wess-Zumino model by applying the exact
renormalization group perturbatively. Using neither superfields nor auxiliary
fields, we construct a supersymmetric action only with complex scalar and
Majorana spinor fields. We adopt the BRST (antifield) formalism to show the
consistency of the construction to all orders in loop expansions. The resulting
action has a quadratically divergent scalar mass term which is absent in the
superfield formalism. |
Strong anomaly and phases of chiral gauge theories: We present a simple argument which seems to favor, when applied to a large
class of strongly-coupled chiral gauge theories, a dynamical-Higgs-phase
scenario, characterized by certain bifermion condensates. Flavor symmetric
confining vacua described in the infrared by a set of baryonlike massless
composite fermions saturating the conventional 't Hooft anomaly matching
equations, appear instead disfavored. Our basic criterion is that it should be
possible to write a strong-anomaly effective action, analogous to the one used
in QCD to describe the solution of the $U(1)_A$ problem in the low-energy
effective action, by using the low-energy degrees of freedom in the
hypothesized infrared theory. We also comment on some well-known ideas such as
the complementarity and the large $N$ planar dominance in the context of these
chiral gauge theories.Some striking analogies and contrasts between the
massless QCD and chiral gauge theories seem to emerge from this discussion. | Symbolic Computing with Grassman Variables: A package of Maple 5.3 commands for doing calculations with anticommutative
variables is presented. |
Aspects of Massive ABJM Models with Inhomogeneous Mass Parameters: Recently, ${\cal N} =3$ mass-deformed ABJM model with arbitrary mass-function
depending on a spatial coordinate was constructed. In addition to the ${\cal N}
= 3$ case, we construct lower supersymmetric ${\cal N} =1$ and ${\cal N} =2$
inhomogeneously mass-deformed ABJM (ImABJM) models, which require three and two
arbitrary mass-functions, respectively. We also construct general vacuum
solutions of the ${\cal N} = 3$ ImABJM model for any periodic mass-function.
There are two classes of vacua, which are diagonal type and GRVV type according
to reference value of mass-functions. We provide explicit examples of the
vacuum solutions and discuss related operators. | Observing braneworld black holes: Spacetime in the vicinity of an event horizon can be probed using
observations which explore the dynamics of the accretion disc. Many high energy
theories of gravity lead to modifications of the near horizon regime,
potentially providing a testing ground for these theories. In this paper, we
explore the impact of braneworld gravity on this region by formulating a method
of deriving the general behaviour of the as yet unknown braneworld black hole
solution. We use simple bounds to constrain the solution close to the horizon. |
Aligned Natural Inflation in String Theory: We propose a scenario for realizing super-Planckian axion decay constants in
Calabi-Yau orientifolds of type IIB string theory, leading to large-field
inflation. Our construction is a simple embedding in string theory of the
mechanism of Kim, Nilles, and Peloso, in which a large effective decay constant
arises from alignment of two smaller decay constants. The key ingredient is
gaugino condensation on magnetized or multiply-wound D7-branes. We argue that,
under very mild assumptions about the topology of the Calabi-Yau, there are
controllable points in moduli space with large effective decay constants. | Simulating seeded vacuum decay in a cold atom system: We propose to test the concept of seeded vacuum decay in cosmology using an
analogue gravity Bose-Einstein condensate system. The role of the nucleation
seed is played by a vortex within the condensate. We present two complementary
theoretical analyses that demonstrate seeded decay is the dominant decay
mechanism of the false vacuum. First, we adapt the standard instanton methods
to the Gross-Pitaevskii equation. Second, we use the truncated Wigner method to
study vacuum decay. |
Null Fluids - A New Viewpoint of Galilean Fluids: This article is a detailed version of our short letter `On equilibrium
partition function for non-relativistic fluid' [arXiv:1505.05677] extended to
include an anomalous $U(1)$ symmetry. We construct a relativistic system, which
we call null fluid and show that it is in one-to-one correspondence with a
Galilean fluid living in one lower dimension. The correspondence is based on
light cone reduction, which is known to reduce the Poincare symmetry of a
theory to Galilean in one lower dimension. We show that the proposed null fluid
and the corresponding Galilean fluid have exactly same symmetries,
thermodynamics, constitutive relations, and equilibrium partition to all orders
in derivative expansion. We also devise a mechanism to introduce $U(1)$ anomaly
in even dimensional Galilean theories using light cone reduction, and study its
effect on the constitutive relations of a Galilean Fluid. | Classical Noncommutative Bicosmology Model: We propose a bicosmology model which is the classical analog of
noncommutative quantum mechanics. From this point of view the sources of the
modified FRW equations are dark energy ones governed by a Chapligyn's equation
state. The parameters of noncommutativity $\theta$ and $B$ are interpreted in
terms of the Planck area and a like-magnetic field, presumably the magnetic
seed of magnetogenesis. |
Axial Symmetry, Anti-BRST Invariance and Modified Anomalies: It is shown that anti-BRST symmetry is the quantized counterpart of local
axial symmetry in gauge theories. An extended form of descent equations is
worked out which yields a set of modified consistent anomalies. | On the Derivation of Chiral Symmetry Breaking in QCD-like Theories and
S-confining Theories: Recent works argue that the pattern of chiral symmetry breaking in QCD-like
theories can be derived from supersymmetric (SUSY) QCD with perturbation of
anomaly-mediated SUSY breaking (AMSB). Nevertheless, despite the fact that AMSB
needs to be a small (but still exact) perturbation, there are two other major
problems remaining unsolved: first, in order to derive the chiral symmetry
breaking pattern, one needs to minimize the potential along a certain specific
direction, identifying this direction fully as an outcome is nontrivial given
the moduli space of degenerate vacua in the SUSY limit; second, when SUSY is
broken, non-holomorphic states might emerge and be relevant for determining the
vacuum structure. In this work, we focus on SUSY QCD with $N_f\leq N_c+1$ and
perturb the theories using AMSB. Without minimizing the potential along a
certain specific direction in the moduli space, we successfully derive the
expected chiral symmetry breaking pattern when $N_f<N_c$. However, when
$N_f=N_c$ and $N_f=N_c+1$, we show that tree-level AMSB would induce runaway
directions, along which baryon number is spontaneously broken, and the vacua
with broken baryon number can be deeper while the field values are not far from
the origin. This implies that phase transitions and/or non-holomorphic physics
are necessary. Moreover, we perform explicit consistency checks on ultraviolet
insensitivity for different $N_f$ by adding the holomorphic mass term for the
last flavor, we find that the jump of AMSB potential indeed matches the
contribution from the holomorphic mass term. We also show in general that, when
tree-level AMSB is not vanishing, the origin of the moduli space in s-confining
theories does not persist as a minimum. |
Heat kernel coefficients for compact fuzzy spaces: I discuss the trace of a heat kernel Tr[e^(-tA)] for compact fuzzy spaces. In
continuum theory its asymptotic expansion for t -> +0 provides geometric
quantities, and therefore may be used to extract effective geometric quantities
for fuzzy spaces. For compact fuzzy spaces, however, an asymptotic expansion
for t -> +0 is not appropriate because of their finiteness. It is shown that
effective geometric quantities are found as coefficients of an approximate
power-law expansion of the trace of a heat kernel valid for intermediate values
of t. An efficient method to obtain these coefficients is presented and applied
to some known fuzzy spaces to check its validity. | The Renormalization Group with Exact beta-Functions: The perturbative $\beta$-function is known exactly in a number of
supersymmetric theories and in the 't Hooft renormalization scheme in the
$\phi_4^4$ model. It is shown how this allows one to compute the effective
action exactly for certain background field configurations and to relate bare
and renormalized couplings. The relationship between the MS and SUSY
subtraction schemes in $N = 1$ super Yang-Mills theory is discussed. |
Tropical Periods for Calabi-Yau Hypersurfaces in non--Fano Toric
