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Anti--de Sitter/ boundary conformal field theory correspondence in the
non-relativistic limit: Boundary conformal field theory (BCFT) is the study of conformal field theory
(CFT) in semi-infinite space-time. In non-relativistic limit
($x\rightarrow\epsilon x, t\rightarrow t, \epsilon\rightarrow 0$), boundary
conformal algebra changes to boundary Galilean conformal algebra (BGCA). In
this work, some aspects of AdS/BCFT in non-relatvistic limit were explored. We
constrain correlation functions of Galilean conformal invariant fields with
BGCA generators. For a situation with a boundary condition at surface $x=0$
($z=\bar{z}$), our result is agree with non-relativistic limit of BCFT
two-point function. We also, introduce holographic dual of boundary Galilean
conformal field theory. | Spacetime defects and group momentum space: We study massive and massless conical defects in Minkowski and de Sitter
spaces in various spacetime dimensions. The energy-momentum of a defect,
considered as an (extended) relativistic object, is completely characterized by
the holonomy of the connection associated with its spacetime metric. The
possible holonomies are given by Lorentz group elements, which are rotations
and null rotations for massive and massless defects respectively. In
particular, if we fix the direction of propagation of a massless defect in
n+1-dimensional Minkowski space, then its space of holonomies is a maximal
abelian subgroup of the AN(n-1) group, which corresponds to the well known
momentum space associated with the n-dimensional $\kappa$-Minkowski
noncommutative spacetime and $\kappa$-deformed Poincar\'{e} algebra. We also
conjecture that massless defects in n-dimensional de Sitter space can be
analogously characterized by holonomies belonging to the same subgroup. This
shows how group-valued momenta related to four-dimensional deformations of
relativistic symmetries can arise in the description of motion of spacetime
defects. |
Brane world effective actions for D-branes with fluxes: We develop systematic string techniques to study brane world effective
actions for models with magnetized (or equivalently intersecting) D-branes. In
particular, we derive the dependence on all NS-NS moduli of the kinetic terms
of the chiral matter in a generic non-supersymmetric brane configurations with
non-commuting open string fluxes. Near a N=1 supersymmetric point the effective
action is consistent with a Fayet-Iliopoulos supersymmetry breaking and the
normalization of the scalar kinetic terms is nothing else than the Kahler
metric. We also discuss, from a stringy perspective, D and F term breaking
mechanisms, and how, in this generic set up, the Kahler metric enters in the
physical Yukawa couplings. | Double Copy for Massive Scalar Field Theories: We explore extensions of the double copy to massive theories and find a new
cubic theory with a local double copy. We consider the nonlinear sigma model
and the special galileon theory, massless versions of which are known to be
related through the double copy. We show that by performing a Kaluza-Klein
reduction of these theories from five dimensions down to four, a double copy
relation exists between the resulting massive four-dimensional scalar field
theories. This requires the vanishing contribution of new galileon terms
arising in high dimensions. We further explore if other interactions that do
not arise from a dimensional reduction of the nonlinear sigma model could be
double copied and find a new cubic interaction which satisfies the BCJ
relations up to 5-point amplitudes. |
Symplectic geometry and Hamiltonian flow of the renormalisation group
equation: It is argued that renormalisation group flow can be interpreted as being a
Hamiltonian vector flow on a phase space which consists of the couplings of the
theory and their conjugate \lq\lq momenta", which are the vacuum expectation
values of the corresponding composite operators. The Hamiltonian is linear in
the conjugate variables and can be identified with the vacuum expectation value
of the trace of the energy-momentum operator. For theories with massive
