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Probing F-theory With Branes: Last week, A. Sen found an explicit type I string compactification dual to
the eight-dimensional F-theory construction with SO(8)^4 nonabelian gauge
symmetry. He found that the perturbations around the enhanced symmetry point
were described by the mathematics of the solution of N=2, d=4 SU(2) gauge
theory with four flavors, and argued more generally that global symmetry
enhancement in CN=2, d=4 gauge theories corresponded to gauge symmetry
enhancement in F-theory. We show that these N=2, d=4 gauge theories have a
physical interpretation in the theory. They are the world-volume theories of
3-branes parallel to the 7-branes. They can be used to probe the structure of
the exact quantum F-theory solutions. On the Higgs branch of the moduli space,
the objects are equivalent to finite size instantons in the 7-brane gauge
theory. | A symplectic covariant formulation of special Kahler geometry in
superconformal calculus: We present a formulation of the coupling of vector multiplets to N=2
supergravity which is symplectic covariant (and thus is not based on a
prepotential) and uses superconformal tensor calculus. We do not start from an
action, but from the combination of the generalised Bianchi identities of the
vector multiplets in superspace, a symplectic definition of special Kahler
geometry, and the supersymmetric partners of the corresponding constraints.
These involve the breaking to super-Poincare symmetry, and lead to on-shell
vector multiplets. This symplectic approach gives the framework to formulate
vector multiplet couplings using a weaker defining constraint for special
Kahler geometry, which is an extension of older definitions of special Kahler
manifolds for some cases with only one vector multiplet. |
Confinement of spinless particles by Coulomb potentials in
two-dimensional space-time: The problem of confinement of spinless particles in 1+1 dimensions is
approached with a linear potential by considering a mixing of Lorentz vector
and scalar couplings. Analytical bound-states solutions are obtained when the
scalar coupling is of sufficient intensity compared to the vector coupling. | Fluid/p-form duality: In this study, we demonstrate that an inviscid fluid in a near-equilibrium
state, when viewed in the Lagrangian picture in d+1 spacetime dimensions, can
be reformulated as a (d-1)-form gauge theory. We construct a fluid/p-form
dictionary and show that volume-preserving diffeomorphisms on the fluid side
manifest as a U(1) gauge symmetry on the {(p+1)-form} gauge theory side.
{Intriguingly, Kelvin's circulation theorem and the mass continuity equation
respectively appear as the Gauss law and the Bianchi identity on the gauge
theory side.} Furthermore, we show that at the level of the sources, the
vortices in the fluid side correspond to the p-branes in the gauge theory side.
We also consider fluid mechanics in the presence of boundaries and examine the
boundary symmetries and corresponding charges from both the fluid and gauge
theory perspectives. |
Susy Theories and QCD: Numerical Approaches: We review on-shell and unitarity methods and discuss their application to
precision predictions for LHC physics. Being universal and numerically robust,
these methods are straight-forward to automate for next-to-leading-order
computations within Standard Model and beyond. Several state-of-the-art results
including studies of W/Z+3-jet and W+4-jet production have explicitly
demonstrated the effectiveness of the unitarity method for describing
multi-parton scattering. Here we review central ideas needed to obtain
efficient numerical implementations. This includes on-shell loop-level
recursions, the unitarity method, color management and further refined tricks. | The thermodynamics of the Hagedorn mass spectrum: No bootstrap assumption is needed to derive the exponential growth of the
Hagedorn hadron mass spectrum: It is a consequence of the second law applied to
a relativistic gas, and the relativistic equivalence between inertial mass and
its heat content. The Hagedorn temperature occurs in the limit as the number of
particles and their internal energy diverge such that their ratio remains
constant. The divergences in the $N$ particle entropy, energy, and free energy
result when this condition is imposed upon a mixture of ideal gases, one
conserving particle number and the other not. The analogy with a droplet in the
presence of vapor explains why the pressure of the droplet continues to
increase as the temperature rises finally leading to its break up when the
Hagedorn temperature is reached. The adiabatic condition relating the particle
volume to the Hagedorn temperature is asymptotic. Since it is a limiting
temperature, and not a critical one, there can be no phase transition of
whatever kind, and the original density of states used to derive such a phase
transition is not thermodynamically admissible because its partition function
does not exist. |
AdS$_3$ vacua and RG flows in three dimensional gauged supergravities: We study $AdS_3$ supersymmetric vacua in N=4 and N=8, three dimensional
gauged supergravities, with scalar manifolds $(\frac{SO(4,4)}{SO(4)\times
SO(4)})^2$ and $\frac{SO(8,8)}{SO(8)\times SO(8)}$, non-semisimple Chern-Simons
gaugings $SO(4)\ltimes {\bf R}^6$ and $(SO(4)\ltimes {\bf R}^6)^2$,
respectively. These are in turn equivalent to SO(4) and $SO(4)\times SO(4)$
Yang-Mills theories coupled to supergravity. For the N=4 case, we study
renormalization group flows between UV and IR $AdS_3$ vacua with the same
amount of supersymmetry: in one case, with (3,1) supersymmetry, we can find an
analytic solution whereas in another, with (2,0) supersymmetry, we give a
numerical solution. In both cases, the flows turn out to be v.e.v. flows, i.e.
they are driven by the expectation value of a relevant operator in the dual
$SCFT_2$. These provide examples of v.e.v. flows between two $AdS_3$ vacua
within a gauged supergravity framework. | Bootstrapping bulk locality. Part I: Sum rules for AdS form factors: The problem of constructing local bulk observables from boundary CFT data is
of paramount importance in holography. In this work, we begin addressing this
question from a modern bootstrap perspective. Our main tool is the boundary
operator expansion (BOE), which holds for any QFT in AdS. Following Kabat and
Lifschytz, we argue that the BOE is strongly constrained by demanding locality
of correlators involving bulk fields. Focusing on 'AdS form factors' of one
bulk and two boundary insertions, we reformulate these locality constraints as
a complete set of sum rules on the BOE data. We show that these sum rules lead
to a manifestly local representation of form factors in terms of 'local
blocks'. The sum rules are valid non-perturbatively, but are especially
well-adapted for perturbative computations in AdS where they allow us to
bootstrap the BOE data in a systematic fashion. Finally, in the flat space
limit, we show that the AdS form factor reduces to an ordinary QFT form factor.
We provide a phase shift formula for it in terms of the BOE and CFT data. In
two dimensions, this formula makes manifest Watson's equations for integrable
form factors under certain extremality assumptions on the CFT. We discuss the
eventual modifications of our formalism to account for dressed operators in
AdS. |
On the Brane Configuration of $N=(4,4)$ 2D supersymmetric gauge theory: We study two dimensional $N=(4,4)$ supersymmetric gauge theories with various
gauge groups and various hypermultiplets in the fundamental as well as
bi-fundamental and adjoint representations. They have " mirror theories " which
become equivalent to them at the strong coupling. The theory with one
fundamental and one adjoint has a Higgs branch which is parametrized by the
adjoint matter. We also consider theories which involve an orientifold plane.
The brane realization of the Matrix theory formulation of NS 5-branes in Type
II string theories is also considered. | Vortex Structure in Charged Condensate: We study magnetic fields in the charged condensate that we have previously
argued should be present in helium-core white dwarf stars. We show that below a
certain critical value the magnetic field is entirely expelled from the
condensate, while for larger values it penetrates the condensate within
flux-tubes that are similar to Abrikosov vortex lines; yet higher fields lead
to the disruption of the condensate. We find the solution for the vortex lines
in both relativistic and nonrelativistic theories that exhibit the charged
condensation. We calculate the energy density of the vortex solution and the
values of the critical magnetic fields. The minimum magnetic field required for
vortices to penetrate the helium white dwarf cores ranges from roughly 10^7 to
10^9 Gauss. Fields of this strength have been observed in white dwarfs. We also
calculate the London magnetic field due to the rotation of a dwarf star and
show that its value is rather small. |
Revisiting Atiyah-Hitchin manifold in the generalized Legendre transform: We revisit construction of the Atiyah-Hitchin manifold in the generalized
Legendre transform approach. This is originally studied by Ivanov and Rocek and
is subsequently investigated more by Ionas, in the latter of which the explicit
forms of the K\"ahler potential and the K\"ahler metric are calculated. There
is a difference between the former and the latter. In the generalized Legendre
transform approach, a K\"ahler potential is constructed from the contour
integration of one function with holomorphic coordinates. The choice of the
contour in the latter is different from the former's one, whose difference may
yield a discrepancy in the K\"ahler potential and eventually in the K\"ahler
metric. We show that the former only gives the real K\"ahler potential, which
is consistent with its definition, while the latter yields the complex one. We
derive the K\"ahler potential and the metric for the Atiyah-Hitchin manifold in
terms of holomorphic coordinates for the contour considered by Ivanov and
Ro\v{c}ek for the first time. | Extension of the Poincaré Symmetry and Its Field Theoretical
Implementation: We define a new algebraic extension of the Poincar\'e symmetry; this algebra
is used to implement a field theoretical model. Free Lagrangians are explicitly
constructed; several discussions regarding degrees of freedom, compatibility
with Abelian gauge invariance etc. are done. Finally we analyse the
possibilities of interaction terms for this model. |
Tachyons and (non)vanishing scalar masses in six-dimensional gauge
theories with flux compactification: In this paper, we study the possibility to obtain a massless scalar boson for
which quantum corrections to the mass vanish at all loop-order, which has been
recently understood to be due to a shift symmetry making the scalar a Goldstone
boson. We present the effective four-dimensional Lagrangian of a
six-dimensional gauge theory compactified on a torus with magnetic flux.
Because of this magnetic field, a symmetry of translation in the extra
dimensions is broken which implies the existence of a massless scalar boson. We
then explicitly check that a model with two U(1) gauge symmetries contains a
scalar boson with finite mass but protected from large quantum corrections.
Finally, we study the presence of tachyons in the model with non-abelian gauge
symmetry. In particular, we propose a way to eliminate these tachyons and we
compute the full mass spectrum of the scalars in this theory. Finally, we show
that our method preserve the chirality of fermions in the model. | Recovery of Dirac Equations from Their Solutions: We deal with quantum field theory in the restriction to external Bose fields.
Let $(i\gamma^\mu\partial_\mu - \mathcal{B})\psi=0$ be the Dirac equation. We
prove that a non-quantized Bose field $\mathcal{B}$ is a functional of the
Dirac field $\psi$, whenever this $\psi$ is strictly canonical. Performing the
trivial verification for the $\mathcal{B} := m = $ constant which yields the
free Dirac field, we also prepare the tedious verifications for all
$\mathcal{B}$ which are non-quantized and static. Such verifications must not
be confused, however, with the easy and rigorous proof of our formula, which is
shown in detail. |
Harmonic Space, Self-Dual Yang Mills and the $N=2$ String: The geometrical structure and the quantum properties of the recently proposed
harmonic space action describing self-dual Yang-Mills (SDYM) theory are
analyzed. The geometrical structure that is revealed is closely related to the
twistor construction of instanton solutions. The theory gets no quantum
corrections and, despite having SDYM as its classical equation of motion, its S
matrix is trivial. It is therefore NOT the theory of the N=2 string. We also
discuss the 5-dimensional actions that have been proposed for SDYM. | A Simple System For Coleman-De Luccia Transitions: This paper presents a simple framework that organizes thin-wall Coleman-De
Luccia instantons based on the Euclidean geometries of their original and
tunneled vacuum patches. We consider all a priori allowed vacuum pairs (de
Sitter or Anti-de Sitter for either patch, Minkowski can be obtained as a limit
of either), and $O(4)$-symmetric thin-wall geometries connecting them. For each
candidate bounce geometry, either a condition under which a solution to the
$O(4)$-invariant equations of motion exists is derived, or the would-be vacuum
transition is ruled out. For the parameter regimes in which a solution exists,
we determine whether expansion/contraction of the bounce supplies a negative
mode in the second variation of the Euclidean action. All results follow from
the monotonicity of a single function. |
Note on generalized gravitational entropy in Lovelock gravity: The recently proposed gravitational entropy generalize the usual black hole
entropy to Euclidean solutions without U(1) symmetry in the framework of
Einstein gravity. The entropy of such smooth configuration is given by the area
of minimal surface, therefore explaining the Ryu-Takayanagi formula of
holographic entanglement entropy. In this note we investigate the generalized
gravitational entropy for general Lovelock gravity in arbitrary dimensions. We
use the replica trick and consider the Euclidean bulk spacetime with conical
singularity localized at a codimension two surface. We obtain a constraint
equation for the surface by requiring the bulk equation of motion to be of good
behavior. When the bulk spacetime is maximally symmetric, the constraints show
that the traces of the extrinsic curvatures of the surface are vanishing, i.e.
the surface has to be geometrically a minimal surface. However the constraint
equation cannot be obtained by the variation of the known functional for
holographic entanglement entropy in Lovelock gravity. | Fermi Liquids from D-Branes: We discuss finite density configurations on probe D-branes, in the presence
of worldvolume fermions. To this end we consider a phenomenological model whose
bosonic sector is governed by the DBI action, and whose charged sector is
purely fermionic. In this model, we demonstrate the existence of a compact
worldvolume embedding, stabilized by a Fermi surface on the D- brane. The
finite density state in the boundary QFT is a Fermi-like liquid. We comment on
the possibility of realizing non-Fermi liquids in this setup. |
Optimisation of the exact renormalisation group: A simple criterion to optimise coarse-grainings for exact renormalisation
group equations is given. It is aimed at improving the convergence of
approximate solutions of flow equations. The optimisation criterion is generic,
as it refers only to the coarse-grained propagator at vanishing field. In
physical terms, it is understood as an optimisation condition for amplitude
expansions. Alternatively, it can be interpreted as the requirement to move
poles of threshold functions away from the physical region. The link to
expansions in field amplitudes is discussed as well. Optimal parameters are
given explicitly for a variety of different coarse-grainings. As a by-product
it is found that the sharp cut-off regulator does not belong to the class of
such optimal coarse-grainings, which explains the poor convergence of amplitude
expansions based on it. | BRST Analysis of QCD_2 as a Perturbed WZW Theory: Integrability of Quantum Chromodynamics in 1+1 dimensions has recently been
suggested by formulating it as a perturbed conformal Wess-Zumino-Witten Theory.
The present paper further elucidates this formulation, by presenting a detailed
BRST analysis. |
Euclidean solutions of Yang-Mills theory coupled to a massive dilaton: The Euclidean version of Yang-Mills theory coupled to a massive dilaton is
investigated. Our analytical and numerical results imply existence of infinite
number of branches of globally regular, spherically symmetric, dyonic type
solutions for any values of dilaton mass $m$. Solutions on different branches
are labelled by the number of nodes of gauge field amplitude $W$. They have
finite reduced action and provide new saddle points in the Euclidean path
integral. | Magnetic Branes Supported by Nonlinear Electromagnetic Field: Considering the nonlinear electromagnetic field coupled to Einstein gravity
in the presence of cosmological constant, we obtain a new class of
$d$-dimensional magnetic brane solutions. This class of solutions yields a
spacetime with a longitudinal nonlinear magnetic field generated by a static
source. These solutions have no curvature singularity and no horizons but have
a conic geometry with a deficit angle $\delta \phi$. We investigate the effects
of nonlinearity on the metric function and deficit angle and also find that for
the special range of the nonlinear parameter, the solutions are not asymptotic
AdS. We generalize this class of solutions to the case of spinning magnetic
solutions, and find that when one or more rotation parameters are nonzero, the
brane has a net electric charge which is proportional to the magnitude of the
rotation parameters. Then, we use the counterterm method and compute the
conserved quantities of these spacetimes. Finally, we obtain a constrain on the
nonlinear parameter, such that the nonlinear electromagnetic field is
conformally invariant. |
Non-Unitary Evolution in the General Extended EFT of Inflation & Excited
Initial States: I study the "general" case that arises in the Extended Effective Field Theory
of Inflation (gEEFToI), in which the coefficients of the sixth order polynomial
dispersion relation depend on the physical wavelength of the fluctuation mode,
hence they are time-dependent. At arbitrarily short wavelengths the unitarity
is lost for each mode. Depending on the values of the gEEFToI parameters in the
unitary gauge action, two scenarios can arise: in one, the coefficients of the
polynomial become singular, flip signs at some physical wavelength and
asymptote to a constant value as the wavelength of the mode is stretched to
infinity. Starting from the WKB vacuum, the two-point function is essentially
singular in the infinite IR limit. In the other case, the coefficients of the
dispersion relation evolve monotonically from zero to a constant value in the
infinite IR. In order to have a finite power spectrum starting from the vacuum
in this case, the mode function has to be an eigensolution of the Confluent
Heun (CH) equation, which leads to a very confined parameter space for gEEFToI.