Varieties: We consider multi-polytopes to describe non-Fano toric varieties and their
associated anticanonical Calabi-Yau hypersurfaces. From the periods of the
mirror manifold the $\widehat{\Gamma}$-conjecture is shown to hold for examples
of Calabi-Yau hypersurfaces in non-Fano ambient spaces, extending earlier work
by Abouzaid et al by employing a generalized Duistermaat-Heckman measure. | Real-Time Instantons and Suppression of Collision-Induced Tunneling: We consider tunneling processes in QFT induced by collisions of elementary
particles. We propose a semiclassical method for estimating the probability of
these processes in the limit of very high collision energy. As an illustration,
we evaluate the maximum probability of induced tunneling between different
vacua in a (1+1)-dimensional scalar model with boundary interaction. |
Baby de Sitter Black Holes and dS$_3$/CFT$_2$: Unlike three-dimensional Einstein gravity, three-dimensional massive gravity
admits asymptotically de Sitter space (dS) black hole solutions. These black
holes present interesting features and provide us with toy models to study the
dS/CFT correspondence. A remarkable property of these black holes is that they
are always in thermal equilibrium with the cosmological horizon of the space
that hosts them. This invites us to study the thermodynamics of these solutions
within the context of dS/CFT. We study the asymptotic symmetry group of the
theory and find that it indeed coincides with the local two-dimensional
conformal algebra. The charge algebra associated to the asymptotic Killing
vectors consists of two copies of the Virasoro algebra with non-vanishing
central extension. We compute the mass and angular momentum of the dS black
holes and verify that a naive application of Cardy's formula exactly reproduces
the entropy of both the black hole and the cosmological horizon. By adapting
the holographic renormalization techniques to the case of dS space, we define
the boundary stress tensor of the dual Euclidean conformal field theory. | Higher Spin Currents in the Enhanced N=3 Kazama-Suzuki Model: The N=3 Kazama-Suzuki model at the `critical' level has been found by
Creutzig, Hikida and Ronne. We construct the lowest higher spin currents of
spins (3/2, 2,2,2,5/2, 5/2, 5/2, 3) in terms of various fermions. In order to
obtain the operator product expansions (OPEs) between these higher spin
currents, we describe three N=2 OPEs between the two N=2 higher spin currents
denoted by (3/2, 2, 2, 5/2) and (2, 5/2, 5/2, 3) (corresponding 36 OPEs in the
component approach). Using the various Jacobi identities, the coefficient
functions appearing on the right hand side of these N=2 OPEs are determined in
terms of central charge completely. Then we describe them as one single N=3 OPE
in the N=3 superspace. The right hand side of this N=3 OPE contains the
SO(3)-singlet N=3 higher spin multiplet of spins (2, 5/2, 5/2, 5/2, 3,3,3,
7/2), the SO(3)-singlet N=3 higher spin multiplet of spins (5/2, 3,3,3, 7/2,
7/2, 7/2, 4), and the SO(3)-triplet N=3 higher spin multiplets where each
multiplet has the spins (3, 7/2, 7/2, 7/2, 4,4,4, 9/2), in addition to N=3
superconformal family of the identity operator. Finally, by factoring out the
spin-1/2 current of N=3 linear superconformal algebra generated by eight
currents of spins (1/2, 1,1,1, 3/2, 3/2, 3/2, 2), we obtain the extension of
so-called SO(3) nonlinear Knizhnik Bershadsky algebra. |
Nonlinear Responses of Chiral Fluids from Kinetic Theory: The second-order nonlinear responses of inviscid chiral fluids near local
equilibrium are investigated by applying the chiral kinetic theory (CKT)
incorporating side-jump effects. It is shown that the local equilibrium
distribution function can be non-trivially introduced in a co-moving frame with
respect to the fluid velocity when the quantum corrections in collisions are
involved. For the study of anomalous transport, contributions from both quantum
corrections in anomalous hydrodynamic equations of motion and those from the
CKT and Wigner functions are considered under the relaxation-time (RT)
approximation, which result in anomalous charge Hall currents propagating along
the cross product of the background electric field and the temperature (or
chemical-potential) gradient and of the temperature and chemical-potential
gradients. On the other hand, the nonlinear quantum correction on the charge
density vanishes in the classical RT approximation, which in fact satisfies the
matching condition given by the anomalous equation obtained from the CKT. | Condensates beyond the horizons: In this work we continue our previous studies concerning the possibility of
the existence of a Bose-Einstein condensate in the interior of a static black
hole, a possibility first advocated by Dvali and G\'omez. We find that the
phenomenon seems to be rather generic and it is associated to the presence of
an horizon, acting as a confining potential. We extend the previous
considerations to a Reissner-Nordstr\"om black hole and to the de Sitter
cosmological horizon. In the latter case the use of static coordinates is
essential to understand the physical picture. In order to see whether a BEC is
preferred, we use the Brown-York quasilocal energy, finding that a condensate
is energetically favourable in all cases in the classically forbidden region.
The Brown-York quasilocal energy also allows us to derive a quasilocal
potential, whose consequences we explore. Assuming the validity of this
quasilocal potential allows us to suggest a possible mechanism to generate a
graviton condensate in black holes. However, this mechanism appears not to be
feasible in order to generate a quantum condensate behind the cosmological de
Sitter horizon. |
Surface Operators in Abelian Gauge Theory: We consider arbitrary embeddings of surface operators in a pure,
non-supersymmetric abelian gauge theory on spin (non-spin) four-manifolds. For
any surface operator with a priori simultaneously non-vanishing parameters, we
explicitly show that the parameters transform naturally under an SL(2, Z) (or a
congruence subgroup thereof) duality of the theory. However, for
non-trivially-embedded surface operators, exact S-duality holds only if the
quantum parameter effectively vanishes, while the overall SL(2, Z) (or a
congruence subgroup thereof) duality holds up to a c-number at most,
regardless. Via the formalism of duality walls, we furnish an alternative
derivation of the transformation of parameters - found also to be consistent
with a switch from Wilson to 't Hooft loop operators under S-duality. With any
background embedding of surface operators, the partition function and the
correlation functions of non-singular, gauge-invariant local operators on any
curved four-manifold, are found to transform like modular forms under the
respective duality groups. | Finite energy shifts in SU(n) supersymmetric Yang-Mills theory on T^3xR
at weak coupling: We consider a semi-classical treatment, in the regime of weak gauge coupling,
of supersymmetric Yang-Mills theory in a space-time of the form T^3xR with
SU(n)/Z_n gauge group and a non-trivial gauge bundle. More specifically, we
consider the theories obtained as power series expansions around a certain
class of normalizable vacua of the classical theory, corresponding to isolated
points in the moduli space of flat connections, and the perturbative
corrections to the free energy eigenstates and eigenvalues in the weakly
interacting theory. The perturbation theory construction of the interacting
Hilbert space is complicated by the divergence of the norm of the interacting
states. Consequently, the free and interacting Hilbert furnish unitarily
inequivalent representation of the algebra of creation and annihilation
operators of the quantum theory. We discuss a consistent redefinition of the
Hilbert space norm to obtain the interacting Hilbert space and the properties
of the interacting representation. In particular, we consider the lowest
non-vanishing corrections to the free energy spectrum and discuss the crucial
importance of supersymmetry for these corrections to be finite. |
Three and Four Point Functions of Stress Energy Tensors in D=3 for the
Analysis of Cosmological Non-Gaussianities: We compute the correlation functions of 3 and 4 stress energy tensors $(T)$
in D=3 in free field theories of scalars, abelian gauge fields, and fermions,
which are relevant in the analysis of cosmological non-gaussianities. These
correlators appear in the holographic expressions of the scalar and tensor
perturbations derived for holographic cosmological models. The result is simply
adapted to describe the leading contributions in the gauge coupling to the same
correlators also for a non abelian SU(N) gauge theory. In the case of the
bispectrum, our results are mapped and shown to be in full agreement with the
corresponding expressions given in a recent holographic study by Bzowski,