couplings the identity operator plays a central role and its associated
coupling gives rise to a potential in the flow equations. The evolution of any
quantity , such as $N$-point Green functions, under renormalisation group flow
can be obtained from its Poisson bracket with the Hamiltonian. Ward identities
can be represented as constants of the motion which act as symmetry generators
on the phase space via the Poisson bracket structure. | A Toy Model For Single Field Open Inflation: Inflation in an open universe produced by Coleman-De Luccia (CDL) tunneling
induces a friction term that is strong enough to allow for successful
small-field inflation in models that would otherwise suffer from a severe
overshoot problem. In this paper, we present a polynomial scalar potential
which allows for a full analysis. This provides a simple model of single-field
open inflation on a small-field inflection point after tunneling. We present
numerical results and compare them with analytic approximations. |
Brick Walls on the Brane: The so-called ``brick-wall model'' is a semi-classical approach that has been
used to explain black hole entropy in terms of thermal matter fields. Here, we
apply the brick-wall formalism to thermal bulk fields in a Randall-Sundrum
brane world scenario. In this case, the black hole entity is really a
string-like object in the anti-de Sitter bulk, while appearing as a
Schwarzchild black hole to observers living on the brane. In spite of these
exotic circumstances, we establish that the Bekenstein-Hawking entropy law is
preserved. Although a similar calculation was recently considered in the
literature, this prior work invoked a simplifying assumption (which we avoid)
that can not be adequately justified. | More on chaos at weak coupling: We discuss aspects of the quantum Lyapunov exponent $\lambda_L$ in theories
with an exactly marginal SYK-like random interaction, where $\lambda_L$ can be
computed as a continuous function of the interaction strength $\mathcal{J}$. In
$1d$, we prove a conjecture from arXiv:2111.06108 which states that at small
$\mathcal{J}$, $\lambda_L$ can be found by considering a specific limit of the
four-point function in the decoupled theory. We then provide additional
evidence for the $2d$ version of this conjecture by discussing new examples of
Lyapunov exponents which can be computed at weak coupling. |
Higher derivative effects for 4d AdS gravity: Motivated by holography, we explore higher derivative corrections to
four-dimensional Anti-de Sitter (AdS) gravity. We point out that in such a
theory the variational problem is generically not well-posed given only a
boundary condition for the metric. However, when one evaluates the higher
derivative terms perturbatively on a leading order Einstein solution, the
equations of motion are always second order and therefore the variational
problem indeed requires only a boundary condition for the metric. The equations
of motion required to compute the spectrum around the corrected background are
still generically higher order, with the additional boundary conditions being
associated with new operators in the dual conformal field theory. We discuss
which higher derivative curvature invariants are expected to arise in the
four-dimensional action from a top-down perspective and compute the corrections
to planar AdS black holes and to the spectrum around AdS in various cases.
Requiring that the dual theory is unitary strongly constrains the higher
derivative terms in the action, as the operators associated with the extra
boundary conditions generically have complex conformal dimensions and
non-positive norms. | Chromo-Natural Inflation: Natural inflation on a steep potential with
classical non-Abelian gauge fields: We propose a model for inflation consisting of an axionic scalar field
coupled to a set of three non-Abelian gauge fields. Our model's novel
requirement is that the gauge fields begin inflation with a rotationally
invariant vacuum expectation value (VEV) that is preserved through
identification of SU(2) gauge invariance with rotations in three dimensions.