Finally, I look at a solution of the CH equation which is regular in the
infinite IR limit and yields a finite power spectrum in either scenario. I
demonstrate that this solution asymptotes to an excited state in past infinity
in both cases. The result is interpreted in the light of the loss of unitarity
for very small wavelengths. The outcome of such a non-unitary phase evolution
should prepare each mode in the excited initial state that yields a finite
two-point function for all the parameter space. This will be constraining of
the new physics that UV completes such scenarios. | Resurgence and Lefschetz thimble in 3d N=2 supersymmetric Chern-Simons
matter theories: We study a certain class of supersymmetric (SUSY) observables in 3d
$\mathcal{N}=2$ SUSY Chern-Simons (CS) matter theories and investigate how
their exact results are related to the perturbative series with respect to
coupling constants given by inverse CS levels. We show that the observables
have nontrivial resurgent structures by expressing the exact results as a full
transseries consisting of perturbative and non-perturbative parts. As real mass
parameters are varied, we encounter Stokes phenomena at an infinite number of
points, where the perturbative series becomes non-Borel-summable due to
singularities on the positive real axis of the Borel plane. We also investigate
the Stokes phenomena when the phase of the coupling constant is varied. For
these cases, we find that the Borel ambiguities in the perturbative sector are
canceled by those in nonperturbative sectors and end up with an unambiguous
result which agrees with the exact result even on the Stokes lines. We also
decompose the Coulomb branch localization formula, which is an integral
representation for the exact results, into Lefschetz thimble contributions and
study how they are related to the resurgent transseries. We interpret the
non-perturbative effects appearing in the transseries as contributions of
complexified SUSY solutions which formally satisfy the SUSY conditions but are
not on the original path integral contour. |
Logarithmic Negativity in Lifshitz Harmonic Models: Recently generalizations of the harmonic lattice model has been introduced as
a discrete approximation of bosonic field theories with Lifshitz symmetry with
a generic dynamical exponent z. In such models in (1+1) and (2+1)-dimensions,
we study logarithmic negativity in the vacuum state and also finite temperature
states. We investigate various features of logarithmic negativity such as the
universal term, its z-dependence and also its temperature dependence in various
configurations. We present both analytical and numerical evidences for linear
z-dependence of logarithmic negativity in almost all range of parameters both
in (1+1) and (2+1)-dimensions. We also investigate the validity of area law
behavior of logarithmic negativity in these generalized models and find that
this behavior is still correct for small enough dynamical exponents. | Calculating the Superconformal Index and Seiberg Duality: We develop techniques to calculate an index for four dimensional
superconformal field theories. This superconformal index is counting BPS
operators which preserve only one supercharge. To calculate the superconformal
index we quantize the field theory on S^3 X R and show that the twisted theory
has an appropriate mass gap. This allows for the interactions to be switched
off continuously without the superconformal index being changed. We test those
techniques for theories which go through a non-trivial RG flow and for Seiberg
dual theories. This leads to the conjecture of some group/number theoretical
identities. |
Superfield BRST Charge and the Master Action: Using a superfield formulation of extended phase space, we propose a new form
of the Hamiltonian action functional. A remarkable feature of this construction
is that it directly leads to the BV master action on phase space. Conversely,
superspace can be used to construct nilpotent BRST charges directly from
solutions to the classical Lagrangian Master Equation. We comment on the
relation between these constructions and the specific master action proposal of
Alexandrov, Kontsevich, Schwarz and Zaboronsky. | On manifestly sp(2) invariant formulation of quadratic higher spin
Lagrangians: The Lagrangian frame-like formulation of free higher spin symmetric bosonic
AdS(d) fields is given within a manifestly sp(2) invariant framework. It is
designed to deal with infinite multiplets of fields appearing as gauge
connections of the higher spin algebras. |
Negative magnetoresistivity in chiral fluids and holography: In four dimensions Weyl fermions possess a chiral anomaly which leads to
several special features in the transport phenomena, such as the negative
longitudinal magnetoresistivity. In this paper, we study its inverse, the
longitudinal magnetoconductivity, in the case of a chiral anomalous system with
a background magnetic field B using the linear response method in the
hydrodynamic limit and from holography. Our hydrodynamic results show that in
general we need to have energy, momentum and charge dissipations to get a
finite DC longitudinal magnetoconductivity due to the existence of the chiral
anomaly. Applying the formula that we get from hydrodynamics to the holographic
system in the probe limit, we find that the result in the hydrodynamic regime
matches that calculated from holography via Kubo formula. The holographic
result shows that in an intermediate regime of B there is naturally a negative
magnetoresistivity which decreases as 1/B. At small B direct calculations in
the holographic system suggest that holography provides a new explanation for
the small B positive magnetoresistivity behavior seen in experiment, i.e. the
small B behavior comes from the quantum critical conductivity being affected by
the chiral anomaly. | Extremal black holes in D=4 Gauss-Bonnet gravity: We show that four-dimensional Einstein-Maxwell-Dilaton-Gauss-Bonnet gravity
admits asymptotically flat black hole solutions with a degenerate event horizon
of the Reissner-Nordstr\"om type $AdS_2\times S^2$. Such black holes exist for
the dilaton coupling constant within the interval $0\leq a^2<a^2_{\rm cr}$.
Black holes must be endowed with an electric charge and (possibly) with
magnetic charge (dyons) but they can not be purely magnetic. Purely electric
solutions are constructed numerically and the critical dilaton coupling is
determined $a_{\rm cr}\simeq 0.488219703$. For each value of the dilaton
coupling $a$ within this interval and for a fixed value of the Gauss--Bonnet
coupling $\alpha$ we have a family of black holes parameterized by their
electric charge. Relation between the mass, the electric charge and the dilaton
charge at both ends of the allowed interval of $a$ is reminiscent of the BPS
condition for dilaton black holes in the Einstein-Maxwell-Dilaton theory. The
entropy of the DGB extremal black holes is twice the Bekenstein-Hawking
entropy. |
Curved space resolution of singularity of fractional D3-branes on
conifold: We construct a supergravity dual to the cascading $SU(N+M) x SU(N)$
supersymmetric gauge theory (related to fractional D3-branes on conifold
according to Klebanov et al) in the case when the 3-space is compactified on
$S^3$ and in the phase with unbroken chiral symmetry. The size of $S^3$ serves
as an infrared cutoff on the gauge theory dynamics. For a sufficiently large
$S^3$ the dual supergravity background is expected to be nonsingular. We
demonstrate that this is indeed the case: we find a smooth type IIB
supergravity solution using a perturbation theory that is valid when the radius
of $S^3$ is large. We consider also the case with the euclidean world-volume
being $S^4$ instead of $R x S^3$, where the supergravity solution is again
found to be regular. This ``curved space'' resolution of the singularity of the
fractional D3-branes on conifold solution is analogous to the one in the
non-extremal (finite temperature) case discussed in our previous work. | Null boundary phase space: slicings, news and memory: We construct the boundary phase space in $D$-dimensional Einstein gravity
with a generic given co-dimension one null surface ${\cal N}$ as the boundary.
The associated boundary symmetry algebra is a semi-direct sum of
diffeomorphisms of $\cal N$ and Weyl rescalings. It is generated by $D$ towers
of surface charges that are generic functions over $\cal N$. These surface
charges can be rendered integrable for appropriate slicings of the phase space,
provided there is no graviton flux through $\cal N$. In one particular slicing
of this type, the charge algebra is the direct sum of the Heisenberg algebra
and diffeomorphisms of the transverse space, ${\cal N}_v$ for any fixed value
of the advanced time $v$. Finally, we introduce null surface expansion- and
spin-memories, and discuss associated memory effects that encode the passage of
gravitational waves through $\cal N$, imprinted in a change of the surface
charges. |
Introduction to Supersymmetry: These are expanded notes of lectures given at the summer school "Gif 2000" in
Paris. They constitute the first part of an "Introduction to supersymmetry and
supergravity" with the second part on supergravity by J.-P. Derendinger to
appear soon. The present introduction is elementary and pragmatic. I discuss:
spinors and the Poincar\'e group, the susy algebra and susy multiplets,
superfields and susy lagrangians, susy gauge theories, spontaneously broken
susy, the non-linear sigma model, N=2 susy gauge theories, and finally
Seiberg-Witten duality. | Calculation of QCD Instanton Determinant with Arbitrary Mass: The precise quark mass dependence of the one-loop effective action in an
instanton background has recently been computed [arXiv:hep-th/0410190]. The
result interpolates smoothly between the previously known extreme small and
large mass limits. The computational method makes use of the fact that the
single instanton background has radial symmetry, so that the computation can be
reduced to a sum over partial waves of logarithms of radial determinants, each
of which can be computed numerically in an efficient manner. The bare sum over
partial waves is divergent and must be regulated and renormalized. In this
paper we provide more details of this computation, including both the
renormalization procedure and the numerical approach. We conclude with
comparisons of our precise numerical results with a simple interpolating
function that connects the small and large mass limits, and with the leading
order of the derivative expansion. |
A Note on Polytopes for Scattering Amplitudes: In this note we continue the exploration of the polytope picture for
scattering amplitudes, where amplitudes are associated with the volumes of
polytopes in generalized momentum-twistor spaces. After a quick warm-up example
illustrating the essential ideas with the elementary geometry of polygons in
CP^2, we interpret the 1-loop MHV integrand as the volume of a polytope in
CP^3x CP^3, which can be thought of as the space obtained by taking the
geometric dual of the Wilson loop in each CP^3 of the product. We then review
the polytope picture for the NMHV tree amplitude and give it a more direct and
intrinsic definition as the geometric dual of a canonical "square" of the
Wilson-Loop polygon, living in a certain extension of momentum-twistor space
into CP^4. In both cases, one natural class of triangulations of the polytope
produces the BCFW/CSW representations of the amplitudes; another class of
triangulations leads to a striking new form, which is both remarkably simple as
well as manifestly cyclic and local. | De-Higgsing In Eleven-Dimensional Supergravity On The Squashed $S^7$: In this paper we construct the subset of modes on $S^7$ that are relevant in
the compactification of eleven-dimensional supergravity on a squashed $S^7$
when restricted to the sector that comprises singlets under the $Sp(1)\times
Sp(2)$ isometry of the squashed sphere. Some of the properties of these modes,
connected to the transition from the round $S^7$ to the squashed $S^7$, are
analysed in detail. Special features of the Rarita-Schwinger operator,
described in earlier work by Buchdahl, are explained and related to properties
of the squashed $S^7$ operator spectrum obtained in previous work by the
authors. We then discuss how the singlet modes give rise to supermultiplets in
the left-squashed case, the phenomenon of de-Higgsing, and what happens to the
AdS$_4$ fields in these supermultiplets under an orientation reversal
(``skew-whiffing'') of the squashed $S^7$. Finally, we consider the possible
choices of boundary conditions that appear for some of these fields in AdS$_4$
in the case of the right-squashed non-supersymmetric compactification, and how
these choices may affect the stability of the gravity theory. |
The gauge structure of Exceptional Field Theories and the tensor
hierarchy: We address the construction of manifest U-duality invariant generalized
diffeomorphisms. The closure of the algebra requires an extension of the
tangent space to include a tensor hierarchy indicating the existence of an
underlying unifying structure, compatible with E_{11} and Borcherds algebras
constructions. We begin with four-dimensional gauged maximal supergravity, and
build a generalized Lie derivative that encodes all the gauge transformations
of the theory. A generalized frame is introduced, which accommodates for all
the degrees of freedom, including the tensor hierarchy. The generalized Lie
derivative defines generalized field-dependent fluxes containing all the
covariant quantities in the theory, and the closure conditions give rise to
their corresponding Bianchi Identities. We then move towards the construction
of a full generalized Lie derivative defined on an extended space, analyze the
closure conditions, and explore the connection with that of maximal gauged
supergravity via a generalized Scherk-Schwarz reduction, and with
11-dimensional supergravity. | Baby Skyrme models for a class of potentials: We consider a class of (2+1) dimensional baby Skyrme models with potentials
that have more than one vacum. These potentials are generalisation of old and
new baby Skyrme models;they involve more complicated dependence on phi_3.We
find that when the potential is invariant under phi_3 -> -phi_3 the
configuration corresponding to the baby skyrmions lying "on top of each other"
are the minima of the energy. However when the potential breaks this symmetry
the lowest field configurations correspond to separated baby skyrmions. We
compute the energy distributions for skyrmions of degrees between one and eight
and discuss their geometrical shapes and binding energies. We also compare the
2-skyrmion states for these potentials. Most of our work has been performed
numerically with the model being formulated in terms of three real scalar
fields (satisfying one constraint). |
Aspects of Quantum Corrections in a Lorentz-violating Extension of the
Abelian Higgs Model: We investigate new aspects related to the abelian gauge-Higgs model with the
addition of the Carroll-Field-Jackiw term. We focus on one-loop quantum
corrections to the photon and Higgs sectors due to spontaneous breaking of
gauge symmetry and show that new finite and definite Lorentz-breaking terms are
induced. Specifically in the gauge sector, a CPT-even aether term is induced.
Besides, aspects of the one-loop renormalization of the background vector
dependent terms are discussed. | Confinement On the Moose Lattice: In this work we present a new class of N=1 supersymmetric confining gauge
theories, with strikingly simple infrared theories that descend from intricate
interconnected networks of product gauge groups. A diagram of the gauge groups
and the charged matter content of the ultraviolet theory has the structure of a
triangular lattice, with $SU(N)$ or $SU(3 N)$ gauge groups at each of the
vertices, connected by bifundamental chiral superfields. This structure admits
a $U(1)_R$ conserving superpotential with marginal trilinear operators. With
the introduction of this superpotential, the $SU(3N)$ and $SU(N)$ gauge groups
confine: in the far infrared limit of the supersymmetric theory, the relevant
degrees of freedom are gauge invariant "mesons" and "baryons." In this paper we
show how the properties of the infrared degrees of freedom depend on the
topology and shape of the moose/quiver ``lattice'' of the original gauge
theory. We investigate various deformations of the theory, and propose some
phenomenological applications for BSM models. |
Towards a proof of AGT conjecture by methods of matrix models: A matrix model approach to proof of the AGT relation is briefly reviewed. It
starts from the substitution of conformal blocks by the Dotsenko-Fateev
beta-ensemble averages and Nekrasov functions by a double deformation of the
exponentiated Seiberg-Witten prepotential in beta \neq 1 and g_s \neq 0
directions. Establishing the equality of these two quantities is a typical
matrix model problem, and it presumably can be ascertained by investigation of
integrability properties and developing an associated Harer-Zagier technique
for evaluation of the exact resolvent. | Noncommutative Quantum Field Theories: We start by reviewing the formulation of noncommutative quantum mechanics as
a constrained system. Then, we address to the problem of field theories defined
on a noncommutative space-time manifold. The Moyal product is introduced and
the appearance of the UV/IR mechanism is exemplified. The emphasis is on
finding and analyzing noncommutative quantum field theories which are
renormalizable and free of nonintegrable infrared singularities. In this last
connection we give a detailed discussion of the quantization of the
noncommutative Wess-Zumino model as well as of its low energy behavior. |
Moduli Axions, Stabilizing Moduli and the Large Field Swampland
Conjecture in Heterotic M-Theory: We compute the potential energy for the dilaton, complex structure and Kahler
moduli and search of realistic vacua of heterotic M-theory compactified on
Calabi-Yau threefolds. We present a protocol for deriving the potential that
combines the non-perturbative complex structure, gaugino condensate and
worldsheet instanton superpotentials in theories in which the hidden sector
contains an anomalous $U(1)$ structure group. The Green-Schwarz anomaly
cancellation induces inhomogeneous axion transformations for the imaginary
components of the dilaton and Kahler modulus. Using this protocol we obtain
explicit examples in which potential has a global minimum at negative or zero
vacuum density or a metastable minimum with positive vacuum density. In all
three cases, the dilaton, Kahler modulus and associated axion moduli are
completely stabilized. Finally, we show that, for any of these vacua, the
potential energy satisfies the large scalar field Swampland conjecture. | Relationship between High-Energy Absorption Cross Section and Strong
Gravitational Lensing for Black Hole: In this paper, we obtain a relation between the high-energy absorption cross
section and the strong gravitational lensing for a static and spherically
symmetric black hole. It provides us a possible way to measure the high-energy
absorption cross section for a black hole from strong gravitational lensing
through astronomical observation. More importantly, it allows us to compute the
total energy emission rate for high-energy particles emitted from the black
hole acting as a gravitational lens. It could tell us the range of the
frequency, among which the black hole emits the most of its energy and the
gravitational waves are most likely to be observed. We also apply it to the
Janis-Newman-Winicour solution. The results suggest that we can test the cosmic
censorship hypothesis through the observation of gravitational lensing by the
weakly naked singularities acting as gravitational lenses. |
Carrollian and Non-relativistic Jackiw-Teitelboim Supergravity: We present non- and ultra-relativistic Jackiw-Teitelboim (JT) supergravity as
metric BF theories based on the extended Newton-Hooke and extended AdS Carroll
superalgebras in two spacetime dimensions, respectively. The extended
Newton-Hooke structure, and, in particular, the invariant metric necessary for
the BF construction of non-relativistic JT supergravity, is obtained by
performing an expansion of the $\mathcal{N}=2$ AdS$_2$ superalgebra.
Subsequently, we introduce the extended AdS$_2$ Carroll superalgebra, and the
associated invariant metric, as a suitable redefinition of the extended
Newton-Hooke superalgebra. The mapping involved can be seen as the
supersymmetric extension of the duality existing at the purely bosonic level
between the extended Newton-Hooke algebra with (positive) negative cosmological
constant and the extended (A)dS Carroll algebra in two dimensions. Finally, we
provide the Carrollian JT supergravity action in the BF formalism. Moreover, we
show that both the non-relativistic and the ultra-relativistic theories
presented can also be obtained by direct expansion of $\mathcal{N}=2$ JT
supergravity. | Integrability and Diffeomorphisms on Target Space: We briefly review the concepts of generalized zero curvature conditions and
integrability in higher dimensions, where integrability in this context is
related to the existence of infinitely many conservation laws. Under certain
assumptions, it turns out that these conservation laws are, in fact, generated
by a class of geometric target space transformations, namely the
volume-preserving diffeomorphisms. We classify the possible conservation laws
of field theories for the case of a three-dimensional target space. Further, we
discuss some explicit examples. |
Thermal Stress Tensor Correlators near Lightcone and Holography: We consider thermal stress-tensor two-point functions in holographic theories
in the near-lightcone regime and analyse them using the operator product
expansion (OPE). In the limit we consider only the leading-twist multi-stress
tensors contribute and the correlators depend on a particular combination of
lightcone momenta. We argue that such correlators are described by three
universal functions, which can be holographically computed in Einstein gravity;
higher-derivative terms in the gravitational Lagrangian enter the arguments of
these functions via the cubic stress-tensor couplings and the thermal
stress-tensor expectation value in the dual CFT. We compute the retarded
correlators and observe that in addition to the perturbative OPE, which
contributes to the real part, there is a non-perturbative contribution to the
imaginary part. | Thermodynamic Bethe Ansatz for G_k x G_l / G_{k+l} Coset Models
Perturbed by Their φ_{1,1,Adj} Operator: We propose a Thermodynamic Bethe Ansatz (TBA) for G_k x G_l / G_{k+l}
conformal coset models (G any simply-laced Lie algebra) perturbed by their
operator \phi_{1,1,Adj}. An interesting adjacency structure appears and can be
depicted in a sort of ``product'' of Dynkin diagrams of G and A_{k+l-1}. UV and
IR limits are computed and reproduce the expected values for the central
charges. For k->\infty, l fixed we obtain the TBA of the G_l WZW model
perturbed by J_a\bar{J}_a, and for k,l->\infty, k-l fixed, that of Principal
Chiral model with WZ term at level k-l. |
Generalised Raychaudhuri Equations for Strings and Membranes: A recent generalisation of the Raychaudhuri equations for timelike geodesic
congruences to families of $D$ dimensional extremal, timelike, Nambu--Goto
surfaces embedded in an $N$ dimensional Lorentzian background is reviewed.