McFadden and Skenderis. In the 4-T case we present the completely traced
amplitude plus all the contact terms. These are expected to appear in a fourth
order extension of the holographic formulas for the 4-point functions of scalar
metric perturbations. | Spectral curve for open strings attached to the Y=0 brane: The concept of spectral curve is generalized to open strings in AdS/CFT with
integrability preserving boundary conditions. Our definition is based on the
logarithms of the eigenvalues of the open monodromy matrix and makes possible
to determine all the analytic, symmetry and asymptotic properties of the
quasimomenta. We work out the details of the whole construction for the Y = 0
brane boundary condition. The quasimomenta of open circular strings are
explicitly calculated. We use the asymptotic solutions of the Y -system and the
boundary Bethe Ansatz equations to recover the spectral curve in the strong
coupling scaling limit. Using the curve the quasiclassical fluctuations of some
open string solutions are also studied. |
BPS Algebras in 2D String Theory: We discuss a set of heterotic and type II string theory compactifications to
1+1 dimensions that are characterized by factorized internal worldsheet CFTs of
the form $V_1\otimes \bar V_2$, where $V_1, V_2$ are self-dual (super) vertex
operator algebras. In the cases with spacetime supersymmetry, we show that the
BPS states form a module for a Borcherds-Kac-Moody (BKM) (super)algebra, and we
prove that for each model the BKM (super)algebra is a symmetry of genus zero
BPS string amplitudes. We compute the supersymmetric indices of these models
using both Hamiltonian and path integral formalisms. The path integrals are
manifestly automorphic forms closely related to the Borcherds-Weyl-Kac
denominator. Along the way, we comment on various subtleties inherent to these
low-dimensional string compactifications. | Exact WKB analysis of the vacuum pair production by time-dependent
electric fields: We study the vacuum pair production by a time-dependent strong electric field
based on the exact WKB analysis. We identify the generic structure of a Stokes
graph for systems with the vacuum pair production and show that the number of
produced pairs is given by a product of connection matrices for Stokes segments
connecting pairs of turning points. We derive an explicit formula for the
number of produced pairs, assuming the semi-classical limit. The obtained
formula can be understood as a generalization of the divergent asymptotic
series method by Berry, and is consistent with other semi-classical methods
such as the worldline instanton method and the steepest descent evaluation of
the Bogoliubov coefficients done by Brezin and Izykson. We also use the formula
to discuss effects of time-dependence of the applied strong electric field
including the interplay between the perturbative multi-photon pair production
and non-peturbative Schwinger mechanism, and the dynamically assisted Schwinger
mechanism. |
Quantization of (1+1)-dimensional Hořava-Lifshitz theory of gravity: In this paper, we study the quantization of the (1+1)-dimensional projectable
Ho\v{r}ava-Lifshitz (HL) gravity, and find that, when only gravity is present,
the system can be quantized by following the canonical Dirac quantization, and
the corresponding wavefunction is normalizable for some orderings of the
operators. The corresponding Hamilton can also be written in terms of a simple
harmonic oscillator, whereby the quantization can be carried out quantum
mechanically in the standard way. When the HL gravity minimally couples to a
scalar field, the momentum constraint is solved explicitly in the case where
the fundamental variables are functions of time only. In this case, the coupled
system can also be quantized by following the Dirac process, and the
corresponding wavefunction is also normalizable for some particular orderings
of the operators. The Hamilton can be also written in terms of two interacting
harmonic oscillators. But, when the interaction is turned off, one of the
harmonic oscillators has positive energy, while the other has negative energy.
A remarkable feature is that orderings of the operators from a classical
Hamilton to a quantum mechanical one play a fundamental role in order for the
Wheeler-DeWitt equation to have nontrivial solutions. In addition, the
space-time is well quantized, even when it is classically singular. | Strings, Branes and Cosmology: What can we hope to learn?: This article briefly summarizes the motivations for -- and recent progress in
-- searching for cosmological configurations within string theory, with a focus
on how much we might reasonably hope to learn about fundamental physics from
precision cosmological measurements. |
Algebraic structure of Gravity with Torsion: The BRS transformations for gravity with torsion are discussed by using the
Maurer-Cartan horizontality conditions. With the help of an operator $\d$ which
allows to decompose the exterior space-time derivative as a BRS commutator we
solve the Wess-Zumino consistency condition corresponding to invariant
Lagrangians and anomalies. | On a Boundary CFT Description of Nonperturbative N=2 Yang-Mills Theory: We describe a simple method for determining the strong-coupling BPS spectrum
of four dimensional N=2 supersymmetric Yang-Mills theory. The idea is to
represent the magnetic monopoles and dyons in terms of D-brane boundary states
of a non-compact d=2 N=2 Landau-Ginzburg model. In this way the quantum
truncated BPS spectrum at the origin of the moduli space can be directly mapped
to the finite number of primary fields of the superconformal minimal models. |
Tauberian-Cardy formula with spin: We prove a $2$ dimensional Tauberian theorem in context of $2$ dimensional
conformal field theory. The asymptotic density of states with conformal weight
$(h,\bar{h})\to (\infty,\infty)$ for any arbitrary spin is derived using the
theorem. We further rigorously show that the error term is controlled by the
twist parameter and insensitive to spin. The sensitivity of the leading piece
towards spin is discussed. We identify a universal piece in microcanonical
entropy when the averaging window is large. An asymptotic spectral gap on
$(h,\bar{h})$ plane, hence the asymptotic twist gap is derived. We prove an
universal inequality stating that in a compact unitary $2$D CFT without any
conserved current $Ag\leq \frac{\pi(c-1)r^2}{24}$ is satisfied, where $g$ is
the twist gap over vacuum and $A$ is the minimal "areal gap", generalizing the
minimal gap in dimension to $(h',\bar{h}')$ plane and
$r=\frac{4\sqrt{3}}{\pi}\simeq 2.21$. We investigate density of states in the
regime where spin is parametrically larger than twist with both going to
infinity. Moreover, the large central charge regime is studied. We also probe
finite twist, large spin behavior of density of states. | Ghost anomalous dimension in asymptotically safe quantum gravity: We compute the ghost anomalous dimension within the asymptotic-safety
scenario for quantum gravity. For a class of covariant gauge fixings and using
a functional RG scheme, the anomalous dimension $\eta_c$ is negative, implying
an improved UV behavior of ghost fluctuations. At the non-Gaussian UV fixed
point, we observe a maximum value of $\eta_c\simeq -0.78$ for the Landau-deWitt
gauge within the given scheme and truncation. Most importantly, the
backreaction of the ghost flow onto the Einstein-Hilbert sector preserves the
non-Gaussian fixed point with only mild modifications of the fixed-point values
for the gravitational coupling and cosmological constant and the associated
critical exponents; also their gauge dependence is slightly reduced. Our
results provide further evidence for the asymptotic-safety scenario of quantum
gravity. |
Proof of the fundamental BCJ relations for QCD amplitudes: The fundamental BCJ-relation is a linear relation between primitive tree
amplitudes with different cyclic orderings. The cyclic orderings differ by the
insertion place of one gluon. The coefficients of the fundamental BCJ-relation
are linear in the Lorentz invariants $2 p_i p_j$. The BCJ-relations are well
established for pure gluonic amplitudes as well as for amplitudes in ${\mathcal
N}=4$ super-Yang-Mills theory. Recently, it has been conjectured that the
BCJ-relations hold also for QCD amplitudes. In this paper we give a proof of
this conjecture. The proof is valid for massless and massive quarks. | Can the Red Shift be a consequence of the Dilaton field?: The possibility that the expansion rate of the Universe, as reflected by the
Red Shift, could be produced by the existence of the dilaton field is explored.
The analysis starts from previously studied solutions of the Einstein equations
for gravity interacting with a massive scalar field. It is firstly underlined
that such solutions can produce the observed values of the Hubble constant.