Specialising to $D=2$ (i.e the case of string worldsheets) we reduce the
equation for the generalised expansion $\theta _{a}, (a =\sigma,\tau)$ to a
second order, linear, hyperbolic partial differential equation which resembles
a variable--mass wave equation in $1+1$ dimensions. Consequences, such as a
generalisation of geodesic focussing to families of worldsheets as well as
exactly solvable cases are explored and analysed in some detail. Several
possible directions of future research are also pointed out. | Comment on "Turnaround in Cyclic Cosmology": We comment on a recent paper by L. Baum and P. H. Frampton [Phys. Rev. Lett.
98, 071301 (2007)] where it was argued that the entropy problem can be resolved
in a peculiar cyclic universe model through a deflation mechanism (i.e., the
universe is fragmented into many disconnected causal patches at the
turnaround). We point out that in this cyclic model the Hubble length will
become infinity at the turnaround, thus the deflation scenario is not valid. |
Varieties of Quantum Measurement: Quantum measurement theory has fallen under the resticting influence of the
attempt to explain the fundamental axioms of quantum theory in terms of the
theory itself. This has not only led to confusion but has also restricted our
attention to a limited class of measurements. This paper outlines some of the
novel types of measurements which fall outside the usual textbook description. | Short Distance Properties from Large Distance Behaviour: For slowly varying fields the vacuum functional of a quantum field theory may
be expanded in terms of local functionals. This expansion satisfies its own
form of the Schr\"odinger equation from which the expansion coefficents can be
found. For scalar field theory in 1+1 dimensions we show that this approach
correctly reproduces the short-distance properties as contained in the
counter-terms. We also describe an approximate simplification that occurs for
the Sine-Gordon and Sinh-Gordon vacuum functionals. |
Non-manifest symmetries in quantum field theory: Non-manifest symmetries are an important feature of quantum field theories
(QFTs), and yet their characteristics are not fully understood. In particular,
the construction of the charge operators associated with these symmetries is
ambiguous. In this paper we adopt a rigorous axiomatic approach in order to
address this issue. It turns out that charge operators of non-manifest
symmetries are not unique, and that although this does not affect their
property as generators of the corresponding symmetry transformations,
additional physical input is required in order to determine how they act on
states. Applying these results to the examples of spacetime translation and
Lorentz symmetry, it follows that the assumption that the vacuum is the unique
translationally invariant state is sufficient to uniquely define the charges
associated with these symmetries. In the case of supersymmetry though there
exists no such physical requirement, and this therefore implies that the
supersymmetric charge, and hence the supersymmetric space of states, is not
uniquely defined. | Radion stabilization in the presence of Wilson line phase: We study the stabilization of an extra-dimensional radius in the presence of
a Wilson line phase of an extra $U(1)$ gauge symmetry on a five-dimensional
space-time, using the effective potential relating both the radion and the
Wilson line phase at the one-loop level. We find that the radion can be
stabilized by the introduction of a small number of fermions. |
Quantum hypermultiplet moduli spaces in N=2 string vacua: a review: The hypermultiplet moduli space M_H in type II string theories compactified
on a Calabi-Yau threefold X is largely constrained by supersymmetry (which
demands quaternion-K\"ahlerity), S-duality (which requires an isometric action
of SL(2, Z)) and regularity. Mathematically, M_H ought to encode all
generalized Donaldson-Thomas invariants on X consistently with wall-crossing,
modularity and homological mirror symmetry. We review recent progress towards
computing the exact metric on M_H, or rather the exact complex contact
structure on its twistor space. | Thermodynamics of nonlinear charged Lifshitz black branes with
hyperscaling violation: In this paper, we investigate the thermodynamics of hyperscaling violating
Lifshitz black branes in the presence of a nonlinear massless electromagnetic
field. We, first, obtain analytic nonlinear charged black brane solutions with
hyperscaling violating factor in dilaton gravity and give the condition on the
parameters of the metric for having black brane solutions. Second, we introduce
the appropriate finite action in grand-canonical and canonical ensembles for
nonlinear electromagnetic field. Next, by generalizing the counterterm method
for the asymptotic Lifshitz spacetimes with hyperscaling violating factor, we
calculate the energy density of our solutions. Then, we present a relation
between the energy density and the thermodynamic quantities, electric
potential, charge density, temperature and entropy density. This relation is
the generalization of Smarr formula for anti-de Sitter black branes and charged
Lifshiz solutions. Finally, we perform a stability analysis in both the
canonical and grand-canonical ensemble. We show that the nonlinearity of
electromagnetic field can make the solutions unstable in grand-canonical
ensemble. |
Semi-classical strings in $(2+1)-$dimensional backgrounds: This study analyzes the geometrical relationship between a classical string
and its semi-classical quantum model. From an arbitrary $(2+1)-$dimensional
geometry, a specific ansatz for a classical string is used to generate a
semi-classical quantum model. In this framework, examples of quantum
oscillations and quantum free particles are presented that uniquely determine a
classical string and the space-time geometry where its motion takes place. | On higher order geometric and renormalisation group flows: Renormalisation group flows of the bosonic nonlinear \sigma-model are
governed, perturbatively, at different orders of \alpha', by the perturbatively
evaluated \beta--functions. In regions where \frac{\alpha'}{R_c^2} << 1 the
flow equations at various orders in \alpha' can be thought of as \em
approximating the full, non-perturbative RG flow. On the other hand, taking a
different viewpoint, we may consider the abovementioned RG flow equations as
viable {\em geometric} flows in their own right and without any reference to
the RG aspect. Looked at as purely geometric flows where higher order terms
appear, we no longer have the perturbative restrictions . In this paper, we
perform our analysis from both these perspectives using specific target
manifolds such as S^2, H^2, unwarped S^2 x H^2 and simple warped products. We
analyze and solve the higher order RG flow equations within the appropriate
perturbative domains and find the \em corrections arising due to the inclusion
of higher order terms. Such corrections, within the perturbative regime, are
shown to be small and they provide an estimate of the error which arises when
higher orders are ignored.
We also investigate the higher order geometric flows on the same manifolds
and figure out generic features of geometric evolution, the appearance of
singularities and solitons. The aim, in this context, is to demonstrate the
role of the higher order terms in modifying the flow. One interesting aspect of
our analysis is that, separable solutions of the higher order flow equations
for simple warped spacetimes, correspond to constant curvature Anti-de Sitter
(AdS) spacetime, modulo an overall flow--parameter dependent scale factor. The
functional form of this scale factor (which we obtain) changes on the inclusion
of successive higher order terms in the flow. |
Kinematic Space and Wormholes: The kinematic space could play a key role in constructing the bulk geometry
from dual CFT. In this paper, we study the kinematic space from geometric
points of view, without resorting to differential entropy. We find that the
kinematic space could be intrinsically defined in the embedding space. For each
oriented geodesic in the Poincar\'e disk, there is a corresponding point in the
kinematic space. This point is the tip of the causal diamond of the disk whose
intersection with the Poincar\'e disk determines the geodesic. In this
geometric construction, the causal structure in the kinematic space can be seen
clearly. Moreover, we find that every transformation in the $SL(2,\mathbb{R})$
leads to a geodesic in the kinematic space. In particular, for a hyperbolic
transformation defining a BTZ black hole, it is a timelike geodesic in the
kinematic space. We show that the horizon length of the static BTZ black hole
could be computed by the geodesic length of corresponding points in the
kinematic space. Furthermore, we discuss the fundamental regions in the
kinematic space for the BTZ blackhole and multi-boundary wormholes. | Four coupled SYK models and Nearly AdS$_2$ gravities: Phase Transitions
in Traversable wormholes and in Bra-ket wormholes: We study four coupled SYK models and nearly AdS$_2$ gravities. In the SYK
model side, we construct a model that couples two copies of two coupled SYK
models. In nearly AdS$_2$ gravity side, we entangle matter fields in two copies
of traversable wormholes. In both cases, the systems show first order phase
transitions at zero temperature by changing couplings, which is understood as
the exchange of traversable wormhole configurations. In nearly AdS$_2$ gravity
cases, by exchanging the role of space and time the wormholes are interpreted
as bra-ket wormholes. In Lorentzian signature, these bra-ket wormholes lead to
two closed universes that are entangled with each other as well as matter
fields in the flat space without dynamical gravity. We study the effect of
projection or entangling operation for matters on flat spaces and they cause
phase transitions in bra-ket wormholes, which leads to the pair annihilation of
closed universes. Using these bra-ket wormholes, we discuss the way to embed
states in 2d holographic CFTs into Hilbert space of many 2d free fields. |
Viscosity bound for anisotropic superfluids with dark matter sector: The shear viscosity to the entropy density ratio $\eta/s$ of the anisotropic
superfluid has been calculated by means of the gauge/gravity duality in the
presence of the {\it dark matter} sector. The {\it dark matter} has been
described by the Yang-Mills field analogous to the one describing visible
matter sector and it is assumed to interact with the visible field with
coupling constant $\alpha$. Close to the superfluid transition temperature
($T_c$) the analytical solution has been given up to the leading order in a
symmetry breaking parameter and the ratio of the gravitational constant and
Yang-Mils coupling. The tensor element of ratio $\eta/s$ remains unaffected by
the {\it dark matter} for the viscosity tensor in the plane perpendicular to
the symmetry breaking direction (here $yz$). The temperature dependence and the
linear correction in $(1-\alpha)$ in the plane containing this direction (here
$xy$) was also revealed. The correction linearly vanishes for temperature
tending to the critical one $T\rightarrow T_c$. | Scaling Violation in O(N) Vector Models: We investigate $O(N)$-symmetric vector field theories in the double scaling
limit. Our model describes branched polymeric systems in $D$ dimensions, whose
multicritical series interpolates between the Cayley tree and the ordinary
random walk. We give explicit forms of residual divergences in the free energy,
analogous to those observed in the strings in one dimension. |
Inflation in multi-field random Gaussian landscapes: We investigate slow-roll inflation in a multi-field random Gaussian
landscape. The landscape is assumed to be small-field, with a correlation
length much smaller than the Planck scale. Inflation then typically occurs in
small patches of the landscape, localized near inflection or saddle points. We
find that the inflationary track is typically close to a straight line in the
field space, and the statistical properties of inflation are similar to those
in a one-dimensional landscape. This picture of multi-field inflation is rather
different from that suggested by the Dyson Brownian motion model; we discuss
the reasons for this difference. We also discuss tunneling from inflating false
vacua to the neighborhood of inflection and saddle points and show that the
tunneling endpoints tend to concentrate along the flat direction in the
landscape. | BRST, anti-BRST and their geometry: We continue the comparison between the field theoretical and geometrical
approaches to the gauge field theories of various types, by deriving their
Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST trasformation properties and
comparing them with the geometrical properties of the bundles and gerbes. In
particular, we provide the geometrical interpretation of the so--called
Curci-Ferrari conditions that are invoked for the absolute anticommutativity of
the BRST and anti-BRST symmetry transformations in the context of non-Abelian
1-form gauge theories as well as Abelian gauge theory that incorporates a
2-form gauge field. We also carry out the explicit construction of the 3-form
gauge fields and compare it with the geometry of 2--gerbes. |
Localizing non-linear ${\cal N}=(2,2)$ sigma model on $S^2$: We present a systematic study of ${\cal N}=(2,2)$ supersymmetric non-linear
sigma models on $S^2$ with the target being a K\"ahler manifold. We discuss
their reformulation in terms of cohomological field theory. In the
cohomological formulation we use a novel version of 2D self-duality which
involves a $U(1)$ action on $S^2$. In addition to the generic model we discuss
the theory with target space equivariance corresponding to a supersymmetric
sigma model coupled to a non-dynamical supersymmetric background gauge
multiplet. We discuss the localization locus and perform a one-loop calculation
around the constant maps. We argue that the theory can be reduced to some
exotic model over the moduli space of holomorphic disks. | On the 3-point functions of Aging Dynamics and the AdS/CFT
Correspondence: Aging can be realized as a sub-algebra of Schr\"odinger algebra by discarding
the time-translation generator. While the 2-point functions of the Age algebra
have been known for some time, little else was known about the higher $n$-point
correlators. In this letter we present novel 3-point correlators of scalar
primary operators. We find that the Aging correlators are distinct from the
Schr\"odinger correlators by more than certain dressings with time-dependent
factors, as was the case with 2-point functions. In the existing literature,
the holographic geometry of Aging is obtained by performing certain general
coordinate transformations on the holographic dual of the Schr\"odinger theory.
Consequently, the Aging 2-point functions derived from holography look as the
Schr\"odinger 2-point functions dressed by time-dependent factors. However,
since the 3-point functions obtained in this letter are not merely dressed
Schr\"odinger correlators and instead depend on an additional time-translation
breaking variable, we conclude that the most general holographic realization of
Aging is yet to be found. |
Simple Brane World Scenario with Positive Five Dimensional Cosmological
Constant: We present a simple brane-world model in five dimensions. In this model we do
not need any fine-tuning between the five dimensional cosmological constant and
the brane tension to obtain four dimensional flat Minkowski space. The
space-time of our solution has no naked singularities. Further the
compactification scale of the fifth direction is automatically determined. | Non-Perturbative Quantum Geometry: The beta-ensemble with cubic potential can be used to study a quantum
particle in a double-well potential with symmetry breaking term. The quantum
mechanical perturbative energy arises from the ensemble free energy in a novel
large N limit. A relation between the generating functions of the exact
non-perturbative energy, similar in spirit to the one of Dunne-Unsal, is found.
The exact quantization condition of Zinn-Justin and Jentschura is equivalent to
the Nekrasov-Shatashvili quantization condition on the level of the ensemble.
Refined topological string theory in the Nekrasov-Shatashvili limit arises as a
large N limit of quantum mechanics. |
Lax matrix solution of c=1 Conformal Field Theory: To a correlation function in a two-dimensional conformal field theory with
the central charge $c=1$, we associate a matrix differential equation $\Psi' =
L \Psi$, where the Lax matrix $L$ is a matrix square root of the
energy-momentum tensor. Then local conformal symmetry implies that the
differential equation is isomonodromic. This provides a justification for the
recently observed relation between four-point conformal blocks and solutions of
the Painlev\'e VI equation. This also provides a direct way to compute the
three-point function of Runkel-Watts theory -- the common $c\rightarrow 1$
limit of Minimal Models and Liouville theory. | Perturbative construction of the two-dimensional O(N) non-linear sigma
model with ERG: We use the exact renormalization group (ERG) perturbatively to construct the
Wilson action for the two-dimensional O(N) non-linear sigma model. The
construction amounts to regularization of a non-linear symmetry with a momentum
cutoff. A quadratically divergent potential is generated by the momentum
cutoff, but its non-invariance is compensated by the jacobian of the non-linear
symmetry transformation. |
New Perspectives on Attractor Flows and Trees from CFT: In this note, we use the first order formalism for attractor flows in N=2
SUGRA extremal black hole backgrounds to establish a formal correspondence
between the RG flow of moduli in the underlying N=(2,2) SCFT and bulk attractor
flows. Starting from a study of moduli flow trajectories in the CFT, we derive
a potential which generates the aforesaid flow. This potential is shown to be a
symplectic invariant with the same form as the black hole potential which
drives the attractor flows in the bulk. We use these results to make comments
on the non-renormalization of extremal black hole entropy and indicate a
similar correspondence for two-centered forked flows in CFT. | Quantum field theory of relic nonequilibrium systems: In terms of the de Broglie-Bohm pilot-wave formulation of quantum theory, we
develop field-theoretical models of quantum nonequilibrium systems which could
exist today as relics from the very early universe. We consider relic excited
states generated by inflaton decay, as well as relic vacuum modes, for particle
species that decoupled close to the Planck temperature. Simple estimates
suggest that, at least in principle, quantum nonequilibrium could survive to
the present day for some relic systems. The main focus of this paper is to
describe the behaviour of such systems in terms of field theory, with the aim
of understanding how relic quantum nonequilibrium might manifest
experimentally. We show by explicit calculation that simple perturbative
couplings will transfer quantum nonequilibrium from one field to another (for
example from the inflaton field to its decay products). We also show that
fields in a state of quantum nonequilibrium will generate anomalous spectra for
standard energy measurements. Possible connections to current astrophysical
observations are briefly addressed. |
Hidden Conformal Symmetry of Extremal Kerr-Bolt Spacetimes: We show that extremal Kerr-Bolt spacetimes have a hidden conformal symmetry.
In this regard, we consider the wave equation of a massless scalar field
propagating in extremal Kerr-Bolt spacetimes and find in the "near region", the
wave equation in extremal limit can be written in terms of the $SL(2,R)$
quadratic Casimir. Moreover, we obtain the microscopic entropy of the extremal
Kerr-Bolt spacetimes also we calculate the correlation function of a
near-region scalar field and find perfect agreement with the dual 2D CFT. | Dynamical noncommutative quantum mechanics: We study some basic and interesting quantum mechanical systems in dynamical
noncommutative spaces in which the space- space commutation relations are
position dependent. It is observed that the fundamental objects in the
dynamical noncommutative space introduced here are stringlike. We show that the
Stark effect can be employed to determine whether the noncommutativity of space
is dynamical or non-dynamical. It appears that unlike non-dynamical case there
is a fundamental energy $\dfrac{\tau\hbar^{2}}{m}$ in this dynamical space.} |
On the motion of particles in covariant Horava-Lifshitz gravity and the
meaning of the A-field: We studied the low energy motion of particles in the general covariant
version of Horava-Lifshitz gravity proposed by Horava and Melby-Thompson. Using
a scalar field coupled to gravity according to the minimal substitution recipe
proposed by da Silva and taking the geometrical optics limit, we could write an
effective relativistic metric for a general solution. As a result, we
discovered that the equivalence principle is not in general recovered at low
energies, unless the spatial Laplacian of A vanishes. Finally, we analyzed the
motion on the spherical symmetric solution proposed by Horava and
Melby-Thompson, where we could find its effective line element and compute
spin-0 geodesics. Using standard methods we have shown that such an effective
metric cannot reproduce Newton's gravity law even in the weak gravitational
field approximation. | Generalized uncertainty principle with maximal observable momentum and
no minimal length indeterminacy: We present a novel generalization of the Heisenberg uncertainty principle
which introduces the existence of a maximal observable momentum and at the same
time does not entail a minimal indeterminacy in position. The above result is
an exact generalized uncertainty principle (GUP), valid at all energy scales.
For small values of the deformation parameter $\beta$, our ansatz is consistent
with the usual expression for GUP borrowed from string theory, doubly special
relativity and other quantum gravity candidates that provide $\beta$ with a
negative sign. As a preliminary analysis, we study the implications of this new
model on some quantum mechanical applications and on the black hole
thermodynamics. |
Half-BPS half-BPS twist two at four loops in N=4 SYM: We consider a double OPE limit of the planar four-point function of stress
tensor multiplets in N = 4 SYM theory. Loop integrands for this correlator have
been constructed to very high order, but the corresponding integrals are
explicitly known only up to three loops. Fortunately, the double coincidence
limit of the four-loop integrals can be found by the method of expansion by
regions, which reduces the problem of computing the four-point integrals to the
evaluation of a large set of massless propagator integrals. These can in turn
be evaluated by IBP reduction.
The OPE limit of the stress tensor four-point function allows us to extract
the (square of the) three-point couplings between two stress tensor multiplets
and one twist two operator in the 20' of SU(4). The latest available IBP
software accomplishes this task up to and including spin 8. With the data
obtained we hope to further the development of the recent integrable systems
picture for correlation functions. | Vacuum Structure and $θ$ States of Adjoint QCD in Two Dimensions: We address the issue of topological angles in the context of two dimensional
SU(N) Yang-Mills theory coupled to massive fermions in the adjoint
representation. Classification of the resulting multiplicity of vacua is
carried outin terms of asymptotic fundamental Wilson loops, or equivalently,
charges at the boundary of the world. We explicitly demonstrate that the
multiplicity of vacuum states is equal to N for SU(N) gauge group. Different
worlds of the theory are classified by the integer number k=0,1,...N-1
(superselection rules) which plays an analogous role to the $\theta$ parameter
in QCD. Via two completely independent approaches we study the physical
properties of these unconnected worlds as a function of k. First, we apply the
well known machinery of the loop calculus in order to calculate the effective
string tensions in the theory as function of $k$. The second way of doing the
same physics is the standard particle/field theoretic calculation for the
binding potential of a pair of infinitely massive fermions. We also calculate
the vacuum energy as function of k. |
Instantons in AdS$_4$ From (anti)Membranes Wrapping $S^7$ To Bose-Fermi
Duality in CFT$_3$'s: We present new SO(4)-invariant and non-supersymmetric instanton solutions for
the conformally coupled m^2=-2 and massive m^2=+4 (pseudo)scalars arising from
a consistent truncation of 11-dimensional supergravity over AdS_4 x S^7/Z_k
when the internal space is a S^1 Hopf fibration on CP^3, and we consider
backreaction. In fact, the bulk configurations associate with (anti)membranes
wrapped around mixed internal (and external) directions, which in turn probe
the Wick-rotated or skew-whiffed background, break all supersymmetries as well
as parity invariance. From near the boundary behavior of the closed solution
for the coupled bulk (pseudo)scalar, we get a marginal triple-trace deformation
with mixed boundary condition (valid also for the bulk massless m^2=0
(pseudo)scalar, raised when considering the external space backreaction, with
Dirichlet boundary condition) and as a result, the corresponding boundary
effective potential is unbounded from below and causes an instability because
of the Fubini-like instanton. Presenting dual effective actions, we see that
the boundary solutions and counterparts realize in singlet sectors of
three-dimensional U(N) and O(N) Chern--Simons-matter field theories. In
particular, we use versions of massless and mass-deformed regular and critical
boson and fermion models, find instantons and confirm state-operator
AdS_4/CFT_3 correspondence and also Bose-Fermi duality at the level of the
solutions. In addition, we discuss on relations of our setups with Vasiliev's
Higher-Spin theories, deformations of the Aharony-Bergman-Jafferis-Maldacena
model and other related studies. | Black holes and the quark-gluon plasma: I discuss the possibility that the quark-gluon plasma at strong coupling
admits a description in terms of a black hole in asymptotically anti-de Sitter
space. |
Twisted Boundary Conditions and Matching to the Effective Four
Dimensional Theory: Nontrivial twisted boundary conditions associated with extra compact
dimensions produce an ambiguity in the value of the four dimensional coupling
constants of the renormalizable interactions of the twisted fields' zero modes.
Resolving this indeterminancy would require a knowledge of the exact form of
the higher dimensional action including the coefficients of higher dimensional
operators. For the case of moderately sized extra dimensions, the uncertainty
in the coupling constants can be of order one and may lead to modifications in
the stability of the model. | Diffeomorphisms in momentum space: physical implications of different
choices of momentum coordinates in the Galilean Snyder model: It has been pointed out that different choices of momenta can be associated
to the same noncommutative spacetime model. The question of whether these
momentum spaces, related by diffeomorphisms, produce the same physical
predictions is still debated. In this work, we focus our attention on a few
different momentum spaces that can be associated to the Galilean Snyder
noncommutative spacetime model and show that they produce different predictions
for the energy spectrum of the harmonic oscillator. |
An Alternative Interpretation for the Moduli Fields of the Cosmology
Associated to Type IIB Supergravity with Fluxes: We start with a particular cosmological model derived from type IIB
supergravity theory with fluxes, where usually the dilaton is interpreted as a
Quintessence field. Instead of that, in this letter we interpret the dilaton as
the dark matter of the universe. With this alternative interpretation we find
that in this supergravity model gives a similar evolution and structure
formation of the universe compared with the $\Lambda$CDM model in the linear
regime of fluctuations of the structure formation. Some free parameters of the
theory are fixed using the present cosmological observations. In the non-linear
regimen there are some differences between the type IIB supergravity theory
with the traditional CDM paradigm. The supergravity theory predicts the
formation of galaxies earlier than the CDM and there is no density cusp in the
center of galaxies. These differences can distinguish both models and can give
a distinctive feature to the phenomenology of the cosmology coming from
superstring theory with fluxes. | Fractional S-branes on a Spacetime Orbifold: Unstable D-branes are central objects in string theory, and exist also in
time-dependent backgrounds. In this paper we take first steps to studying brane
decay in spacetime orbifolds. As a concrete model we focus on the R^{1,d}/Z_2
orbifold. We point out that on a spacetime orbifold there exist two kinds of
S-branes, fractional S-branes in addition to the usual ones. We investigate
their construction in the open string and closed string boundary state
approach. As an application of these constructions, we consider a scenario
where an unstable brane nucleates at the origin of time of a spacetime, its
initial energy then converting into energy flux in the form of closed strings.
The dual open string description allows for a well-defined description of this
process even if it originates at a singular origin of the spacetime. |
Supersymmetric twisting of carbon nanotubes: We construct exactly solvable models of twisted carbon nanotubes via
supersymmetry, by applying the matrix Darboux transformation. We derive the
Green's function for these systems and compute the local density of states.
Explicit examples of twisted carbon nanotubes are produced, where the
back-scattering is suppressed and bound states are present. We find that the
local density of states decreases in the regions where the bound states are
localized. Dependence of bound-state energies on the asymptotic twist of the
nanotubes is determined. We also show that each of the constructed unextended
first order matrix systems possesses a proper nonlinear hidden supersymmetric
structure with a nontrivial grading operator. | Large $N$ Universality of 4d $\mathcal{N}=1$ Superconformal Index and
AdS Black Holes: We study the large $N$ limit of the matrix models associated with the
superconformal indices of four-dimensional $\mathcal{N}=1$ superconformal field
theories. We find that for a large class of $\mathcal{N}=1$ superconformal
gauge theories, the superconformal indices in the large $N$ limit of such
theories are dominated by the 'parallelogram' saddle, providing $O(N^2)$ free
energy for the generic value of chemical potentials. This saddle corresponds to
BPS black holes in AdS$_5$ whenever a holographic dual description is
available. Our saddle applies to a large class of gauge theories, including ADE
quiver gauge theories, and the theories with rank-2 tensor matters. Our
analysis works for most $\mathcal{N}=1$ superconformal gauge theories that
admit a suitable large $N$ limit while keeping the flavor symmetry fixed. We
also find 'multi-cut' saddle points, which correspond to the orbifolded
Euclidean black holes in AdS$_5$. |
Wormholes in Maximal Supergravity: In this brief note, we reconsider the problem of finding Euclidean wormhole
solutions to maximal supergravity in d dimensions. We find that such solutions
exists for all d less than or equal to 9. However, we argue that, in
toroidally-compactified string theories, these saddle points never contribute
to the path integral because of a tension with U-duality. | On the temporal Wilson loop in the Hamiltonian approach in Coulomb gauge: We investigate the temporal Wilson loop using the Hamiltonian approach to
Yang-Mills theory. In simple cases such as the Abelian theory or the
non-Abelian theory in (1+1) dimensions, the known results can be reproduced
using unitary transformations to take care of time evolution. We show how
Coulomb gauge can be used for an alternative solution if the exact ground state
wave functional is known. In the most interesting case of Yang-Mills theory in
(3+1) dimensions, the vacuum wave functional is not known, but recent
variational approaches in Coulomb gauge give a decent approximation. We use
this formulation to compute the temporal Wilson loop and find that the Wilson
and Coulomb string tension agree within our approximation scheme. Possible
improvements of these findings are briefly discussed. |
Novel BPS Wilson loops in three-dimensional quiver Chern-Simons-matter
theories: We show that generic three-dimensional $\mathcal N=2$ quiver super
Chern-Simons-matter theories admit Bogomol'nyi-Prasad-Sommerfield (BPS)
Drukker-Trancanelli (DT) type Wilson loops. We investigate both Wilson loops
along timelike infinite straight lines in Minkowski spacetime and circular
Wilson loops in Euclidean space. In Aharnoy-Bergman-Jafferis-Maldacena theory,
we find that generic BPS DT type Wilson loops preserve the same number of
supersymmetries as Gaiotto-Yin type Wilson loops. There are several free
parameters for generic BPS DT type Wilson loops in the construction, and
supersymmetry enhancement for Wilson loops happens for special values of the
parameters. | Induced Magnetic moments in three-dimensional gauge theories with
external magnetic fields: We study the appearance of induced parity-violating magnetic moment, in the
presence of external magnetic fields, for even-number of fermion species
coupled to dynamical fields in three dimensions. Specifically, we use a
SU(2)xU(1) gauge model for dynamical gauge symmetry breaking, which is also
proposed recently as a field theoretical model for high-temperature
superconductors. By decomposing the fermionic degrees of freedom in terms of
Landau levels, we show that, in the effective theory with the lowest Landau
levels, a parity-violating magnetic moment interaction is induced by the higher
Landau levels when the fermions are massive. The possible relevance of this
result for a recently observed phenomenon in high-temperature superconductors
is also discussed. |
Phase structures emerging from holography with Einstein gravity --
dilaton models at finite temperature: Asymptotic AdS Riemann space-times in five dimensions with a black brane
(horizon) sourced by a fully back-reacted scalar field (dilaton) offer -- via
the holographic dictionary -- various options for the thermodynamics of the
flat four-dimensional boundary theory, uncovering Hawking-Page, first-order and
second-order phase transitions up to a cross-over or featureless behavior. The
relation of these phase structures to the dilaton potential is clarified and
illustrating examples are presented. Having in mind applications to QCD we
study probe vector mesons with the goal to figure out conditions for forming
Regge type series of radial excitations and address the issue of meson melting. | A Solitonic 3-Brane in 6D Bulk: We construct a solitonic 3-brane solution in the 6-dimensional
Einstein-Hilbert-Gauss-Bonnet theory with a (negative) cosmological term. This
solitonic brane world is delta-function-like. Near the brane the metric is that
for a product of the 4-dimensional flat Minkowski space with a 2-dimensional
``wedge'' with a deficit angle (which depends on the solitonic brane tension).
Far from the brane the metric approaches that for a product of the
5-dimensional AdS space and a circle. This solitonic solution exists for a
special value of the Gauss-Bonnet coupling (for which we also have a
delta-function-like codimension-1 solitonic solution), and the solitonic brane
tension can take values in a continuous range. We discuss various properties of
this solitonic brane world, including coupling between gravity and matter
localized on the brane. |
Multiplicative Anomaly matches Casimir Energy for GJMS Operators on
Spheres: An explicit formula to compute the multiplicative anomaly or defect of
$\zeta$-regularized products of linear factors is derived, by using a Feynman
parametrization, generalizing Shintani-Mizuno formulas. Firstly, this is
applied on $n$-spheres, reproducing known results in the literature. Then, this
framework is applied to a closed Einstein universe at finite temperature,
namely $S^1_{\beta}\times S^{n-1}$. In doing so, it is shown that the standard
Casimir energy for GJMS operators coincides with the accumulated multiplicative
anomaly for the shifted Laplacians that build them up. This equivalence between
Casimir energy and multiplicative anomaly, unnoticed so far to our knowledge,
brings about a new turn regarding the physical significance of the
multiplicative anomaly, putting both now on equal footing. An emergent improved
Casimir energy, that takes into account the multiplicative anomaly among the
building Laplacians, is also discussed. | Topics in 3D N=2 AdS supergravity in superspace: We review some recent results on the construction in superspace of 3D N=2 AdS
supergravities and on the formulation of rigid supersymmetric theories in (1,1)
and (2,0) AdS superspaces. |
Heavy quark potential at finite temperature from gauge/string duality: A static string in an AdS Schwarzschild space is dual to a heavy quark
anti-quark pair in a gauge theory at high temperature. This space is non
confining in the sense that the energy is finite for infinite quark anti-quark
separation. We introduce an infrared cut off in this space and calculate the
corresponding string energy. We find a deconfining phase transition at a
critical temperature T_C. Above T_C the string tension vanishes representing
the deconfined phase. Below T_C we find a linear confining behavior for large
quark anti-quark separation. This simple phenomenological model leads to the
appropriate zero temperature limit, corresponding to the Cornell potential and
also describes a thermal deconfining phase transition. However the temperature
corrections to the string tension do not recover the expected results for low
temperatures. | Effective lagrangian for a mass dimension one fermionic field in curved
spacetime: In this work we use momentum-space techniques to evaluate the propagator
$G(x,x^{\prime})$ for a spin $1/2$ mass dimension one spinor field on a curved
Friedmann-Robertson-Walker spacetime. As a consequence, we built the one-loop
correction to the effective lagrangian in the coincidence limit. Going further
we compute the effective lagrangian in the finite temperature regime. We arrive
at interesting cosmological consequences, as time-dependent cosmological
`constant', fully explaining the functional form of previous cosmological
models. |
Strings vs Spins on the Null Orbifold: We study the null orbifold singularity in 2+1 d flat space higher spin theory
as well as string theory. Using the Chern-Simons formulation of 2+1 d Einstein
gravity, we first observe that despite the singular nature of this geometry,
the eigenvalues of its Chern-Simons holonomy are trivial. Next, we construct a
resolution of the singularity in higher spin theory: a Kundt spacetime with
vanishing scalar curvature invariants. We also point out that the UV
divergences previously observed in the 2-to-2 tachyon tree level string
amplitude on the null orbifold do not arise in the $\alpha^\prime\to \infty$
limit. We find all the divergences of the amplitude and demonstrate that the
ones remaining in the tensionless limit are physical IR-type divergences. We
conclude with a discussion on the meaning and limitations of higher spin
(cosmological) singularity resolution and its potential connection to string
theory. | Kaluza-Klein Towers on General Manifolds: A higher-dimensional universe with compactified extra dimensions admits a
four-dimensional description consisting of an infinite Kaluza-Klein tower of
fields. We revisit the problem of describing the free part of the complete
Kaluza-Klein tower of gauge fields, p-forms, gravity, and flux
compactifications. In contrast to previous studies, we work with a generic
internal manifold of any dimension, completely at the level of the action, in a
gauge invariant formulation, and without resorting to the equations of motion
or analysis of propagators. We demonstrate that the physical fields and
Stuckelberg fields are naturally described by ingredients of the Hodge
decomposition and its analog for symmetric tensors. The spectrum of states and
stability conditions, in terms of the eigenvalues of various Laplacians on the
internal manifold, is easily read from the action. |
Discontinuity relations for the AdS(4)/CFT(3) correspondence: We study in detail the analytic properties of the Thermodynamic Bethe Ansatz
(TBA) equations for the anomalous dimensions of composite operators in the
planar limit of the 3D N=6 superconformal Chern-Simons gauge theory and derive
functional relations for the jump discontinuities across the branch cuts in the
complex rapidity plane. These relations encode the analytic structure of the Y
functions and are extremely similar to the ones obtained for the
previously-studied AdS(5)/CFT(4) case. Together with the Y-system and more
basic analyticity conditions, they are completely equivalent to the TBA
equations. We expect these results to be useful to derive alternative nonlinear
integral equations for the AdS(4)/CFT(3) spectrum. | D-Brane Instability as a Large N Phase Transition: In AdS/CFT analyticity suggests that certain singular behaviors expected at
large 't Hooft coupling should continue smoothly to weak 't Hooft coupling
where the gauge theory is tractable. This may provide a window into stringy
singularity resolution and is a promising technique for studying the signature
of the black hole singularity discussed in hep-th/0306170. We comment briefly
on its status. Our main goal, though, is to study a simple example of this
technique. Gross and Ooguri (hep-th/9805129) have pointed out that the D-brane
minimal surface spanning a pair of 't Hooft loops undergoes a phase transition
as the distance between the loops is varied. We find the analog of this
behavior in the weakly coupled Super Yang Mills theory by computing 't Hooft
loop expectation values there. |
N=(0,2) Deformation of CP(1) Model: Two-dimensional Analog of N=1
Yang-Mills Theory in Four Dimensions: We consider two-dimensional $\mathcal{N}=(0,2)$ sigma models with the CP(1)
target space. A minimal model of this type has one left-handed fermion.