Since the Einstein-Klein-Gordon lagrangian could be expected to appear as an
effective one for the dilaton in some approximation, the mentioned solutions
are applied to study this field. Therefore, the vacuum expectation value for
the dilaton is selected to be of the order of the Planck mass, as it is
frequently fixed in string phenomenology. Then, it follows that the value of
its effective mass should be as low as m=3.9 10^(-29) cm^(-1) in order produce
the observed expansion rate. The discussion can also predict a radius of the
Universe of the order of 10^(29) cm. Finally, after adopting the view advanced
ina previous work, in which these mentioned solutions are associated to
interior configurations of collapsed scalar fields, a picture of our Universe
as a black hole interior is suggested. |
On gauge coupling constant in linearization of nonlinear supersymmetry: We study in two space-time dimensions (d = 2) the relation between N = 2
supersymmetric (SUSY) QED theory and N = 2 nonlinear (NL) SUSY model by
linearizing N = 2 NLSUSY generally based upon the fundamental notions of the
basic theory. We find a remarkable mechanism which determines theoretically the
magnitude of the bare gauge coupling constant from the general structure of
auxiliary fields. We show explicitly in d = 2 that the NL/linear SUSY relation
(i.e. a SUSY compositeness condition for all particles) determines the
magnitude of the bare electromagnetic coupling constant (i.e. the fine
structure constant) of N = 2 SUSY QED. | On the Non-relativistic Limit of Linear Wave Equations for Zero and
Unity Spin Particles: The non-relativistic limit of the linear wave equation for zero and unity
spin bosons of mass $m$ in the Duffin-Kemmer-Petiau representation is
investigated by means of a unitary transformation, analogous to the
Foldy-Wouthuysen canonical transformation for a relativistic electron. The
interacting case is also analyzed, by considering a power series expansion of
the transformed Hamiltonian, thus demonstrating that all features of particle
dynamics can be recovered if corrections of order $1/m^{2}$ are taken into
account through a recursive iteration procedure. |
Magnetising the ${\cal N}=4$ Super Yang-Mills plasma: We investigate the thermodynamics of the anisotropic magnetic $\rm AdS_5$
black brane solution found by D'Hoker and Kraus arXiv:0908.3875. This solution
is the gravity dual of a strongly coupled ${\cal N}=4$ Super Yang-Mills plasma
in ${\mathbb R}^{3,1}$, with temperature $T$, in the presence of a magnetic
field ${\cal B}$. Following the procedure of holographic renormalisation we
calculate the Gibbs free energy and the holographic stress tensor of the
conformal plasma. We evaluate several thermodynamic quantities including the
magnetisation, the anisotropic pressures and the speeds of sound. Our results
are consistent with an RG flow from a perturbed $\rm AdS_5$ black brane at
small ${\cal B}/T^2$ to a $\rm \bf BTZ \times {\mathbb R}^2$ black brane at
large ${\cal B}/T^2$. We also perform a phenomenological analysis where we
compare the thermodynamics of a magnetised conformal plasma against the lattice
QCD results for the thermodynamics of the magnetised quark-gluon plasma. | Minimal cut-off vacuum state constraints from CMB bispectrum statistics: In this short note we translate the best available observational bounds on
the CMB bispectrum amplitudes into constraints on a specific scale-invariant
New Physics Hypersurface (NPH) model of vacuum state modifications, as first
proposed by Danielsson, in general models of single-field inflation. As
compared to the power spectrum the bispectrum constraints are less ambiguous
and provide an interesting upper bound on the cut-off scale in general models
of single-field inflation with a small speed of sound. This upper bound is
incompatible with the power spectrum constraint for most of the parameter
domain, leaving very little room for minimal cut-off vacuum state modifications
in general single-field models with a small speed of sound. |
Counting Supertubes: The quantum states of the supertube are counted by directly quantizing the
linearized Born-Infeld action near the round tube. The result is an entropy $S
= 2\pi \sqrt{2 (Q_{D0}Q_{F1}-J)}$, in accord with conjectures in the
literature. As a result, supertubes may be the generic D0-F1 bound state. Our
approach also shows directly that supertubes are marginal bound states with a
discrete spectrum. We also discuss the relation to recent suggestions of Mathur
et al involving three-charge black holes. | Gauss-Bonnet braneworld redux: A novel scenario for the bouncing
universe: We propose a new scenario for the bouncing universe in a simple
five-dimensional braneworld model in the framework of Einstein-Gauss-Bonnet
gravity, which works even with ordinary matter on the brane. In this scenario,
the so-called branch singularity located at a finite physical radius in the
bulk spacetime plays an essential role. We show that a three-brane moving in
the bulk may reach and pass through it in spite of the fact that it is a
curvature singularity. The bulk spacetime is extended beyond the branch
singularity in the C^0 sense and then the branch singularity is identified as a
massive thin shell. From the bulk point of view, this process is the collision
of the three-brane with the shell of branch singularity. From the point of view
on the brane, this process is a sudden transition from the collapsing phase to
the expanding phase of the universe. The present result opens a completely new
possibility to achieve the bouncing brane universe as a higher-curvature
effect. |
Instanton corrections to the effective action of N=4 SYM: We compute the one-instanton effective action of N=4 super Yang-Mills theory
with gauge group Sp(2N). The result can be written in a very compact and
manifestly supersymmetric form involving an integral over the superspace of an
irrational function of the N=4 on-shell superfields. In the Coulomb branch, the
instanton corrects both the MHV and next-to-next-MHV higher derivative terms
D^4F^{2n+2} and F^{2n+4}. We confirm at the non-perturbative level the
non-renormalization theorems for MHV F^{2n+2} terms that are expected to
receive perturbative corrections only at n-loops. We compute also the one and
two-loop corrections to the D^4F^4 term and show that its completion under
SL(2,Z) duality is consistent with the one-instanton results of U(2) gauge
group. | Poisson equations, higher derivative automorphic forms and string
parameter limits: This paper considers the higher derivative terms in the effective action of
type II string theory and in particular the behaviour of the automorphic forms
they contain in all the different possible limits of the string parameters. The
automorphic forms are thought to obey Poisson equations which contain the
Laplacian defined on the coset space to which the scalars fields belong and we
compute this Laplacian in all the possible string theory limits. We also
consider these Poisson equations in the decompactification limit of a single
dimension and by making two assumptions, one on the generic form of this
equation and the other on the behaviour of the automorphic forms in this limit,
we find strong constraints on the allowed form of this differential equation.
We show that these constraints allow one to recover much of what was previously
known about the automorphic forms corresponding to terms in the effective
action that have fourteen or fewer space-time derivatives in a simple way. |
Massive selfdual perturbed gauge theory: Spontaneously broken gauge theories are described as a perturbation of
selfdual gauge theory. Instead of the incorporation of scalar degrees of
freedom, the massive component of the gauge field is obtained from an
anti-selfdual field strength consisting of three components before gauge
fixing. The interactions describe a massive gauge theory that is non-polynomial
with an expansion containing an infinite number of terms. The Lagrangian
generalizes the form of the axial anomaly in two dimensions. Unitary
propagation of the tensor field occurs upon gauge fixing an additional
symmetry. | BPS D-branes after Tachyon Condensation: We construct an effective action describing brane-antibrane system containing
N D-branes and N \bar{D}-branes. BPS equations for remaining D-branes after
tachyon condensation are derived and their properties are investigated. The
value of the D-brane tension and the number of brane bound states are
discussed. |
The D(2,1;α) Particle: The exceptional superalgebra $D(2,1;\alpha)$ has been classified as a
candidate conformal supersymmetry algebra in two dimensions. We propose an
alternative interpretation of it as extended BFV-BRST quantisation
superalgebras in 2D ($D(2,1;1) \simeq osp(2,2|2)$). A superfield realization is
presented wherein the standard extended phase space coordinates can be
identified. The physical states are studied via the cohomology of the BRST
operator. It is conjectured that the underlying model giving rise to this
`quantisation' is that of a scalar relativistic particle in 1+1 dimensions, for
which the light cone coordinates $x_R$, $x_L$ transform under worldline
diffeomorphisms as scalar densities of appropriate weight. | D-Branes and Vanishing Cycles in Higher Dimensions: We investigate the quantum volume of D-branes wrapped around cycles of
various dimension in Calabi-Yau fourfolds and fivefolds. Examining the cases of
the sextic and heptic hypersurface Calabi-Yau varieties, as well as one example
in weighted projective space, we find expressions for periods which vanish at
the singular point analogous to the conifold point. As in the known
three-dimensional cases, it is the top dimensional cycle which attains zero
quantum volume, even though lower dimensional cycles remain non-degenerate,
indicating this phenomena to be a general feature of quantum geometry. |
Branes with Brains: Exploring String Vacua with Deep Reinforcement