Nonminimal extensions contain, in addition, $N_f$ right-handed fermions. Our
task is to derive expressions for the $\beta$ functions valid to all orders. To
this end we use a variety of methods: (i) perturbative analysis; (ii) instanton
calculus; (iii) analysis of the supercurrent supermultiplet (the so-called
hypercurrent) and its anomalies, and some other arguments. All these arguments,
combined, indicate a direct parallel between the heterotic $\mathcal{N}=(0,2)$
CP(1) models and four-dimensional super-Yang-Mills theories. In particular, the
minimal $\mathcal{N}=(0,2)$ CP(1) model is similar to ${\mathcal N}=1$
supersymmetric gluodynamics. Its exact $\beta$ function can be found; it has
the structure of the Novikov-Shifman-Vainshtein-Zakharov (NSVZ) $\beta$
function of supersymmetric gluodynamics. The passage to nonminimal
$\mathcal{N}=(0,2)$ sigma models is equivalent to adding matter. In this case
an NSVZ-type exact relation between the $\beta$ function and the anomalous
dimensions $\gamma$ of the "matter" fields is established. We derive an analog
of the Konishi anomaly. At large $N_f$ our $\beta$ function develops an
infrared fixed point at small values of the coupling constant (analogous to the
Banks-Zaks fixed point). Thus, we reliably predict the existence of a conformal
window. At $N_f=1$ the model under consideration reduces to the well-known
$\mathcal{N}=(2,2)$ CP(1) model. | Double field theory, twistors, and integrability in 4-manifolds: The search for a geometrical understanding of dualities in string theory, in
particular T-duality, has led to the development of modern T-duality covariant
frameworks such as Double Field Theory, whose mathematical structure can be
understood in terms of generalized geometry and, more recently, para-Hermitian
geometry. In this work we apply techniques associated to this doubled geometry
to four-dimensional manifolds, and we show that they are particularly
well-suited to the analysis of integrability in special spacetimes, especially
in connection with Penrose's twistor theory and its applications to general
relativity. This shows a close relationship between some of the geometrical
structures in the para-Hermitian approach to double field theory and those in
algebraically special solutions to the Einstein equations. Particular results
include the classification of four-dimensional, possibly complex-valued,
(para-)Hermitian structures in different signatures, the Lie and Courant
algebroid structures of special spacetimes, and the analysis of deformations of
(para-)complex structures. We also discuss a notion of "weighted algebroids" in
relation to a natural gauge freedom in the framework. Finally, we analyse the
connection with two- and three-dimensional (real and complex) twistor spaces,
and how the former can be understood in terms of the latter, in particular in
terms of twistor families. |
The Lorentz-Dirac Equation: One More Paradox of Preacceleration: One more paradox of classical Lorentz-Dirac preaccelerative solution is
found: the formation of the event horizon. | Solitons in the Gauged Skyrme-Maxwell Model: We consider soliton solutions of the U(1) gauged Skyrme model with the pion
mass term. The domain of existence of gauged Skyrmions is restricted from above
by the value of the pion mass. Concentrating on the solutions of topological
degree one, we find that coupling to the electromagnetic field breaks the
symmetry of the configurations, the Skyrmions carrying both an electric charge
and a magnetic flux, with an induced dipole magnetic moment. The Skyrmions also
possess an angular momentum, which is quantized in the units of the electric
charge. The mass of the gauged Skyrmions monotonically decreases with increase
of the gauge coupling. |
Non-holomorphic Corrections from Threebranes in F Theory: We construct solutions of type IIB supergravity dual to N=2 super Yang-Mills
theories. By considering a probe moving in a background with constant coupling
and an AdS_{5} component in its geometry, we are able to reproduce the exact
low energy effective action for the theory with gauge group SU(2) and N_{f}=4
massless flavors. After turning on a mass for the flavors we find corrections
to the AdS_{5} geometry. In addition, the coupling shows a power law dependence
on the energy scale of the theory. The origin of the power law behaviour of the
coupling is traced back to instanton corrections. Instanton corrections to the
four derivative terms in the low energy effective action are correctly obtained
from a probe analysis. By considering a Wilson loop in this geometry we are
also able to compute the instanton effects on the quark-antiquark potential.
Finally we consider a solution corresponding to an asymptotically free field
theory. Again, the leading form of the four derivative terms in the low energy
effective action are in complete agreement with field theory expectations. | On the spin geometry of supergravity and string theory: We summarize the main results of our recent investigation of bundles of real
Clifford modules and briefly touch on some applications to string theory and
supergravity. |
Two Massive and One Massless Sp(4) Monopoles: Starting from Nahm's equations, we explore BPS magnetic monopoles in the
Yang-Mills Higgs theory of gauge group $Sp(4)$ which is broken to $SU(2)\times
U(1)$. A family of BPS field configurations with purely Abelian magnetic charge
describe two identical massive monopoles and one massless monopole. We
construct the field configurations with axial symmetry by employing the ADHMN
construction, and find the explicit expression of the metrics for the
12-dimensional moduli space of Nahm data and its submanifolds. | Calogero-Sutherland eigenfunctions with mixed boundary conditions and
conformal field theory correlators: We construct certain eigenfunctions of the Calogero-Sutherland hamiltonian
for particles on a circle, with mixed boundary conditions. That is, the
behavior of the eigenfunction, as neighbouring particles collide, depend on the
pair of colliding particles. This behavior is generically a linear combination
of two types of power laws, depending on the statistics of the particles
involved. For fixed ratio of each type at each pair of neighboring particles,
there is an eigenfunction, the ground state, with lowest energy, and there is a
discrete set of eigenstates and eigenvalues, the excited states and the
energies above this ground state. We find the ground state and special excited
states along with their energies in a certain class of mixed boundary
conditions, interpreted as having pairs of neighboring bosons and other
particles being fermions. These particular eigenfunctions are characterised by
the fact that they are in direct correspondence with correlation functions in
boundary conformal field theory. We expect that they have applications to
measures on certain configurations of curves in the statistical O(n) loop
model. The derivation, although completely independent from results of
conformal field theory, uses ideas from the "Coulomb gas" formulation. |
Universal Logarithmic Behavior in Microstate Counting and the Dual
One-loop Entropy of AdS$_4$ Black Holes: We numerically study the topologically twisted index of several
three-dimensional supersymmetric field theories on a genus $g$ Riemann surface
times a circle, $\Sigma_g\times S^1$. We show that for a large class of
theories with leading term of the order $N^{3/2}$, where $N$ is generically the
rank of the gauge group, there is a universal logarithmic correction of the
form $\frac{g-1}{2} \log N$. We explain how this logarithmic subleading
correction can be obtained as a one-loop effect on the dual supergravity theory
for magnetically charged, asymptotically AdS$_4\times M^7$ black holes for a
large class of Sasaki-Einstein manifolds, $M^7$. The matching of the
logarithmic correction relies on a generic cohomological property of $M^7$ and
it is independent of the black hole charges. We argue that our supergravity
results apply also to rotating, electrically charged asymptotically
AdS$_4\times M^7$ black holes. We present explicitly the quiver gauge theories
and the gravity side corresponding to $M^7=N^{0,1,0}, V^{5,2}$ and $Q^{1,1,1}$. | Nilpotent Symmetries of a Modified Massive Abelian 3-Form Theory:
Augmented Superfield Approach: We derive the off-shell nilpotent and absolutely anticommuting (anti-)BRST
symmetry transformations for any arbitrary D-dimensional St$\ddot
u$ckelberg-modified massive Abelian 3-form theory within the framework of
augmented version of superfield approach (AVSA) to Becchi-Rouet-Stora-Tyutin
(BRST) formalism where, in addition to the horizontality condition (HC), we
exploit the theoretical strength of the gauge invariant restriction (GIR) to
deduce the proper transformations for the gauge, associated (anti-)ghost
fields, auxiliary fields, St$\ddot u$ckelberg compensating field, etc. In fact,
it is an elegant and delicate combination of HC and GIR (within the ambit of
AVSA) that is crucial for all our discussions and derivations. One of the
highlights of our present endeavor is the deduction of a new set of (anti-)BRST
invariant Curci-Ferrari (CF)-type restrictions which are not found in the
massless version of our present theory where only the HC plays an important
role in the derivation of all the (anti-)BRST transformations and a very
specific set of CF-type restrictions. The alternative ways of the derivation of
the full set of the latter, from various theoretical considerations, are also
interesting results of our present investigation. |
On The Behavior Of Gravitational Force At Small Scales: We point out the idea that, at small scales, gravity can be described by the
standard degrees of freedom of general relativity, plus a scalar particle and a
degree of freedom of a new type: the fakeon. This possibility leads to
fundamental implications in understanding gravitational force at quantum level
as well as phenomenological consequences in the corresponding classical theory. | On the Matrix Description of Calabi-Yau Compactifications: We point out that the matrix description of M-theory compactified on
Calabi-Yau threefolds is in many respects simpler than the matrix description
of a $T^6$ compactification. This is largely because of the differences between
D6 branes wrapped on Calabi-Yau threefolds and D6 branes wrapped on six-tori.
In particular, if we define the matrix theory following the prescription of Sen
and Seiberg, we find that the remaining degrees of freedom are decoupled from
gravity. |
Hairy black hole entropy and the role of solitons in three dimensions: Scalar fields minimally coupled to General Relativity in three dimensions are
considered. For certain families of self-interaction potentials, new exact
solutions describing solitons and hairy black holes are found. It is shown that
they fit within a relaxed set of asymptotically AdS boundary conditions, whose
asymptotic symmetry group coincides with the one for pure gravity and its
canonical realization possesses the standard central extension. Solitons are
devoid of integration constants and their (negative) mass, fixed and determined
by nontrivial functions of the self-interaction couplings, is shown to be
bounded from below by the mass of AdS spacetime. Remarkably, assuming that a
soliton corresponds to the ground state of the sector of the theory for which
the scalar field is switched on, the semiclassical entropy of the corresponding
hairy black hole is exactly reproduced from Cardy formula once nonvanishing
lowest eigenvalues of the Virasoro operators are taking into account, being
precisely given by the ones associated to the soliton. This provides further
evidence about the robustness of previous results, for which the ground state
energy instead of the central charge appears to play the leading role in order
to reproduce the hairy black hole entropy from a microscopic counting. | Covariant tetraquark equations in quantum field theory: We derive general covariant coupled equations of QCD describing the
tetraquark in terms of a mix of four-quark states $2q2\bar q$, and two-quark
states $q\bar q$. The coupling of $2q2\bar q$ to $q\bar q$ states is achieved
by a simple contraction of a four-quark $q\bar q$-irreducible Green function
down to a two-quark $q\bar q$ Bethe-Salpeter kernel. The resulting tetraquark
equations are expressed in an exact field theoretic form, and are in agreement
with those obtained previously by consideration of disconnected interactions;
however, despite being more general, they have been derived here in a much
simpler and more transparent way. |
Framed Wilson Operators, Fermionic Strings, and Gravitational Anomaly in
4d: We study gapped systems with anomalous time-reversal symmetry and global
gravitational anomaly in three and four spacetime dimensions. These systems
describe topological order on the boundary of bosonic Symmetry Protected
Topological (SPT) Phases. Our description of these phases is via the recent
cobordism proposal for their classification. In particular, the behavior of
these systems is determined by the geometry of Stiefel-Whitney classes. We
discuss electric and magnetic operators defined by these classes, and new types
of Wilson lines and surfaces that sit on their boundary. The lines describe
fermionic particles, while the surfaces describe a sort of fermionic string. We
show that QED with a fermionic monopole exhibits the 4d global gravitational
anomaly and has a fermionic $\pi$-flux. | Finite Size Effects in Integrable Quantum Field Theories: The study of Finite Size Effects in Quantum Field Theory allows the
extraction of precious perturbative and non-perturbative information. The use
of scaling functions can connect the particle content (scattering theory
formulation) of a QFT to its ultraviolet Conformal Field Theory content. If the
model is integrable, a method of investigation through a nonlinear integral
equation equivalent to Bethe Ansatz and deducible from a light-cone lattice
regularization is available. It allows to reconstruct the S-matrix and to
understand the locality properties in terms of Bethe root configurations,
thanks to the link to ultraviolet CFT guaranteed by the exact determination of
scaling function. This method is illustrated in practice for Sine-Gordon /
massive Thirring models, clarifying their locality structure and the issues of
equivalence between the two models. By restriction of the Sine-Gordon model it
is also possible to control the scaling functions of minimal models perturbed
by Phi_1,3 |
Exact absorption probabilities for the D3-brane: We consider a minimal scalar in the presence of a three-brane in ten
dimensions. The linearized equation of motion, which is just the wave equation
in the three-brane metric, can be solved in terms of associated Mathieu
functions. An exact expression for the reflection and absorption probabilities
can be obtained in terms of the characteristic exponent of Mathieu's equation.
We describe an algorithm for obtaining the low-energy behavior as a series
expansion, and discuss the implications for the world-volume theory of
D3-branes. | Quasinormal modes of black holes in anti-de Sitter space: a numerical
study of the eikonal limit: Using series solutions and time-domain evolutions, we probe the eikonal limit
of the gravitational and scalar-field quasinormal modes of large black holes
and black branes in anti-de Sitter backgrounds. These results are particularly
relevant for the AdS/CFT correspondence, since the eikonal regime is
characterized by the existence of long-lived modes which (presumably) dominate
the decay timescale of the perturbations. We confirm all the main qualitative
features of these slowly-damped modes as predicted by Festuccia and Liu
(arXiv:0811.1033) for the scalar-field (tensor-type gravitational)
fluctuations. However, quantitatively we find dimensional-dependent correction
factors. We also investigate the dependence of the QNM frequencies on the
horizon radius of the black hole (brane) and the angular momentum (wavenumber)
of vector- and scalar-type gravitational perturbations. |
Brane Gases in the Early Universe: Over the past decade it has become clear that fundamental strings are not the
only fundamental degrees of freedom in string theory. D-branes are also part of
the spectrum of fundamental states. In this paper we explore some possible
effects of D-branes on early Universe string cosmology, starting with two key
assumptions: firstly that the initial state of the Universe corresponded to a
dense, hot gas in which all degrees of freedom were in thermal equilibrium, and
secondly that the topology of the background space admits one-cycles. We argue
by t-duality that in this context the cosmological singularities are not
present. We derive the equation of state of the brane gases and apply the
results to suggest that, in an expanding background, the winding modes of
fundamental strings will play the most important role at late times. In
particular, we argue that the string winding modes will only allow four
space-time dimensions to become large. The presence of brane winding modes with
$p > 1$ may lead to a hierarchy in the sizes of the extra dimensions. | Two-Matrix String Model as Constrained (2+1)-Dimensional Integrable
System: We show that the 2-matrix string model corresponds to a coupled system of
$2+1$-dimensional KP and modified KP ($\KPm$) integrable equations subject to a
specific ``symmetry'' constraint. The latter together with the
Miura-Konopelchenko map for $\KPm$ are the continuum incarnation of the matrix
string equation. The $\KPm$ Miura and B\"{a}cklund transformations are natural
consequences of the underlying lattice structure. The constrained $\KPm$ system
is equivalent to a $1+1$-dimensional generalized KP-KdV hierarchy related to
graded ${\bf SL(3,1)}$. We provide an explicit representation of this
hierarchy, including the associated ${\bf W(2,1)}$-algebra of the second
Hamiltonian structure, in terms of free currents. |
Identity of the van der Waals Force and the Casimir Effect and the
Irrelevance of these Phenomena to Sonoluminescence: We show that the Casimir, or zero-point, energy of a dilute dielectric ball,
or of a spherical bubble in a dielectric medium, coincides with the sum of the
van der Waals energies between the molecules that make up the medium. That
energy, which is finite and repulsive when self-energy and surface effects are
removed, may be unambiguously calculated by either dimensional continuation or
by zeta function regularization. This physical interpretation of the Casimir
energy seems unambiguous evidence that the bulk self-energy cannot be relevant
to sonoluminescence. | Peeling and Multi-critical Matter Coupled to Quantum Gravity: We show how to determine the unknown functions arising when the peeling
decomposition is applied to multi-critical matter coupled to two-dimensional
quantum gravity and compute the loop-loop correlation functions. The results
that $\eta=2+2/(2K-3)$ and $\nu=1-3/2K$ agree with the slicing decomposition,
and satisfy Fisher scaling. |
Einstein-Cartan gravity, Asymptotic Safety, and the running Immirzi
parameter: In this paper we analyze the functional renormalization group flow of quantum
gravity on the Einstein-Cartan theory space. The latter consists of all action
functionals depending on the spin connection and the vielbein field (co-frame)
which are invariant under both spacetime diffeomorphisms and local frame
rotations. In the first part of the paper we develop a general methodology and
corresponding calculational tools which can be used to analyze the flow
equation for the pertinent effective average action for any truncation of this
theory space. In the second part we apply it to a specific three-dimensional
truncated theory space which is parametrized by Newton's constant, the
cosmological constant, and the Immirzi parameter. A comprehensive analysis of
their scale dependences is performed, and the possibility of defining an
asymptotically safe theory on this hitherto unexplored theory space is
investigated. In principle Asymptotic Safety of metric gravity (at least at the
level of the effective average action) is neither necessary nor sufficient for
Asymptotic Safety on the Einstein-Cartan theory space which might accommodate
different "universality classes" of microscopic quantum gravity theories.
Nevertheless, we do find evidence for the existence of at least one
non-Gaussian renormalization group fixed point which seems suitable for the
Asymptotic Safety construction in a setting where the spin connection and the
vielbein are the fundamental field variables. | Probing analytical and numerical integrability: The curious case of
$(AdS_5\times S^5)_η$: Motivated by recent studies related to integrability of string motion in
various backgrounds via analytical and numerical procedures, we discuss these
procedures for a well known integrable string background $(AdS_5\times
S^5)_{\eta}$. We start by revisiting conclusions from earlier studies on string
motion in $(\mathbb{R}\times S^3)_{\eta}$ and $(AdS_3)_{\eta}$ and then move on
to more complex problems of $(\mathbb{R}\times S^5)_{\eta}$ and
$(AdS_5)_{\eta}$. Discussing both analytically and numerically, we deduce that
while $(AdS_5)_{\eta}$ strings do not encounter any irregular trajectories,
string motion in the deformed five-sphere can indeed, quite surprisingly, run
into chaotic trajectories. We discuss the implications of these results both on
the procedures used and the background itself. |
Condensates in Quantum Chromodynamics and the Cosmological Constant: Casher and Susskind have noted that in the light-front description,
spontaneous chiral symmetry breaking in quantum chromodynamics (QCD) is a
property of hadronic wavefunctions and not of the vacuum. Here we show from
several physical perspectives that, because of color confinement, quark and
gluon QCD condensates are associated with the internal dynamics of hadrons. We
discuss condensates using condensed matter analogues, the AdS/CFT
correspondence, and the Bethe-Salpeter/Dyson-Schwinger approach for bound
states. Our analysis is in agreement with the Casher and Susskind model and the
explicit demonstration of "in-hadron" condensates by Roberts et al., using the
Bethe-Salpeter/Dyson-Schwinger formalism for QCD bound states. These results
imply that QCD condensates give {\it zero} contribution to the cosmological
constant, since all of the gravitational effects of the in-hadron condensates
are already included in the normal contribution from hadron masses. | Algebra for quantum fields: We give an account of the current state of the approch to quantum field
theory via Hopf algebras and Hochschild cohomology. We emphasize the
versatility and mathematical foundation of this algebraic structure, and
collect algebraic structures here in one place which are either scattered over
the literature, or only implicit in previous writings. In particular we point
out mathematical structures which can be helpful to farther develop our
mathematical understanding of quantum fields. |
Lectures on Higher-Gauge Symmetries from Nambu Brackets and
Covariantized M(atrix) Theory: This lecture consists of three parts. In part I, an overview is given on the
so-called Matrix theory in the light-front gauge as a proposal for a concrete
and non-perturbative formulation of M-theory. I emphasize motivations towards
its covariant formulation. Then, in part II, I turn the subject to the
so-called Nambu bracket and Nambu mechanics, which were proposed by Nambu in
1973 as a possible extension of the ordinary Hamiltonian mechanics. After
reviewing briefly Nambu's original work, it will be explained why his idea may
be useful in exploring higher symmetries which would be required for covariant
formulations of Matrix theory. Then, using this opportunity, some comments on
the nature of Nambu mechanics and its quantization are given incidentally:
though they are not particularly relevant for our specialized purpose of
constructing covariant Matrix theory, they may be of some interests for further
developments in view of possible other applications of Nambu mechanics. The
details will be relegated to forthcoming publications. In part III, I give an
expository account of the basic ideas and main results from my recent attempt
to construct a covariantized Matrix theory on the basis of a simple matrix
version of Nambu bracket equipped with some auxiliary variables, which
characterize the scale of M-theory and simultaneously play a crucial role in
realizing (dynamical) supersymmetry in a covariant fashion. | Noncommutative Quantum Field Theory: A Confrontation of Symmetries: The concept of a noncommutative field is formulated based on the interplay
between twisted Poincar\'e symmetry and residual symmetry of the Lorentz group.
Various general dynamical results supporting this construction, such as the
light-wedge causality condition and the integrability condition for
Tomonaga-Schwinger equation, are presented. Based on this analysis, the claim
of the identity between commutative QFT and noncommutative QFT with twisted
Poincar\'e symmetry is refuted. |
Mixing internal and spacetime transformations: some examples and
counterexamples: This note addresses the question whether in a gauge theory coupled to gravity
internal and spacetime transformation can be mixed. It is shown that if the VEV
of the gauge field is flat, the symmetry group is always a product of internal
and spacetime symmetries. On the other hand, if the VEV of the gauge field is
not flat it is impossible to properly define the notion of a ``spacetime''
transformation; as a consequence, if the symmetry group is nontrivial, mixing
generically occurs. | Mixed-symmetry massless gauge fields in AdS(5): Free AdS(5) mixed-symmetry massless bosonic and fermionic gauge fields of
arbitrary spins are described by using su(2,2) spinor language. Manifestly
covariant action functionals are constructed and field equations are derived. |
Cabling procedure for the colored HOMFLY polynomials: In the present paper we discuss the cabling procedure for the colored HOMFLY
polynomial. We describe how it can be used and how one can find all the
quantities such as projectors and $\mathcal{R}$-matrices, which are needed in
this procedure. The constructed matrix forms of the projectors and the
fundamental $\mathcal{R}$-matrices allow one in principle (neglecting the
computational difficulties) to find the HOMFLY polynomial in any representation
for any knot. We also discuss the group theory explanation of the cabling
procedure. This leads to the explanations of the form of the fundamental
$\mathcal{R}$-matrices and illuminates several conjectures proposed in previous
papers. | Kronecker anomalies and gravitational striction: We study quantum field theories in which the number of degrees of freedom
changes discontinuously across the momentum space. This discontinuity which we
call "Kronecker anomaly" leads to non-local effective actions and can be
represented as a theory with the random, self-tuning coupling constants. |
p-Adic description of Higgs mechanism III: calculation of elementary
particle masses: This paper belongs to the series devoted to the calculation of particle
masses in the framework of p-adic conformal field theory limit of Topological
GeometroDynamics. In paper II the general formulation of p-adic Higgs mechanism
was given. In this paper the calculation of the fermionic and bosonic masses is
carried out. The calculation of the masses necessitates the evaluation of dege-
neracies for states as a function of conformal weight in certain tensor product
of Super Virasoro algebras. The masses are very sen- sitive to the degeneracy
ratios: Planck mass results unless the ratio for the degeneracies for first
excited states and massless states is an integer multiple of 2/3. For leptons,
quarks and gauge bosons this miracle occurs. The main deviation from standard
model is the prediction of light color excited leptons and quarks as well as
colored boson exotics. Higgs particle is absent from spectrum as is also
graviton: the latter is due to the basic approximation of p-adic TGD. Reason
for replacement: the recently identified light colored boson exotics making
theory asymptotically free in standard sense. | Holographic phase transitions from higgsed, non abelian charged black
holes: We find solutions of a gravity-Yang-Mills-Higgs theory in four dimensions
that represent asymptotic anti-de Sitter charged black holes with partial/full
gauge symmetry breaking. We then apply the AdS/CFT correspondence to study the
strong coupling regime of a $2+1$ quantum field theory at temperature $T$ and
finite chemical potential, which undergoes transitions to phases exhibiting the
condensation of a composite charged vector operator below a critical
temperature $T_c$, presumably describing $p+ip/p$-wave superconductors. In the
case of $p+ip$-wave superconductors the transitions are always of second order.
But for $p$-wave superconductors we determine the existence of a critical value
$\alpha_c$ of the gravitational coupling (for fixed Higgs v.e.v. parameter
$\hat m_W$) beyond which the transitions become of first order. As a
by-product, we show that the $p$-wave phase is energetically favored over the
$p+ip$ one, for any values of the parameters. We also find the ground state
solutions corresponding to zero temperature. Such states are described by
domain wall geometries that interpolate between $AdS_4$ spaces with different
light velocities, and for a given $\hat m_{W}$, they exist below a critical
value of the coupling. The behavior of the order parameter as function of the
gravitational coupling near the critical coupling suggests the presence of
second order quantum phase transitions. We finally study the dependence of the
solution on the Higgs coupling, and find the existence of a critical value
beyond which no condensed solution is present. |
Origin of fermion generations from extended noncommutative geometry: We propose a way to understand the 3 fermion generations by the algebraic
structures of noncommutative geometry, which is a promising framework to unify
the standard model and general relativity. We make the tensor product extension
and the quaternion extension on the framework. Each of the two extensions alone
keeps the action invariant, and we consider them as the almost trivial
structures of the geometry. We combine the two extensions, and show the
corresponding physical effects, i.e., the emergence of 3 fermion generations
and the mass relationships among those generations. We define the coordinate
fiber space of the bundle of the manifold as the space in which the classical
noncommutative geometry is expressed, then the tensor product extension
explicitly shows the contribution of structures in the non-coordinate base
space of the bundle to the action. The quaternion extension plays an essential
role to reveal the physical effect of the structure in the non-coordinate base
space. | Splitting of surface defect partition functions and integrable systems: We study Bethe/gauge correspondence at the special locus of Coulomb moduli
where the integrable system exhibits the splitting of degenerate levels. For
this investigation, we consider the four-dimensional pure $\mathcal{N}=2$
supersymmetric $U(N)$ gauge theory, with a half-BPS surface defect constructed
with the help of an orbifold or a degenerate gauge vertex. We show that the
non-perturbative Dyson-Schwinger equations imply the Schr\"odinger-type and the
Baxter-type differential equations satisfied by the respective surface defect
partition functions. At the special locus of Coulomb moduli the surface defect
partition function splits into parts. We recover the Bethe/gauge dictionary for
each summand. |
Notes on gauging noneffective group actions: In this paper we study sigma models in which a noneffective group action has
been gauged. Such gauged sigma models turn out to be different from gauged
sigma models in which an effectively-acting group is gauged, because of
nonperturbative effects on the worldsheet. We concentrate on finite
noneffectively-acting groups, though we also outline how analogous phenomena
also happen in nonfinite noneffectively-acting groups. We find that
understanding deformations along twisted sector moduli in these theories leads
one to new presentations of CFT's, defined by fields valued in roots of unity. | Deformation of Conifold and Intersecting Branes: We study the relation between intersecting NS5-branes whose intersection is
smoothed out and the deformed conifold in terms of the supergravity solution.
We solve the condition of preserved supersymmetry on a metric inspired by the
deformed conifold metric and obtain a solution of the NS5-branes which is
delocalized except for one of the overall transverse directions. The solution
has consistent properties with other configurations obtained by string
dualities. |
Quantum corrections to the kinetic term in the Randall-Sundrum model: The effective action of the radion in the Randall-Sundrum model is analysed.
Fine tunings are needed to obtain the observed mass hierarchy and an invisible
radion. since the kinetic terms are important for determining the radion mass,
the finite quantum corrections from massless conformally coupled fermions are
analysed and found to vanish at one loop order. | The off-shell 4D/5D connection: A systematic off-shell reduction scheme from five to four space-time
dimensions is presented for supergravity theories with eight supercharges. It
is applicable to theories with higher-derivative couplings and it is used to
address a number of open questions regarding BPS black holes in five
dimensions. Under this reduction the 5D Weyl multiplet becomes reducible and
decomposes into the 4D Weyl multiplet and an extra Kaluza-Klein vector
multiplet. The emergence of the pseudoscalar field of the latter multiplet and
the emergence of the 4D R-symmetry group are subtle features of the reduction.
The reduction scheme enables to determine how a 5D supersymmetric Lagrangian
with higher-derivative couplings decomposes upon dimensional reduction into a
variety of independent 4D supersymmetric invariants, without the need for
imposing field equations. In this way we establish, for example, the existence
of a new N=2 supersymmetric invariant that involves the square of the Ricci
tensor. Finally we resolve the questions associated with the 5D Chern-Simons
terms for spinning BPS black holes and their relation to the corresponding 4D
black holes. |
Exact Wavefunctions in a Noncommutative Field Theory: We consider the nonrelativistic field theory with a quartic interaction on a
noncommutative plane. We compute the four point scattering amplitude within
perturbative analysis to all orders and identify the beta function and the
running of the coupling constant. Since the theory admits an equivalent
description via the N particle Schrodinger equation, we regain the scattering
amplitude by finding an exact scattering wavefunction of the two body equation.
The wave function for the bound state is also identified. These wave functions
unusually have two center positions in the relative coordinates. The separation
of the centers is in the transverse direction of the total momentum and grows
linearly with the noncommutativity scale and the total momentum, exhibiting the
stringy nature of the noncommutative field theory. | N=2 SuperTime Dependent Oscillator and spontaneous Breaking of
Supersymmetry: Using the nonlinear realizations of the N=2 superVirasoro group we construct
the action of the N=2 Superconformal Quantum Mechanics(SCQM) with additional
harmonic potential.We show that SU(1,1|1) invariance group of this action is
nontrivially embedded in the N=2 Super Virasoro group.The generalization for
the (super)time dependent oscillator is constructed.In a particular case when
the oscillator frequency depends on the proper-time anticommuting coordinates
the unusual effect of spontaneous breaking of the supersymmetry takes place:
the Masses of bosons and fermions can have different nonzero values. |
A Metric for Heterotic Moduli: Heterotic vacua of string theory are realised, at large radius, by a compact
threefold with vanishing first Chern class together with a choice of stable
holomorphic vector bundle. These form a wide class of potentially realistic
four-dimensional vacua of string theory. Despite all their phenomenological
promise, there is little understanding of the metric on the moduli space of
these. What is sought is the analogue of special geometry for these vacua. The
metric on the moduli space is important in phenomenology as it normalises
D-terms and Yukawa couplings. It is also of interest in mathematics, since it
generalises the metric, first found by Kobayashi, on the space of gauge field
connections, to a more general context. Here we construct this metric, correct
to first order in alpha', in two ways: first by postulating a metric that is
invariant under background gauge transformations of the gauge field, and also
by dimensionally reducing heterotic supergravity. These methods agree and the
resulting metric is Kahler, as is required by supersymmetry. Checking that the
metric is in fact Kahler is quite intricate and uses the anomaly cancellation
equation for the H-field, in an essential way. The Kahler potential
nevertheless takes a remarkably simple form: it is Kahler potential for special
geometry with the Kahler form replaced by the alpha'-corrected hermitian form. | Observable algebra for the rational and trigonometric Euler Calogero
Moser models: We construct polynomial Poisson algebras of observables for the classical
Euler-Calogero-Moser (ECM) models. The conserved Hamiltonians and symmetry
algebras derived in a previous work are subsets of these algebras. We define
their linear, $N \rightarrow \infty$ limits, realizing $\w_{\infty}$ type
algebras coupled to current algebras. |
A New Family of Diagonal Ade-Related Scattering Theories: We propose the factorizable S-matrices of the massive excitations of the
non-unitary minimal model $M_{2,11}$ perturbed by the operator $\Phi_{1,4}$.
The massive excitations and the whole set of two particle S-matrices of the
theory is simply related to the $E_8$ unitary minimal scattering theory. The
counting argument and the Thermodynamic Bethe Ansatz (TBA) are applied to this
scattering theory in order to support this interpretation. Generalizing this
result, we describe a new family of NON UNITARY and DIAGONAL $ADE$-related
scattering theories. A further generalization suggests the magnonic TBA for a
large class of non-unitary $\G\otimes\G/\G$ coset models
($\G=A_{odd},D_n,E_{6,7,8}$) perturbed by $\Phi_{id,id,adj}$, described by
non-diagonal S-matrices. | Exact Solution of the One-Dimensional Non-Abelian Coulomb Gas at Large N: The problem of computing the thermodynamic properties of a one-dimensional
gas of particles which transform in the adjoint representation of the gauge
group and interact through non-Abelian electric fields is formulated and solved
in the large $N$ limit. The explicit solution exhibits a first order
confinement-deconfinement phase transition with computable properties and
describes two dimensional adjoint QCD in the limit where matter field masses
are large. |
Chains of N=2, D=4 heterotic/type II duals: We report on a search for $N=2$ heterotic strings that are dual candidates of
type II compactifications on Calabi-Yau threefolds described as $K3$
fibrations. We find many new heterotic duals by using standard orbifold
techniques. The associated type II compactifications fall into chains in which
the proposed duals are heterotic compactifications related one another by a
sequential Higgs mechanism. This breaking in the heterotic side typically
involves the sequence $SU(4)\rightarrow SU(3)\rightarrow $ $SU(2)\rightarrow
0$, while in the type II side the weights of the complex hypersurfaces and the
structure of the $K3$ quotient singularities also follow specific patterns. | Quasinormal modes of Reissner-Nordstr$\ddot{o}$m Anti-de Sitter Black
Holes: Complex frequencies associated with quasinormal modes for large
Reissner-Nordstr$\ddot{o}$m Anti-de Sitter black holes have been computed.
These frequencies have close relation to the black hole charge and do not
linearly scale with the black hole temperature as in Schwarzschild Anti-de
Sitter case. In terms of AdS/CFT correspondence, we found that the bigger the
black hole charge is, the quicker for the approach to thermal equilibrium in
the CFT. The properties of quasinormal modes for $l>0$ have also been studied. |
Truncated Conformal Space at c=1, Nonlinear Integral Equation and
Quantization Rules for Multi-Soliton States: We develop Truncated Conformal Space (TCS) technique for perturbations of c=1
Conformal Field Theories. We use it to give the first numerical evidence of the
validity of the non-linear integral equation (NLIE) derived from light-cone
lattice regularization at intermediate scales. A controversy on the
quantization of Bethe states is solved by this numerical comparison and by
using the locality principle at the ultra- violet fixed point. It turns out
that the correct quantization for pure hole states is the one with half-integer
quantum numbers originally proposed by Mariottini et al. Once the correct rule
is imposed, the agreement between TCS and NLIE for pure hole states turns out
to be impressive. | String Theory and Unification: The use of the AdS/CFT correspondence to arrive at quiver gauge field
theories is discussed. An abelian orbifold with the finite group $Z_{p}$ can
give rise to a nonsupersymmetric $G = U(N)^p$ gauge theory with chiral fermions
and complex scalars in different bi-fundamental representations of $G$. The
precision measurements at the $Z$ resonance suggest the values $p = 12$ and $N
= 3$, and a unifications scale $M_U \sim 4$ TeV. Dedicated to the 65th birthday
of Pran Nath. |
Quartic propagators, negative norms and the physical spectrum: Many arguments against quartic propagators, negative norm states and related
effects concern the sicknesses which occur when the spectrum of the free
particle Hamiltonian is formed. However, if the theory is more complicated, for
example involving confinement such that the particle in question does not
appear in the physical spectrum, those considerations do not apply directly.