Learning: We propose deep reinforcement learning as a model-free method for exploring
the landscape of string vacua. As a concrete application, we utilize an
artificial intelligence agent known as an asynchronous advantage actor-critic
to explore type IIA compactifications with intersecting D6-branes. As different
string background configurations are explored by changing D6-brane
configurations, the agent receives rewards and punishments related to string
consistency conditions and proximity to Standard Model vacua. These are in turn
utilized to update the agent's policy and value neural networks to improve its
behavior. By reinforcement learning, the agent's performance in both tasks is
significantly improved, and for some tasks it finds a factor of O(200) more
solutions than a random walker. In one case, we demonstrate that the agent
learns a human-derived strategy for finding consistent string models. In
another case, where no human-derived strategy exists, the agent learns a
genuinely new strategy that achieves the same goal twice as efficiently per
unit time. Our results demonstrate that the agent learns to solve various
string theory consistency conditions simultaneously, which are phrased in terms
of non-linear, coupled Diophantine equations. | p-adic Strings Then and Now: After a brief review of the idea and main results of the original p-adic
string work, I describe the recent interest in p-adic strings in the context of
AdS/CFT duality |
$\mathbb{1}$-Loop Theory: A new formalism for lattice gauge theory is developed that preserves
Poincar\'e symmetry in a discrete universe. We define the $\mathbb{1}$-loop, a
generalization of the Wilson loop that reformulates classical differential
equations of motion as identity-valued multiplicative loops of Lie group
elements of the form ${[g_1\cdots g_n]=\mathbb{1}}$. A lattice Poincar\'e gauge
theory of gravity is thus derived that employs a novel matter field
construction and recovers Einstein's vacuum equations in the appropriate limit. | QCD Cosmology from the Lattice Equation of State: We numerically determine the time dependence of the scale factor from the
lattice QCD equation of state, which can be used to define a QCD driven
cosmology. We compare a lattice approach to QCD cosmology at late times with
other models of the low temperature equation of state including the hadronic
resonance gas model, Hagedorn model and AdS/CFT. |
Exact N=4 Supersymmetric Low-Energy Effective Action in N=4
Super-Yang-Mills Theory: We review a recent progress in constructing the low-energy effective action
of N=4 SYM theory. This theory is formulated in terms of N=2 harmonic
superfields corresponding to N=2 vector multiplet and hypermultiplet. Such a
formulation possesses the manifest N=2 supersymmetry and an extra hidden
on-shell supersymmetry. Exploring the hidden N=2 supersymmetry we proved that
the known non-holomorphic potentials of the form ln W ln \bar{W} can be
explicitly completed by the appropriate hypermultiplet-dependent terms to the
entire N=4 supersymmetric form. The non-logarithmic effective potentials do not
admit an N=4 completion and, hence, such potentials cannot occur in N=4
supersymmetric theory. As a result we obtain the exact N=4 supersymmetric
low-energy effective action in N=4 SYM theory. | On the Lorentz-breaking theory with higher derivatives in spinor sector: We consider the two-point function of the gauge field in Lorentz-breaking
theories with higher-derivative extension of the Dirac Lagrangian. We show that
the Carroll-Field-Jackiw term naturally arises in this theory as a quantum
correction being perfectly finite and thus displaying no ambiguities. Also, the
finiteness of this term at low energy limit and the absence of large Lorentz
violating corrections allows to avoid the fine-tuning problem. |
Stability of the nonperturbative bosonic string vacuum: Quantization of the bosonic string around the classical, perturbative vacuum
is not consistent for spacetime dimensions 2<d<26. Recently we have showed that
at large d there is another so-called mean field vacuum. Here we extend this
mean field calculation to finite d and show that the corresponding mean field
vacuum is stable under quadratic fluctuations for 2<d<26. We point out the
analogy with the two-dimensional O(N)-symmetric sigma-model, where the
1/N-vacuum is very close to the real vacuum state even for finite N, in
contrast to the perturbative vacuum. | Gauge theory of second class constraints without extra variables: We show that any theory with second class constraints may be cast into a
gauge theory if one makes use of solutions of the constraints expressed in
terms of the coordinates of the original phase space. We perform a Lagrangian
path integral quantization of the resulting gauge theory and show that the
natural measure follows from a superfield formulation. |
Equivalence of a Complex $\cP\cT$-Symmetric Quartic Hamiltonian and a
Hermitian Quartic Hamiltonian with an Anomaly: In a recent paper Jones and Mateo used operator techniques to show that the
non-Hermitian $\cP\cT$-symmetric wrong-sign quartic Hamiltonian $H=\half
p^2-gx^4$ has the same spectrum as the conventional Hermitian Hamiltonian
$\tilde H=\half p^2+4g x^4-\sqrt{2g} x$. Here, this equivalence is demonstrated
very simply by means of differential-equation techniques and, more importantly,
by means of functional-integration techniques. It is shown that the linear term
in the Hermitian Hamiltonian is anomalous; that is, this linear term has no
classical analog. The anomaly arises because of the broken parity symmetry of
the original non-Hermitian $\cP\cT$-symmetric Hamiltonian. This anomaly in the
Hermitian form of a $\cP\cT$-symmetric quartic Hamiltonian is unchanged if a
harmonic term is introduced into $H$. When there is a harmonic term, an
immediate physical consequence of the anomaly is the appearance of bound
states; if there were no anomaly term, there would be no bound states. Possible
extensions of this work to $-\phi^4$ quantum field theory in higher-dimensional
space-time are discussed. | Dessins d'Enfants in $\mathcal{N}=2$ Generalised Quiver Theories: We study Grothendieck's dessins d'enfants in the context of the
$\mathcal{N}=2$ supersymmetric gauge theories in $\left(3+1\right)$ dimensions
with product $SU\left(2\right)$ gauge groups which have recently been
considered by Gaiotto et al. We identify the precise context in which dessins
arise in these theories: they are the so-called ribbon graphs of such theories
at certain isolated points in the Coulomb branch of the moduli space. With this
point in mind, we highlight connections to other work on trivalent dessins,
gauge theories, and the modular group. |
Higher Order Corrections to the Hagedorn Temperature at Strong Coupling: We propose a general formula for higher order corrections to the value of the
Hagedorn temperature of a class of holographic confining gauge theories in the
strong coupling expansion. Inspired by recent proposals in the literature, the
formula combines the sigma-model string expansion with an effective approach.
In particular, it includes the sigma-model contributions to the Hagedorn
temperature at next-to-next-to leading order, which are computed in full
generality. For ${\cal N}=4$ SYM on $S^3$ our result agrees with numerical
field theory estimates with excellent precision. We use the general formula to
predict the value of the Hagedorn temperature for ABJM on $S^2$ and for the
dual of purely RR global $AdS_3$. | Analytical Solution for Bosonic Fields in the FRW Multiply Warped
Braneworld: In this paper we find analytical solutions for the scalar and gauge fields in
the Freedman-Robertson-Walker multiply warped braneworld scenario. With this we
find the precise mass spectra for these fields. We compare these spectra with
that previously found in the literature for the static case. |
Notes on relativistic superfluidity and gauge/string duality: We consider selected topics of relativistic superfluidity within gauge/string
duality. Non-relativistically, the only conservation law relevant to the
hydrodynamic approximation is the energy-momentum conservation.
Relativistically, one has to introduce an extra conserved U(1) current and an
extra three-dimensional scalar field which is condensed. Finding out a proper
U(1) symmetry becomes a crucial point. We emphasize that in dual models there
do arise extra U(1) symmetries associated with wrapping of the strings around
(extra) compact directions in Euclidean space-time. Moreover, if the geometry
associated with an extra compact dimension is cigar-like then the corresponding
U(1) symmetry could well be spontaneously broken. The emerging Goldstone
particle survives in the hydrodynamic limit. A specific point is that the
chemical potential conjugated with the corresponding U(1) charge is vanishing.
Within the standard approach the vanishing chemical potential implies no
superfluidity. We argue that an exotic liquid, introduced recently in the
literature, with vanishing energy density and non-vanishing pressure represents
a viable description of the liquid associated with 3d Goldstone particles in
Euclidean space-time. Since it lives on the stretched membrane, it describes
energy-momentum transport in the deep infrared. We discuss briefly possible
applications to the quark-gluon plasma. | $W$ Strings and Cohomology in Parafermionic Theories: By enforcing locality we relate the cohomology found in parafermionic
theories to that occurring in $W$ strings. This link provides a systematic
method of finding states in the cohomology of $W_{2,s}$ strings. |
Supergravity at One Loop II: Chiral and Yang-Mills Matter: We present the full calculation of the divergent one-loop contribution to the
effective boson Lagrangian for supergravity, including the Yang-Mills sector
and the helicity-odd operators that arise from integration over fermion fields.