Path integral methods suggest that some of these may be acceptable theories. I
provide an example that should be able to be simulated on a lattice which then
allows a non-perturbative resolution of this question. In its SU(2) version it
involves a scalar triplet with a quartic derivative Lagrangian coupled to the
SU(2) gauge field. If this is verified to be a healthy theory, it could open
new avenues in model building. I also discuss how strong interactions can
dynamically modify the dispersion relation leaving a healthy effective field
theory, using conformal gravity coupled to a Yang-Mills theory as an example.
Such a theory could possibly form a UV completion for quantum gravity. | Scattering of Open and Closed Strings in 1+1 Dimensions: The ground ring structure of 1+1 dimensional string theory leads to an
infinite set of non linear recursion relations among the `bulk' scattering
amplitudes of open and closed tachyons on the disk, which fix them uniquely.
The relations are generated by the action of the ring on the tachyon modules;
associativity of this action determines all structure constants. This algebraic
structure may allow one to relate the continuum picture to a matrix model. |
Solitons in Brane Worlds: We study some aspects of dilatonic domain walls in relation to the idea on
the noncompact internal space. We find that the warp factor in the spacetime
metric increases as one moves away from the domain wall for all the
supersymmetric dilatonic domain wall solutions obtained from the (intersecting)
BPS branes in string theories through toroidal compactifications, unlike the
case of the Randall-Sundrum model. On the other hand, when the dilaton coupling
parameter a for the D-dimensional extreme dilatonic domain wall takes the
values |a|<2/(D-2), the Kaluza-Klein spectrum of graviton has the same
structure as that of the Randall-Sundrum model (and the warp factor decreases
in the finite interval around the dilatonic domain wall), thereby implying the
possibility of extending the Randall-Sundrum model to the |a|<2/(D-2) case. We
construct fully localized solutions describing extreme dilatonic branes within
extreme dilatonic domain walls and the supersymmetric branes within the
supersymmetric domain walls of string theories. These solutions are valid in
any region of spacetime, not just in the region close to the domain walls. | Spherical functions on affine Lie groups: We describe vector valued conjugacy equivariant functions on a group K in two
cases -- K is a compact simple Lie group, and K is an affine Lie group.
We construct such functions as weighted traces of certain intertwining
operators between representations of K. For a compact group $K$, Peter-Weyl
theorem implies that all equivariant functions can be written as linear
combinations of such traces. Next, we compute the radial parts of the Laplace
operators of $K$ acting on conjugacy equivariant functions and obtain a comple-
tely integrable quantum system with matrix coefficients, which in a special
case coincides with the trigonometric Calogero-Sutherland-Moser multi-particle
system. In the affine Lie group case, we prove that the space of equivariant
functions having a fixed homogeneity degree with respect to the action of the
center of the group is finite-dimensional and spanned by weighted traces of
intertwining operators. This space coincides with the space of
Wess-Zumino-Witten conformal blocks on an elliptic curve. We compute the radial
part of the second order Laplace operator on the affine Lie group acting on
equivariant functions, and find that it is a certain parabolic partial
differential operator, which degenerates to the elliptic
Calogero-Sutherland-Moser hamiltonian as the central charge tends to minus the
dual Coxeter number (the critical level). Quantum integrals of this hamiltonian
are obtained as radial part of the higher Sugawara operators which are central
at the critical level. |
Magnetic monopole loops supported by a meron pair as the quark confiner: We give a definition of gauge-invariant magnetic monopoles in Yang-Mills
theory without using the Abelian projection due to 't Hooft. They automatically
appear from the Wilson loop operator. This is shown by rewriting the Wilson
loop operator using a non-Abelian Stokes theorem. The magnetic monopole defined
in this way is a topological object of co-dimension 3, i.e., a loop in
four-dimensions. We show that such magnetic loops indeed exist in
four-dimensional Yang-Mills theory. In fact, we give an analytical solution
representing circular magnetic monopole loops joining a pair of merons in the
four-dimensional Euclidean SU(2) Yang-Mills theory. This is achieved by solving
the differential equation for the adjoint color (magnetic monopole) field in
the two--meron background field within the recently developed reformulation of
the Yang-Mills theory. Our analytical solution corresponds to the numerical
solution found by Montero and Negele on a lattice. This result strongly
suggests that a meron pair is the most relevant quark confiner in the original
Yang-Mills theory, as Callan, Dashen and Gross suggested long ago. | Generalized $μ$-Terms from Orbifolds and M-Theory: We consider solutions to the $\mu$-problem originating in the effective low
energy theories, of N=1 orbifold compactifications of the heterotic string,
after supersymmetry breaking. They are consistent with the invariance of the
one loop corrected effective action in the linear representation of the
dilaton. The proposed $\mu$-terms naturally generalize solutions proposed
previously, in the literature, in the context of minimal low energy
supergravity models. They emanate from the connection of the non-perturbative
superpotential to the determinant of the mass matrix of the chiral
compactification modes. Within this approach we discuss the lifting of our
solutions to their M-theory compactification counterparts. |
Quantum Graphity: We introduce a new model of background independent physics in which the
degrees of freedom live on a complete graph and the physics is invariant under
the permutations of all the points. We argue that the model has a low energy
phase in which physics on a low dimensional lattice emerges and the permutation
symmetry is broken to the translation group of that lattice. In the high
temperature, or disordered, phase the permutation symmetry is respected and the
average distance between degrees of freedom is small. This may serve as a
tractable model for the emergence of classical geometry in background
independent models of spacetime. We use this model to argue for a cosmological
scenario in which the universe underwent a transition from the high to the low
temperature phase, thus avoiding the horizon problem. | Noncommutative spectral geometry: A guided tour for theoretical
physicists: We review a gravitational model based on noncommutative geometry and the
spectral action principle. The space-time geometry is described by the tensor
product of a four-dimensional Riemanian manifold by a discrete noncommutative
space consisting of only two points. With a specific choice of the finite
dimensional involutive algebra, the noncommutative spectral action leads to the
standard model of electroweak and strong interactions minimally coupled to
Einstein and Weyl gravity. We present the main mathematical ingredients of this
model and discuss their physical implications. We argue that the doubling of
the algebra is intimately related to dissipation and the gauge field structure.
We then show how this noncommutative spectral geometry model, a purely
classical construction, carries implicit in the doubling of the algebra the
seeds of quantization. After a short review on the phenomenological
consequences of this geometric model as an approach to unification, we discuss
some of its cosmological consequences. In particular, we study deviations of
the Friedmann equation, propagation of gravitational waves, and investigate
whether any of the scalar fields in this model could play the role of the
inflaton. |
E{7(7)} Symmetry and Finiteness of N=8 Supergravity: We study N=8 supergravity deformed by the presence of the candidate
counterterms. We show that even though they are invariant under undeformed
E{7(7)}, all of the candidate counterterms violate the deformed E{7(7)} current
conservation. The same conclusion follows from the uniqueness of the Lorentz
and SU(8) covariant, E{7(7)} invariant unitarity constraint expressing the
56-dimensional E{7(7)} doublet via 28 independent vectors. Therefore E{7(7)}
duality predicts the all-loop UV finiteness of perturbative N=8 supergravity. | Gauge and Gravitational Anomalies and Hawking Radiation of Rotating BTZ
Black Holes: In this paper we obtain the flux of Hawking radiation from Rotating BTZ black
holes from gauge and gravitational anomalies point of view. Then we show that
the gauge and gravitational anomaly in the BTZ spacetime is cancelled by the
total flux of a 2-dimensional blackbody at the Hawking temperature of the
spacetime. |
On canonical quantization of the gauged WZW model with permutation
branes: In this paper we perform canonical quantization of the product of the gauged
WZW models on a strip with boundary conditions specified by permutation branes.
We show that the phase space of the $N$-fold product of the gauged WZW model
$G/H$ on a strip with boundary conditions given by permutation branes is
symplectomorphic to the phase space of the double Chern-Simons theory on a
sphere with $N$ holes times the time-line with $G$ and $H$ gauge fields both
coupled to two Wilson lines. For the special case of the topological coset
$G/G$ we arrive at the conclusion that the phase space of the $N$-fold product
of the topological coset $G/G$ on a strip with boundary conditions given by
permutation branes is symplectomorphic to the phase space of Chern-Simons
theory on a Riemann surface of the genus $N-1$ times the time-line with four
Wilson lines. | Black hole thermodynamics and information loss in two dimensions: Black hole evaporation is investigated in a (1+1)-dimensional model of
quantum gravity. Quantum corrections to the black hole entropy are computed,
and the fine-grained entropy of the Hawking radiation is studied. A generalized
second law of thermodynamics is formulated, and shown to be valid under
suitable conditions. It is also shown that, in this model, a black hole can
consume an arbitrarily large amount of information. |
Off-Shell Dynamics of the O(3) Nonlinear Sigma-Model -- Beyond
Monte-Carlo and Perturbation Theory: The off-shell dynamics of the O(3) nonlinear sigma-model is probed in terms
of spectral densities and two-point functions by means of the form factor
approach. The exact form factors of the Spin field, Noether-current, EM-tensor
and the topological charge density are computed up to 6-particles. The
corresponding $n\leq 6$ particle spectral densities are used to compute the
two-point functions, and are argued to deviate at most a few per mille from the
exact answer in the entire energy range below 10^3 in units of the mass gap. To
cover yet higher energies we propose an extrapolation scheme to arbitrary
particle numbers based on a novel scaling hypothesis for the spectral
densities. It yields candidate results for the exact two-point functions at all
energy scales and allows us to exactly determine the values of two, previously
unknown, non-perturbative constants. | A Relation between the Anomalous Dimensions and OPE Coefficients in
Asymptotic Free Field Theories: In asymptotic free field theories we show that part of the OPE of the trace
of the stress-energy tensor and an arbitrary composite field is determined by
the anomalous dimension of the composite field. We take examples from the
two-dimensional O(N) non-linear sigma model. |
$d+id$ Holographic Superconductors: A holographic model of $d+id$ superconductors based on the action proposed by
Benini, Herzog, and Yarom [arXiv:1006.0731] is studied. This model has a
charged spin two field in an AdS black hole spacetime. Working in the probe
limit, the normalizable solution of the spin two field in the bulk gives rise
to a $d+id$ superconducting order parameter at the boundary of the AdS. We
calculate the fermion spectral function in this\ superconducting background and
confirm the existence of fermi arcs for non-vanishing Majorana couplings. By
changing the relative strength $\gamma $ of the $d$ and $id$ condensations, the
position and the size of the fermi arcs are changed. When $\gamma =1$, the
spectrum becomes isotropic and the spectral function is s-wave like. By
changing the fermion mass, the fermi momentum is changed. We also calculate the
conductivity for these holographic $d+id$ superconductors where time reversal
symmetry has been broken spontaneously. A non-vanishing Hall conductivity is
obtained even without an external magnetic field. | The cosmic role of tachyon in the type 0 strings: We present a new class of solution to the ten-dimensional type 0 effective
action. Given a generic potential of tachyon field, there exist phases where
tachyon is either frozen at local extremals or free to propagate along flat
directions. In the latter phase, a cosmology model is proposed where the
tachyon plays the role of time. |
Curved BPS domain wall solutions in four-dimensional N=2 supergravity: We construct four-dimensional domain wall solutions of N=2 gauged
supergravity coupled to vector and to hypermultiplets. The gauged supergravity
theories that we consider are obtained by performing two types of Abelian
gauging. In both cases we find that the behaviour of the scalar fields
belonging to the vector multiplets is governed by the so-called attractor
equations known from the study of BPS black hole solutions in ungauged N=2
supergravity theories. The scalar fields belonging to the hypermultiplets, on
the other hand, are either constant or exhibit a run-away behaviour. These
domain wall solutions preserve 1/2 of supersymmetry and they are, in general,
curved. We briefly comment on the amount of supersymmetry preserved by domain
wall solutions in gauged supergravity theories obtained by more general
gaugings. | Electron-positron pairs production in a macroscopic charged core: Classical and semi-classical energy states of relativistic electrons bounded
by a massive and charged core with the charge-mass-radio Q/M and macroscopic
radius R_c are discussed. We show that the energies of semi-classical (bound)
states can be much smaller than the negative electron mass-energy (-mc^2), and
energy-level crossing to negative energy continuum occurs. Electron-positron
pair production takes place by quantum tunneling, if these bound states are not
occupied. Electrons fill into these bound states and positrons go to infinity.
We explicitly calculate the rate of pair-production, and compare it with the
rates of electron-positron production by the Sauter-Euler-Heisenberg-Schwinger
in a constant electric field. In addition, the pair-production rate for the
electro-gravitational balance ratio Q/M = 10^{-19} is much larger than the
pair-production rate due to the Hawking processes. |
Non-Abelian T-Dualizing the Resolved Conifold with Regular and
Fractional D3-Branes: In this paper we obtain new solutions of Type IIA and massive Type IIA
supergravity. These solutions are the result of implementing a non-abelian
T-duality along the internal $SU(2)$ isometries of several D3-brane
configurations on the resolved conifold, studied by Pando Zayas and Tseytlin.
We first study the pure NS resolved conifold solution, then we add fluxes by
placing a stack of D3-branes at the tip of the resolved conifold and finally we
consider the system of regular and fractional D3-branes at the tip. We present
the non-abelian T-duals associated with these backgrounds and study their
geometries and fluxes. We briefly comment on some field theory features by
studying couplings and the central charge of the dual field theory. We also
analyze the supersymmetry of the dual solutions and show that for the system of
only D3 branes the duality defines a map between backgrounds with $SU(3)$ and
orthogonal $SU(2)$ structures. | Characteristics of the new phase in CDT: Causal Dynamical Triangulations (CDT), a candidate theory of nonperturbative
quantum gravity in 4D, turns out to have a rich phase structure. We investigate
the recently discovered bifurcation phase $C_b$ and relate some of its
characteristics to the presence of singular vertices of very high order. The
transition lines separating this phase from the "time-collapsed" $B$-phase and
the de Sitter phase $C_{dS}$ are of great interest when searching for physical
scaling limits. The work presented here sheds light on the mechanisms behind
these transitions. First, we study how the $B$-$C_b$ transition signal depends
on the volume-fixing implemented in the simulations, and find results
compatible with the previously determined second-order character of the
transition. The transition persists in a transfer matrix formulation, where the
system's time extension is taken to be minimal. Second, we relate the new
$C_b$-$C_{dS}$ transition to the appearance of singular vertices, which leads
to a direct physical interpretation in terms of a breaking of the homogeneity
and isotropy observed in the de Sitter phase when crossing from $C_{dS}$ to the
bifurcation phase $C_b$. |
Domain wall cosmology and multiple accelerations: We classify the cosmological behaviors of the domain wall under junctions
between two spacetimes in terms of various parameters: cosmological constants
of bulk spacetime, a tension of a domain wall, and mass parameters of the black
hole-type metric. Especially, we consider the false-true vacuum type junctions
and the domain wall connecting between an inner AdS space and an outer AdS
Reissner-Nordstr${\rm \ddot{o}}$m black hole. We find that there exist a
solution to the junction equations with an inflation at earlier times and an
accelerating expansion at later times. | Cohomological Reduction of Sigma Models: This article studies some features of quantum field theories with internal
supersymmetry, focusing mainly on 2-dimensional non-linear sigma models which
take values in a coset superspace. It is discussed how BRST operators from the
target space supersymmetry algebra can be used to identify subsectors which are
often simpler than the original model and may allow for an explicit computation
of correlation functions. After an extensive discussion of the general
reduction scheme, we present a number of interesting examples, including
symmetric superspaces $G/G^{\mathbb{Z}_2}$ and coset superspaces of the form
$G/G^{\mathbb{Z}_4}$. |
Interference Phenomenon for Different Chiral Bosonization Schemes: We study, in the framework put forward by Siegel\cite{WS} and by Floreanini
and Jackiw\cite{FJ} (FJ), the relationship between different chiral
bosonization schemes (CBS). This is done in the context of the soldering
formalism\cite{MS}, that considers the phenomenon of interference in the
quantum field theory\cite{ABW}. We propose a field redefinition that discloses
the presence of a noton, a nonmover field, in Siegel's formulation for chiral
bosons. The presence of a noton in the Siegel CBS is a new and surprising
result, that separates dynamics from symmetry. While the FJ component describes
the dynamics, it is the noton that carries the symmetry contents, acquiring
dynamics upon quantization and is fully responsible for the Siegel anomaly. The
diagonal representation proposed here is used to study the effect of quantum
interference between gauged rightons and leftons. | Nekrasov and Argyres-Douglas theories in spherical Hecke algebra
representation: AGT conjecture connects Nekrasov instanton partition function of 4D quiver
gauge theory with 2D Liouville conformal blocks. We re-investigate this
connection using the central extension of spherical Hecke algebra in
q-coordinate representation, q being the instanton expansion parameter. Based
on AFLT basis together with interwiners we construct gauge conformal state and
demonstrate its equivalence to the Liouville conformal state, with careful
attention to the proper scaling behavior of the state. Using the colliding
limit of regular states, we obtain the formal expression of irregular conformal
states corresponding to Argyres-Douglas theory, which involves summation of
functions over Young diagrams. |
Homotopy Algebras in String Field Theory: Homotopy algebra and its involutive generalisation plays an important role in
the construction of string field theory. I will review recent progress in these
applications of homotopy algebra and its relation to moduli spaces. | Non-perturbative particle production and differential geometry: This paper proposes a basic method for understanding stationary particle
production on manifolds by means of the Stokes phenomenon. We studied the
Stokes phenomena of the Schwinger effect, the Unruh effect and Hawking
radiation in detail focusing on the origin of their continuous particle
production. We found a possibility that conventional calculations may not
explain the experimental results. |
Some aspects of free field resolutions in 2D CFT with application to the
quantum Drinfeld-Sokolov reduction: We review some aspects of the free field approach to two-dimensional
conformal field theories. Specifically, we discuss the construction of free
field resolutions for the integrable highest weight modules of untwisted affine
Kac-Moody algebras, and extend the construction to a certain class of
admissible highest weight modules. Using these, we construct resolutions of the
completely degenerate highest weight modules of W-algebras by means of the
quantum Drinfeld-Sokolov reduction. As a corollary we derive character formulae
for these degenerate highest weight modules. | Q-balls without a potential: We study non-topological Q-ball solutions of the (3+1)-dimensional
Friedberg-Lee-Sirlin two-component model. The limiting case of vanishing
potential term yields an example of hairy Q-balls, which possess a long range
massless real field. We discuss the properties of these stationary field
configurations and determine their domain of existence. Considering
Friedberg-Lee-Sirlin model we present numerical evidence for the existence of
spinning axially symmetric Q-balls with different parity. Solution of this type
exist also in the limiting case of vanishing scalar potential. We find that the
hairy Q-balls are classically stable for all range of values of angular
frequency. |
Finite field dependent BRST transformations and its applications to
gauge field theories: The Becchi-Rouet-Stora and Tyutin (BRST) transformation plays a crucial role
in the quantization of gauge theories. The BRST transformation is also very
important tool in characterizing the various renormalizable field theoretic
models. The generalization of the usual BRST transformation, by making the
infinitesimal global parameter finite and field dependent, is commonly known as
the finite field dependent BRST (FFBRST) transformation. In this thesis, we
have extended the FFBRST transformation in an auxiliary field formulation and
have developed both on-shell and off-shell FF-anti-BRST transformations. The
different aspects of such transformation are studied in Batalin-Vilkovisky (BV)
formulation. FFBRST transformation has further been used to study the
celebrated Gribov problem and to analyze the constrained dynamics in gauge
theories. A new finite field dependent symmetry (combination of FFBRST and
FF-anti-BRST) transformation has been invented. The FFBRST transformation is
shown useful in connection of first-class constrained theory to that of
second-class also. Further, we have applied the Batalin-Fradkin-Vilkovisky
(BFV) technique to quantize a field theoretic model in the Hamiltonian
framework. The Hodge de Rham theorem for differential geometry has also been
studied in such context. | The Zeeman Effect for the Relativistic Bound State: In the context of a relativistic quantum mechanics with invariant evolution
parameter, solutions for the relativistic bound state problem have been found,
which yield a spectrum for the total mass coinciding with the nonrelativistic
Schr\"odinger energy spectrum. These spectra were obtained by choosing an
arbitrary spacelike unit vector $n_\mu$ and restricting the support of the
eigenfunctions in spacetime to the subspace of the Minkowski measure space, for
which $(x_\perp )^2 = [x-(x \cdot n) n ]^2 \geq 0$. In this paper, we examine
the Zeeman effect for these bound states, which requires $n_\mu$ to be a
dynamical quantity. We recover the usual Zeeman splitting in a manifestly
covariant form. |
On Continuous 2-Category Symmetries and Yang-Mills Theory: We study a 4d gauge theory $U(1)^{N-1}\rtimes S_N$ obtained from a
$U(1)^{N-1}$ theory by gauging a 0-form symmetry $S_N$. We show that this
theory has a global continuous 2-category symmetry, whose structure is
particularly rich for $N>2$. This example allows us to draw a connection
between the higher gauging procedure and the difference between local and
global fusion, which turns out to be a key feature of higher category
symmetries. By studying the spectrum of local and extended operators, we find a
mapping with gauge invariant operators of 4d $SU(N)$ Yang-Mills theory. The
largest group-like subcategory of the non-invertible symmetries of our theory
is a $\mathbb{Z}_N^{(1)}$ 1-form symmetry, acting on the Wilson lines in the
same way as the center symmetry of Yang-Mills theory does. Supported by a
path-integral argument, we propose that the $U(1)^{N-1}\rtimes S_N$ gauge
theory has a relation with the ultraviolet limit of $SU(N)$ Yang-Mills theory
in which all Gukov-Witten operators become topological, and form a continuous
non-invertible 2-category symmetry, broken down to the center symmetry by the
RG flow. | Radiative Correction to the Casimir Energy for Lorentz-violating Scalar
Field in d+1 Dimensions: The renormalization program in every renormalized theory should be run
consistently with the type of boundary condition imposed on quantum fields. To
maintain this consistency, the counterterms usually appear in the
position-dependent form. In the present study, using such counterterms, we
calculated the radiative correction to the Casimir energy for massive and
massless Lorentz-violating scalar field constrained with Dirichlet boundary
condition between two parallel plates in d spatial dimensions. In the
calculation procedure, to remove infinities appearing in the vacuum energies,
the box subtraction scheme supplemented by the cutoff regularization technique
and analytic continuation technique were employed. Normally, in the box
subtraction scheme, two similar configurations are defined and their vacuum
energies are subtracted from each other in the appropriate limits. Our final
results regarding all spatial dimensions were convergent and consistent with
the expected physical basis. We further plotted the Casimir energy density for
the time-like and space-like Lorentz-violating systems in a number of odd and
even dimensions; multiple aspects of the obtained results were ultimately
discussed. |
A new scale in the sky: The existence of a new ultraviolet scale $\Lambda=g M_P$ for effective
theories with gravity and U(1) gauge fields has recently been conjectured as a
possible criterion for distinguishing parts of the swampland from the string
landscape. Here we discuss a possible phenomenological signature of this scale,
for electromagnetic fields, in astrophysical observations. | Complexity vs. Vorticity: In the study of "holographic complexity", upper bounds on the rate of growth
of the (specific) complexity of field theories with holographic duals have
attracted much attention. Underlying these upper bounds there are inequalities
relating the parameters of the dual black hole. We derive such an inequality in
the case of the five-dimensional AdS-Kerr black hole, dual to a
four-dimensional field theory with a non-zero angular momentum density. We
propose to test these underlying inequalities "experimentally", by using the
conjectured analogy of the field theory with phenomenological models of the
Quark-Gluon Plasma. The test consists of comparing data for the parameters of
the QGP with the upper bound on the relevant combination of black hole
parameters. The bound in the non-rotating case passes the test: in this sense,
it is confirmed "experimentally". In the rotating case, the inequality makes
predictions regarding the entropy density of the vortical plasma, recently
observed by the STAR collaboration. |
Gauge and Poincare properties of the UV cutoff and UV completion in
quantum field theory: The ultraviolet (UV) cutoff on a quantum field theory (QFT) can explicitly
break or conserve the Poincare (translation) symmetry. And the very same cutoff
can explicitly break or conserve the gauge symmetry. In the present work, we
perform a systematic study of the UV cutoff in regard to its gauge and Poincare
properties, and construct UV completions restoring the broken gauge symmetry.
In the case of Poincare-conserving UV cutoff, we find that the gauge symmetry
gets restored via the Higgs mechanism. In the case of Poincare-breaking UV
cutoff, however, we find that the flat spacetime affine curvature takes the
place of the Higgs field and, when taken to curved spacetime, gauge symmetry
gets restored at the extremum of the metric-affine action. We also find that
gravity emerges at the extremum if the QFT under concern consists of new
particles beyond the known ones. The resulting emergent gravity plus
renormalized QFT setup has the potential to reveal itself in various
astrophysical, cosmological and collider phenomena. | Tensor and Matrix models: a one-night stand or a lifetime romance?: The spectra of energy eigenstates of free tensor and matrix models are
organized by Kronecker coefficients and Littlewood-Richardson numbers,
respectively. Exploiting recent results in combinatorics for Kronecker
coefficients, we derive a formula that relates Kronecker coefficients with a
hook shape with Littlewood-Richardson numbers. This formula has a natural
translation into physics: the eigenstates of the hook sector of tensor models
are in one-to-one correspondence with fluctuations of 1/2-BPS states in
multi-matrix models. We then conjecture the duality between both sectors.
Finally, we study the Hagedorn behaviour of tensor models with finite rank of
the symmetry group and, using similar arguments, suggest that the second (high
energy) phase could be entirely described by multi-matrix models. |
Wilson Loops and Vertex Operators in Matrix Model: We systematically construct wave functions and vertex operators in the type
IIB (IKKT) matrix model by expanding a supersymmetric Wilson loop operator.
They form a massless multiplet of the N=2 type IIB supergravity and
automatically satisfy conservation laws. | Exact renormalization group study of fermionic theories: The exact renormalization group approach (ERG) is developed for the case of
pure fermionic theories by deriving a Grassmann version of the ERG equation and
applying it to the study of fixed point solutions and critical exponents of the
two-dimensional chiral Gross-Neveu model. An approximation based on the
derivative expansion and a further truncation in the number of fields is used.
Two solutions are obtained analytically in the limit $N\to \infty $, with N
being the number of fermionic species. For finite N some fixed point solutions,
with their anomalous dimensions and critical exponents, are computed
numerically. The issue of separation of physical results from the numerous
spurious ones is discussed. We argue that one of the solutions we find can be
identified with that of Dashen and Frishman, whereas the others seem to be new
ones. |
Particle Physics Implications of F-theory: We review recent progress in realizing Grand Unified Theories (GUTs) in a
strongly coupled formulation of type IIB string theory known as F-theory. Our
main emphasis is on the expected low-energy phenomenology of a minimal class of
F-theory GUTs. We introduce the primary ingredients in such constructions, and
then present qualitative features of GUT models in this framework such as GUT
breaking, doublet-triplet splitting, and proton decay. Next, we review
proposals for realizing flavor hierarchies in the quark and lepton sectors. We
discuss possible supersymmetry breaking scenarios, and their consequences for
experiment, as well as geometrically minimal realizations of F-theory GUTs
which incorporate most of these features. | Seiberg-Witten maps and scattering amplitudes of NCQED: The connection between tree-level scattering amplitudes and the
Seiberg-Witten (SW) map in the Moyal deformed U(1) noncommutataive quantum
electrodynamics (NCQED) is studied. We show that in the minimal U(1) NCQED
based on a reversible Seiberg-Witten (SW) map, SW map induced interactions
cancel each other in all tree-level scattering amplitudes and leave them
identical to the Moyal NCQED without SW map. On the other hand, the two-by-two
Compton and light-by-light scattering amplitudes deviate from minimal model
when irreversible SW map is used. Therefore the risibility of SW map and
equivalence between NCQED before and after SW map manifest themselves as an
identity between the tree-level scattering amplitudes. |
Noncommutativity and Model Building: We propose a way to introduce matter fields transforming in arbitrary
representations of the gauge group in noncommutative U(N) gauge theories. We
then argue that in the presence of supersymmetry, an ordinary commutative SU(N)
gauge theory with a general matter content can always be embedded into a
noncommutative U(N) theory at energies above the noncommutativity mass scale
M_{NC} ~ \theta^{-1/2}. At energies below M_{NC}, the U(1) degrees of freedom
decouple due to the IR/UV mixing, and the noncommutative theory reduces to its
commutative counterpart. Supersymmetry can be spontaneously broken by a
Fayet-Iliopoulos D-term introduced in the noncommutative U(N) theory. U(1)
degrees of freedom become arbitrarily weakly coupled in the infrared and
naturally play the role of the hidden sector for supersymmetry breaking. To
illustrate these ideas we construct a noncommutative U(5) GUT model with
Fayet-Iliopoulos supersymmetry breaking, which reduces to a realistic
commutative theory in the infrared. | Supersymmetry Breaking In Orbifolds Compactifications: Known mechanisms for breaking of supersymmetry at the level of string theory
imply that at least one of the internal dimensions has a very large size.
Experimental detection of the associated light Kaluza-Klein (KK) excitations
would be a strong hint for the existence of string like elementary objects, as
no consistent field theory describing them is known. We restrict the discussion
to the Scherk-Schwarz mechanism in orbifold compactifications. For this case we
investigate the quantum number of the lightest predicted KK states. |
Exact solution of d=1 Kazakov-Migdal induced gauge theory: We give the exact solution of the Kazakov-Migdal induced gauge model in the
case of a D=1 compactified lattice with a generic number $S$ of sites and for
any value of N. Due to the peculiar features of the model, the partition
function that we obtain also describes the vortex-free sector of the D=1
compactified bosonic string, and it coincides in the continuum limit with the
one obtained by Boulatov and Kazakov in this context. | Bounces/Dyons in the Plane Wave Matrix Model and SU(N) Yang-Mills Theory: We consider SU(N) Yang-Mills theory on the space R^1\times S^3 with Minkowski
signature (-+++). The condition of SO(4)-invariance imposed on gauge fields
yields a bosonic matrix model which is a consistent truncation of the plane
wave matrix model. For matrices parametrized by a scalar \phi, the Yang-Mills
equations are reduced to the equation of a particle moving in the double-well
potential. The classical solution is a bounce, i.e. a particle which begins at
the saddle point \phi=0 of the potential, bounces off the potential wall and
returns to \phi=0. The gauge field tensor components parametrized by \phi are
smooth and for finite time both electric and magnetic fields are nonvanishing.
The energy density of this non-Abelian dyon configuration does not depend on
coordinates of R^1\times S^3 and the total energy is proportional to the
inverse radius of S^3. We also describe similar bounce dyon solutions in SU(N)
Yang-Mills theory on the space R^1\times S^2 with signature (-++). Their energy
is proportional to the square of the inverse radius of S^2. From the viewpoint
of Yang-Mills theory on R^{1,1}\times S^2 these solutions describe non-Abelian
(dyonic) flux tubes extended along the x^3-axis. |
Lightlike Brane as a Gravitational Source of Misner-Wheeler-Type
Wormhole: Consistent Lagrangian description of lightlike p-branes (LL-branes) is
presented in two equivalent forms - a Polyakov-type formulation and a dual to
it Nambu-Goto-type formulation. An important characteristic feature of the
LL-branes is that the brane tension appears as a non-trivial additional
dynamical degree of freedom. Next, properties of p=2 LL-brane dynamics (as a
test brane) in D=4 Kerr or Kerr-Newman gravitational backgrounds are discussed
in some detail. It is shown that the LL-brane automatically positions itself on
the horizon and rotates along with the same angular velocity. Finally, a
Misner-Wheeler-type of Reissner-Nordstroem wormhole is constructed in a
self-consistent electrically sourceless Einstein-Maxwell system in the D=4 bulk
interacting with a LL-brane. The pertinent wormhole throat is located precisely
at the LL-brane sitting on the outer Reissner-Nordstroem horizon with the
Reissner-Nordstroem mass and charge being functions of the dynamical LL-brane
tension. | Pulsar Timing Constraints on Physics Beyond the Standard Model: We argue that massive quantum fields source low-frequency long-wavelength
metric fluctuations through the quantum fluctuations of their stress-energy,
given reasonable assumptions about the analytic structure of its correlators.
This can be traced back to the non-local nature of the gauge symmetry in
General Relativity, which prevents an efficient screening of UV scales (what we
call the cosmological non-constant problem). We define a covariant and
gauge-invariant observable which probes line-of-sight spacetime curvature
fluctuations on an observer's past lightcone, and show that current pulsar
timing data constrains any massive particle to $m\lesssim 600$ GeV. This
astrophysical bound severely limits the possibilities for physics beyond the
standard model below the scale of quantum gravity. |
A note on the asymptotic symmetries of electromagnetism: We extend the asymptotic symmetries of electromagnetism in order to
consistently include angle-dependent $u(1)$ gauge transformations $\epsilon$
that involve terms growing at spatial infinity linearly and logarithmically in
$r$, $\epsilon \sim a(\theta, \varphi) r + b(\theta, \varphi) \ln r + c(\theta,
\varphi)$. The charges of the logarithmic $u(1)$ transformations are found to
be conjugate to those of the $\mathcal O(1)$ transformations (abelian algebra
with invertible central term) while those of the $\mathcal O(r)$
transformations are conjugate to those of the subleading $\mathcal O(r^{-1})$
transformations. Because of this structure, one can decouple the
angle-dependent $u(1)$ asymptotic symmetry from the Poincar\'e algebra, just as
in the case of gravity: the generators of these internal transformations are
Lorentz scalars in the redefined algebra. This implies in particular that one
can give a definition of the angular momentum which is free from $u(1)$ gauge
ambiguities. The change of generators that brings the asymptotic symmetry
algebra to a direct sum form involves non linear redefinitions of the charges.
Our analysis is Hamiltonian throughout and carried at spatial infinity. | W(E_10) Symmetry, M-Theory and Painleve Equations: The Weyl group symmetry W(E_k) is studied from the points of view of the
E-strings, Painleve equations and U-duality. We give a simple reformulation of
the elliptic Painleve equation in such a way that the hidden symmetry W(E_10)
is manifestly realized. This reformulation is based on the birational geometry
of the del Pezzo surface and closely related to Seiberg-Witten curves
describing the E-strings. The relation of the W(E_k) symmetry to the duality of
M-theory on a torus is discussed on the level of string equations of motion. |
Quantum groups, q-dynamics and Rajaji: We sketch briefly the essentials of the quantum groups and their application
to the dynamics of a q-deformed simple harmonic oscillator moving on a quantum
line, defined in the q-deformed cotangent (momentum phase) space. In this
endeavour, the quantum group $GL_{qp} (2)$- and the conventional rotational
invariances are respected together. During the course of this discussion, we
touch upon Rajaji's personality as a critical physicist and a bold and
adventurous man of mathematical physics. | U-duality and non-BPS solutions: We derive the explicit action of the U-duality group of the STU model on both
BPS and non-BPS extremal multi-center solutions. As the class of known non-BPS
extremal solutions is not closed under U-duality, we generate in this way new
solutions. These should represent the most general class of extremal non-BPS
multi-center under-rotating solutions of the STU model. |
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