The only restriction is on the Yang-Mills kinetic energy normalization
function, which is taken diagonal in gauge indices, as in models obtained from
superstrings. | Exact Spectrum of SU(n) Spin Chain with Inverse-Square Exchange: The spectrum and partition function of a model consisting of SU(n) spins
positioned at the equilibrium positions of a classical Calogero model and
interacting through inverse-square exchange are derived. The energy levels are
equidistant and have a high degree of degeneracy, with several SU(n) multiplets
belonging to the same energy eigenspace. The partition function takes the form
of a q-deformed polynomial. This leads to a description of the system by means
of an effective parafermionic hamiltonian, and to a classification of the
states in terms of "modules" consisting of base-n strings of integers. |
"the Instability of String-Theoretic Black Holes": It is demonstrated that static, charged, spherically--symmetric black holes
in string theory are classically and catastrophically unstable to linearized
perturbations in four dimensions, and moreover that unstable modes appear for
arbitrarily small positive values of the charge. This catastrophic classical
instability dominates and is distinct from much smaller and less significant
effects such as possible quantum mechanical evaporation. The classical
instability of the string--theoretic black hole contrasts sharply with the
situation which obtains for the Reissner--Nordstr\"om black hole of general
relativity, which has been shown by Chandrasekhar to be perfectly stable to
linearized perturbations at the event horizon. | A manifestly gauge invariant exact renormalization group: A manifestly gauge invariant exact renormalization group for pure SU(N)
Yang-Mills theory is proposed, allowing gauge invariant calculations, without
any gauge fixing or ghosts. The necessary gauge invariant regularisation which
implements the effective cutoff, is naturally incorporated by embedding the
theory into a spontaneously broken SU(N|N) super-gauge theory. This guarantees
finiteness to all orders in perturbation theory. |
Massive 4D Abelian 2-Form Theory: Nilpotent Symmetries from the
(Anti-)Chiral Superfield Approach: We derive the off-shell nilpotent (anti-)BRST symmetry transformations by
exploiting the (anti-)chiral superfield approach (ACSA) to
Becchi-Rouet-Stora-Tyutin (BRST) formalism for the four (3+1)-dimensional (4D)
St$\ddot{u}$ckelberg-modified massive Abelian 2-form gauge theory. We perform
exactly similar kind of exercise for the derivation of the off-shell nilpotent
(anti-)co-BRST symmetry transformations, too. In the above derivations, the
symmetry invariant restrictions on the superfields play very important and
decisive roles. To prove the sanctity of the above nilpotent symmetries, we
generalize our 4D ordinary theory (defined on the 4D flat Minkowskian spacetime
manifold) to its counterparts (4,1)-dimensional (anti-)chiral super
sub-manifolds of the (4,2)-dimensional supermanifold which is parameterized by
the superspace coordinates $Z^{M} = (x^{\mu},\theta, \bar{\theta} ) $ where
$x^\mu ( \mu = 0,1,2,3 )$ are the bosonic coordinates and a pair of
Grassmannian variables $(\theta, \bar{\theta})$ are fermionic: ($\theta^{2} =
\bar{\theta^{2}} = 0, \,\,\theta\,\bar{\theta} +\bar{\theta}\,\theta = 0$) in
nature. One of the novel observations of our present endeavor is the derivation
of the Curci-Ferrari (CF) type restrictions from the requirement of the
symmetry invariance of the coupled (but equivalent) Lagrangian densities for
our theory within the framework of ACSA to BRST formalism. We also exploit the
standard techniques of ACSA to capture the off-shell nilpotency and absolute
anticommutativity of the conserved (anti-)BRST as well as the (anti-)co-BRST
charges. In a subtle manner, the proof of the absolute anticommutativity of the
above conserved charges also implies the existence of the appropriate CF-type
restrictions on our theory. | Infrared enhancement of supersymmetry in four dimensions: We study a recently-found class of RG flows in four dimensions exhibiting
enhancement of supersymmetry in the infrared, which provides a lagrangian
description of several strongly-coupled N=2 SCFTs. The procedure involves
starting from a N=2 SCFT, coupling a chiral multiplet in the adjoint
representation of the global symmetry to the moment map of the SCFT and turning
on a nilpotent expectation value for this chiral. In this note we show that,
combining considerations based on 't Hooft anomaly matching and basic results
about the N=2 superconformal algebra, it is possible to understand in detail
the mechanism underlying this phenomenon and formulate a simple criterion for
supersymmetry enhancement which allows us to bypass the analysis with
a-maximization. As a byproduct, we propose an algorithm to identify a
lagrangian UV completion of a given N=2 SCFT under an RG flow of this type,
provided there is one. |
Dynamical Symmetry Breaking and Static Limits of Extended
Super-Yang-Mills Theories: A non-Seiberg-Wittian Approach: From a supersymmetry covariant source extension of N=2 SYM we study
non-trivial thermodynamical limits thereof. Using an argument by one of us
about the solution of the strong CP problem and the uniqueness of the QCD
ground state we find that the dependence of the effective potential on the
defining field operators is severely restricted. In contrast to the solution by
Seiberg and Witten an acceptable infrared behavior only exists for broken
supersymmetry while the gauge symmetry remains unbroken. | First Law of p-brane Thermodynamics: We study the physical process version and the equilibrium state version of
the first law of thermodynamics for a charged p-brane. the general setting for
our investigations is (n+p+1)-dimensional Einstein dilaton gravity with (p+2)
strength form fields. |
On the `simple' form of the gravitational action and the
self-interacting graviton: The so-called $\Gamma\Gamma$-form of the gravitational Lagrangian, long known
to provide its most compact expression as well as the most efficient generation
of the graviton vertices, is taken as the starting point for discussing General
Relativity as a theory of the self-interacting graviton. A straightforward but
general method of converting to a covariant formulation by the introduction of
a reference metric is given. It is used to recast the Einstein field equation
as the equation of motion of a spin-2 particle interacting with the canonical
energy-momentum tensor symmetrized by the standard Belinfante method applicable
to any field carrying nonzero spin. This represents the graviton field equation
in a form complying with the precepts of standard field theory. It is then
shown how representations based on other, at face value completely unrelated
definitions of energy-momentum (pseudo)tensors are all related by the addition
of appropriate superpotential terms. Specifically, the superpotentials are
explicitly constructed which connect to: i) the common definition consisting
simply of the nonlinear part of the Einstein tensor; ii) the Landau-Lifshitz
definition. | 5d and 4d SCFTs: Canonical Singularities, Trinions and S-Dualities: Canonical threefold singularities in M-theory and Type IIB string theory give
rise to superconformal field theories (SCFTs) in 5d and 4d, respectively. In
this paper, we study canonical hypersurface singularities whose resolutions
contain residual terminal singularities and/or 3-cycles. We focus on a certain
class of `trinion' singularities which exhibit these properties. In Type IIB,
they give rise to 4d $\mathcal{N}=2$ SCFTs that we call $D_p^b(G)$-trinions,
which are marginal gaugings of three SCFTs with $G$ flavor symmetry. In order
to understand the 5d physics of these trinion singularities in M-theory, we
reduce these 4d and 5d SCFTs to 3d $\mathcal{N}=4$ theories, thus determining
the electric and magnetic quivers (or, more generally, quiverines). In
M-theory, residual terminal singularities give rise to free sectors of massless
hypermultiplets, which often are discretely gauged. These free sectors appear
as `ugly' components of the magnetic quiver of the 5d SCFT. The 3-cycles in the
crepant resolution also give rise to free hypermultiplets, but their physics is
more subtle, and their presence renders the magnetic quiver `bad'. We propose a
way to redeem the badness of these quivers using a class $\mathcal{S}$
realization. We also discover new S-dualities between different
$D_p^b(G)$-trinions. For instance, a certain $E_8$ gauging of the $E_8$
Minahan-Nemeschansky theory is S-dual to an $E_8$-shaped Lagrangian quiver
SCFT. |
Open string models with Scherk-Schwarz SUSY breaking: We apply the well-known Scherk-Schwarz supersymmetry breaking mechanism in an
open string context. We construct a new Z_3\times Z_3^\prime model, containing
only D9-branes, and rederive from a more geometric perspective the known
Z_6^\prime\times Z_2^\prime model, containing D9, D5 and \bar D 5 branes. We
show recent results about the study of quantum instability of these models. | Instanton Counting and Dielectric Branes: We consider the Hanany-Witten type brane configuration in a background of RR
4-form field strength and examine the behavior of Euclidean D0-branes
propagating between two NS5-branes. We evaluate the partition function of the
D0-branes and show that it coincides with the Nekrasov partition function of
instantons for four-dimensional N=2 supersymmetric Yang-Mills theory. In this
analysis, the Myers effect plays a crucial role. We apply the same method to
the brane configuration realizing four-dimensional N=2 theory with
hypermultiplets in the fundamental representation and reproduce the
corresponding Nekrasov partition function. |
Calibrated Geometries and Non Perturbative Superpotentials in M-Theory: We consider non perturbative effects in M-theory compactifications on a
seven-manifold of G_2 holonomy arising from membranes wrapped on supersymmetric
three-cycles. When membranes are wrapped on associative submanifolds they
induce a superpotential that can be calculated using calibrated geometry. This
superpotential is also derived from compactification on a seven-manifold, to
four dimensional Anti-de Sitter spacetime, of eleven dimensional supergravity
with non vanishing expectation value of the four-form field strength. | Even spin $\mathcal{N}=4$ holography: A two-dimensional Sp($2N$) vector model with small $\mathcal{N}=4$
superconformal symmetry is formulated, and its chiral algebra is shown to be
generated by superprimary fields of even conformal weight. This vector model is
the large level limit of a coset theory with large $\mathcal{N}=4$, whose
proposed AdS$_3$ dual is a minimal Vasiliev higher spin theory with gauge
algebra generated by fields of even spin. The relation of this vector model to
the symmetric product orbifold, dual to tensionless strings in AdS$_3$ $\times$
S$^3$ $\times$ $\mathbb{T}^4$, is also worked out. |
Unconstrained SU(2) Yang-Mills Theory with Topological Term in the
Long-Wavelength Approximation: The Hamiltonian reduction of SU(2) Yang-Mills theory for an arbitrary \theta
angle to an unconstrained nonlocal theory of a self-interacting positive
definite symmetric 3 \times 3 matrix field S(x) is performed. It is shown that,
after exact projection to a reduced phase space, the density of the Pontryagin
index remains a pure divergence, proving the \theta independence of the
unconstrained theory obtained. An expansion of the nonlocal kinetic part of the
Hamiltonian in powers of the inverse coupling constant and truncation to lowest
order, however, lead to violation of the \theta independence of the theory. In
order to maintain this property on the level of the local approximate theory, a
modified expansion in the inverse coupling constant is suggested, which for a
vanishing \theta angle coincides with the original expansion. The corresponding
approximate Lagrangian up to second order in derivatives is obtained, and the
explicit form of the unconstrained analogue of the Chern-Simons current linear
in derivatives is given. Finally, for the case of degenerate field
configurations S(x) with rank|S| = 1, a nonlinear \sigma-type model is
obtained, with the Pontryagin topological term reducing to the Hopf invariant
of the mapping from the three-sphere S^3 to the unit two-sphere S^2 in the
Whitehead form. | $W_\infty$ Algebra and Geometric Formulation of QCD$_2$: We review the gauge invariant formulation of 2-dim. QCD. We show that the
non-linear gauge invariant phase space is the coset $W_\infty/W_{+\infty}\times
W_{-\infty}$ ,which is specified by the $N=\infty$ master-field of this model.
The meson fields correspond to the local coordinates of the coset. We comment
on the stringy collective coordinates of the solitons (baryons) in this model. |
Quantum Symmetry Reduction for Diffeomorphism Invariant Theories of
Connections: Given a symmetry group acting on a principal fibre bundle, symmetric states
of the quantum theory of a diffeomorphism invariant theory of connections on
this fibre bundle are defined. These symmetric states, equipped with a scalar
product derived from the Ashtekar-Lewandowski measure for loop quantum gravity,
form a Hilbert space of their own. Restriction to this Hilbert space yields a
quantum symmetry reduction procedure in the framework of spin network states
the structure of which is analyzed in detail. Three illustrating examples are
discussed: Reduction of 3+1 to 2+1 dimensional quantum gravity, spherically
symmetric electromagnetism and spherically symmetric gravity. | Attractor Flows from Defect Lines: Deforming a two dimensional conformal field theory on one side of a trivial
defect line gives rise to a defect separating the original theory from its
deformation. The Casimir force between these defects and other defect lines or
boundaries is used to construct flows on bulk moduli spaces of CFTs. It turns
out, that these flows are constant reparametrizations of gradient flows of the
g-functions of the chosen defect or boundary condition. The special flows
associated to supersymmetric boundary conditions in N=(2,2) superconformal
field theories agree with the attractor flows studied in the context of black
holes in N=2 supergravity. |
On non-stationary Lamé equation from WZW model and spin-1/2 XYZ chain: We study the link between WZW model and the spin-1/2 XYZ chain. This is
achieved by comparing the second-order differential equations from them. In the
former case, the equation is the Ward-Takahashi identity satisfied by one-point
toric conformal blocks. In the latter case, it arises from Baxter's TQ
relation. We find that the dimension of the representation space w.r.t. the
V-valued primary field in these conformal blocks gets mapped to the total
number of chain sites. By doing so, Stroganov's "The Importance of being Odd"
(cond-mat/0012035) can be consistently understood in terms of WZW model
language. We first confirm this correspondence by taking a trigonometric limit
of the XYZ chain. That eigenstates of the resultant two-body Sutherland model
from Baxter's TQ relation can be obtained by deforming toric conformal blocks
supports our proposal. | On the Tree-Level S-Matrix of Yang-Mills Theory: In this note we further investigate the procedure for computing tree-level
amplitudes in Yang-Mills theory from connected instantons in the B-model on
P^{3|4}, emphasizing that the problem of calculating Feynman diagrams is recast
into the problem of finding solutions to a certain set of algebraic equations.
We show that the B-model correctly reproduces all 6-particle amplitudes,
including non-MHV amplitudes with three negative and three positive helicity
gluons. As a further check, we also show that n-particle amplitudes obtained
from the B-model obey a number of properties required of gauge theory, such as
parity symmetry (which relates an integral over degree d curves to one over
degree n-d-2 curves) and the soft and collinear gluon poles. |
Unruh radiation produced by a uniformly accelerating charged particle in
thermal random motions: In this study, we investigate the signature of the Unruh effect in quantum
radiation from an accelerated charged particle interacting with vacuum
fluctuations. Because a charged particle in uniformly accelerated motion
exhibits thermal random motion around the classical trajectory because of the
Unruh effect, its quantum radiation might be termed Unruh radiation. We show
that the energy flux of the quantum radiation is negative and that its
amplitude is smaller than the classical Larmor radiation by a factor of $a/m$,
where $a$ is the acceleration and $m$ is the mass of the particle. The total
radiation flux of the classical Larmor radiation and the quantum radiation is
positive; therefore, the quantum radiation appears to suppress the total
radiation. Interestingly, the results are consistent with the prediction for
the quantum correction to classical Larmor radiation, which were obtained using
a different approach. | A Grassmannian Etude in NMHV Minors: Arkani-Hamed, Cachazo, Cheung and Kaplan have proposed a Grassmannian
formulation for the S-matrix of N=4 Yang-Mills as an integral over link
variables. In parallel work, the connected prescription for computing tree
amplitudes in Witten's twistor string theory has also been written in terms of
link variables. In this paper we extend the six- and seven-point results of
arXiv:0909.0229 and arXiv:0909.0499 by providing a simple analytic proof of the
equivalence between the two formulas for all tree-level NMHV superamplitudes.
Also we note that a simple deformation of the connected prescription integrand
gives directly the ACCK Grassmannian integrand in the limit when the
deformation parameters equal zero. |
Dark energy from modified gravity with Lagrange multipliers: We study scalar-tensor theory, k-essence and modified gravity with Lagrange
multiplier constraint which role is to reduce the number of degrees of freedom.
Dark Energy cosmology of different types ($\Lambda$CDM, unified inflation with
DE, smooth non-phantom/phantom transition epoch) is reconstructed in such
models. It is shown that mathematical equivalence between scalar theory and
$F(R)$ gravity is broken due to presence of constraint. The cosmological
dynamics of $F(R)$ gravity is modified by the second $F_2(R)$ function dictated
by the constraint. Dark Energy cosmology is defined by this function while
standard $F_1(R)$ function is relevant for local tests (modification of newton
regime). A general discussion on the role of Lagrange multipliers to make
higher-derivative gravity canonical is developed. | Holographic integration of $T \bar{T}$ and $J \bar{T}$ via $O(d,d)$: Prompted by the recent developments in integrable single trace $T \bar{T}$
and $J \bar{T}$ deformations of 2d CFTs, we analyse such deformations in the
context of $AdS_3/CFT_2$ from the dual string worldsheet CFT viewpoint. We
observe that the finite form of these deformations can be recast as $O(d,d)$
transformations, which are an integrated form of the corresponding Exactly
Marginal Deformations (EMD) in the worldsheet Wess-Zumino-Witten (WZW) model,
thereby generalising the Yang-Baxter class that includes TsT. Furthermore, the
equivalence between $O(d,d)$ transformations and marginal deformations of WZW
models, proposed by Hassan and Sen for Abelian chiral currents, can be extended
to non-Abelian chiral currents to recover a well-known constraint on EMD in the
worldsheet CFT. We also argue that such EMD are also solvable from the
worldsheet theory viewpoint. |
Roper resonances and quasi-normal modes of Skyrmions: Radial vibrations of charge one hedgehog Skyrmions in the full Skyrme model
are analysed. We investigate how the properties of the lowest resonance modes
(quasi normal modes) - their frequencies and widths - depend on the form of the
potential (value of the pion mass as well as the addition of further
potentials) and on the inclusion of the sextic term. Then we consider the
inverse problem, where certain values for the frequencies and widths are
imposed, and the field theoretic Skyrme model potential giving rise to them is
reconstructed. This latter method allows to reproduce the physical Roper
resonances, as well as further physical properties of nucleons, with high
precision. | Conformal $(p,q)$ supergeometries in two dimensions: We propose a superspace formulation for conformal $(p,q)$ supergravity in two
dimensions as a gauge theory of the superconformal group $\mathsf{OSp}_0 (p|2;
{\mathbb R} ) \times \mathsf{OSp}_0 (q|2; {\mathbb R} )$ with a flat
connection. Upon degauging of certain local symmetries, this conformal
superspace is shown to reduce to a conformally flat $\mathsf{SO}(p) \times
\mathsf{SO}(q)$ superspace with the following properties: (i) its structure
group is a direct product of the Lorentz group and $\mathsf{SO}(p) \times
\mathsf{SO}(q)$; and (ii) the residual local scale symmetry is realised by
super-Weyl transformations with an unconstrained real parameter. As an
application of the formalism, we describe ${\cal N}$-extended AdS superspace as
a maximally symmetric supergeometry in the $p=q \equiv \cal N$ case. If at
least one of the parameters $p$ or $q$ is even, alternative superconformal
groups and, thus, conformal superspaces exist. In particular, if $p = 2n$, a
possible choice of the superconformal group is $\mathsf{SU}(1,1|n) \times
\mathsf{OSp}_0 (q|2; {\mathbb R} )$, for $n \neq 2$, and $\mathsf{PSU}(1,1|2)
\times \mathsf{OSp}_0 (q|2; {\mathbb R} )$, when $n=2$. In general, a conformal
superspace formulation is associated with a supergroup $ G = G_L \times G_R$,
where the simple supergroups $G_L$ and $G_R$ can be any of the extended
superconformal groups, which were classified by G\"unaydin, Sierra and
Townsend. Degauging the corresponding conformal superspace leads to a
conformally flat $H_L \times H_R$ superspace, where $H_L $ ($H_R$) is the
$R$-symmetry subgroup of $G_L$ ($G_R$). Additionally, for the $p,q \leq 2$
cases we propose composite primary multiplets which generate the Gauss-Bonnet
invariant and supersymmetric extensions of the Fradkin-Tseytlin term. |
On a semiclassical formula for non-diagonal matrix elements: Let $H(\hbar)=-\hbar^2d^2/dx^2+V(x)$ be a Schr\"odinger operator on the real
line, $W(x)$ be a bounded observable depending only on the coordinate and $k$
be a fixed integer. Suppose that an energy level $E$ intersects the potential
$V(x)$ in exactly two turning points and lies below
$V_\infty=\liminf_{|x|\to\infty} V(x)$. We consider the semiclassical limit
$n\to\infty$, $\hbar=\hbar_n\to0$ and $E_n=E$ where $E_n$ is the $n$th
eigen-energy of $H(\hbar)$. An asymptotic formula for $<{}n|W(x)|n+k>$, the
non-diagonal matrix elements of $W(x)$ in the eigenbasis of $H(\hbar)$, has
been known in the theoretical physics for a long time. Here it is proved in a
mathematically rigorous manner. | BPS/CFT correspondence II: Instantons at crossroads, Moduli and
Compactness Theorem: Gieseker-Nakajima moduli spaces $M_{k}(n)$ parametrize the charge $k$
noncommutative $U(n)$ instantons on ${\bf R}^{4}$ and framed rank $n$ torsion
free sheaves $\mathcal{E}$ on ${\bf C\bf P}^{2}$ with ${\rm
ch}_{2}({\mathcal{E}}) = k$. They also serve as local models of the moduli
spaces of instantons on general four-manifolds. We study the generalization of
gauge theory in which the four dimensional spacetime is a stratified space $X$
immersed into a Calabi-Yau fourfold $Z$. The local model ${\bf M}_{k}({\vec
n})$ of the corresponding instanton moduli space is the moduli space of charge
$k$ (noncommutative) instantons on origami spacetimes. There, $X$ is modelled
on a union of (up to six) coordinate complex planes ${\bf C}^{2}$ intersecting
in $Z$ modelled on ${\bf C}^{4}$. The instantons are shared by the collection
of four dimensional gauge theories sewn along two dimensional defect surfaces
and defect points. We also define several quiver versions ${\bf M}_{\bf
k}^{\gamma}({\vec{\bf n}})$ of ${\bf M}_{k}({\vec n})$, motivated by the
considerations of sewn gauge theories on orbifolds ${\bf C}^{4}/{\Gamma}$.
The geometry of the spaces ${\bf M}_{\bf k}^{\gamma}({\vec{\bf n}})$, more
specifically the compactness of the set of torus-fixed points, for various
tori, underlies the non-perturbative Dyson-Schwinger identities recently found
to be satisfied by the correlation functions of $qq$-characters viewed as local
gauge invariant operators in the ${\mathcal{N}}=2$ quiver gauge theories.
The cohomological and K-theoretic operations defined using ${\bf M}_{k}({\vec
n})$ and their quiver versions as correspondences provide the geometric
counterpart of the $qq$-characters, line and surface defects. |
Integrability and duality in two-dimensional QCD: We consider bosonized $QCD_2$, and prove that after rewritting the theory in
terms of gauge invariant fields, there exists an integrability condition valid
for the quantum theory as well. Furthermore, performing a duality type
transformation we obtain an appropriate action for the description of the
strong coupling limit, which is still integrable. We also prove that the model
displays a complicated set of constraints, restricting the dynamics of part of
the theory, but which are necessary to maintain the positive metric Hilbert
space. | Gravity, Horizons and Open EFTs: Wilsonian effective theories exploit hierarchies of scale to simplify the
description of low-energy behaviour and play as central a role for gravity as
for the rest of physics. They are useful both when hierarchies of scale are
explicit in a gravitating system and more generally for understanding precisely
what controls the size of quantum corrections in gravitational systems. But
effective descriptions are also relevant for open systems (e.g. fluid mechanics
as a long-distance description of statistical systems) for which the
`integrating out' of unobserved low-energy degrees of freedom complicate a
straightforward application of Wilsonian methods. Observations performed only
on one side of an apparent horizon provide examples where open system
descriptions also arise in gravitational physics. This chapter describes some
early adaptations of Open Effective Theories (i.e. techniques for exploiting
hierarchies of scale in open systems) in gravitational settings. Besides
allowing the description of new types of phenomena (such as decoherence) these
techniques also have an additional benefit: they sometimes can be used to resum
perturbative expansions at late times and thereby to obtain controlled
predictions in a regime where perturbative predictions otherwise generically
fail. |
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