The gauge VEV interacts with the background value of the axion, leading to an
attractor solution that exhibits slow roll inflation even when the axion decay
constant has a natural value ($<M_{\rm Pl}$). Assuming a sinusoidal potential
for the axion, we find that inflation continues until the axionic potential
vanishes. The speed at which the axion moves along its potential is modulated
by its interactions with the gauge VEV, rather than being determined by the
slope of its bare potential. For sub-Plankian axion decay constants vanishingly
small tensor to scalar ratios are predicted, a direct consequence of the Lyth
bound. The parameter that controls the interaction strength between the axion
and the gauge fields requires a technically natural tuning of
$\mathcal{O}$(100). |
Implications of the Weak Gravity Conjecture for Tidal Love Numbers of
Black Holes: The Weak Gravity Conjecture indicates that extremal black holes in the low
energy effective field theory should be able to decay. This criterion gives
rise to non-trivial constraints on the coefficients of higher-order derivative
corrections to gravity. In this paper, we investigate the tidal deformability
of neutral black holes due to higher-order derivative corrections. As a proof
of concept, we consider a correction of cubic order in the Riemann curvature
tensor. The tidal Love numbers of neutral black holes receive leading-order
corrections from higher-order derivative terms, since black holes in pure
General Relativity have vanishing tidal Love number. We conclude that the
interplay between the tidal deformability of black holes and the Weak Gravity
Conjecture provides useful information about the effective field theory. | Fractional Superstring Tree Scattering Amplitudes: The spin-4/3 fractional superstring is characterized by a chiral algebra
involving a spin-4/3 current on the world-sheet in addition to the
energy-momentum tensor. These currents generate physical state conditions on
the fractional superstring Fock space. Scattering amplitudes of these physical
states are described which satisfy both spurious state decoupling and cyclic
symmetry (duality). Examples of such amplitudes are calculated using an
explicit $c=5$ realization of the spin-4/3 current algebra. This representation
has three flat coordinate boson fields and a global SO(2,1) Lorentz symmetry,
permitting a particle interpretation of the amplitudes. |
Geometric Unification of Higgs Bundle Vacua: Higgs bundles are a central tool used to study a range of intersecting brane
systems in string compactifications. Solutions to the internal gauge theory
equations of motion for the corresponding worldvolume theories of branes give
rise to different low energy effective field theories. This has been heavily
used in the study of M-theory on local $G_2$ spaces and F-theory on local
elliptically fibered Calabi-Yau fourfolds. In this paper we show that the 3D
$\mathcal{N} = 1$ effective field theory defined by M-theory on a local
$Spin(7)$ space unifies the Higgs bundle data associated with 4D $\mathcal{N} =
1$ M- and F-theory vacua. This 3D system appears as an interface with finite
thickness between different 4D vacua. We develop the general formalism of
M-theory on such local $Spin(7)$ spaces, and build explicit interpolating
solutions. This provides a complementary local gauge theory analysis of a
recently proposed approach to constructing $Spin(7)$ spaces from generalized
connected sums. | Lamm, Valluri, Jentschura and Weniger comment on "A Convergent Series
for the QED Effective Action" by Cho and Pak [Phys. Rev. Lett. vol. 86, pp.
1947-1950 (2001)]: Complete results were obtained by us in [Can. J. Phys. 71, 389 (1993)] for
convergent series representations of both the real and the imaginary part of
the QED effective action; these derivations were based on correct intermediate
steps. In this comment, we argue that the physical significance of the
"logarithmic correction term" found by Cho and Pak in [Phys. Rev. Lett. 86,
1947 (2001)] in comparison to the usual expression for the QED effective action
remains to be demonstrated. Further information on related subjects can be
found in Appendix A of hep-ph/0308223 and in hep-th/0210240. |
Conformal bridge in a cosmic string background: Hidden symmetries of non-relativistic $\mathfrak{so} (2,1)\cong
\mathfrak{sl}(2, {\mathbb R})$ invariant systems in a cosmic string background
are studied using the conformal bridge transformation. Geometric properties of
this background are analogous to those of a conical surface with a
deficiency/excess angle encoded in the "geometrical parameter" $\alpha$,
determined by the linear positive/negative mass density of the string. The free
particle and the harmonic oscillator on this background are shown to be related
by the conformal bridge transformation. To identify the integrals of the free
system, we employ a local canonical transformation that relates the model with
its planar version. The conformal bridge transformation is then used to map the
obtained integrals to those of the harmonic oscillator on the cone.
Well-defined classical integrals in both models exist only at $\alpha=q/k$ with
$q,k=1,2,\ldots,$ which for $q>1$ are higher-order generators of finite
nonlinear algebras. The systems are quantized for arbitrary values of $\alpha$;
however, the well-defined hidden symmetry operators associated with spectral
degeneracies only exist when $\alpha$ is an integer, that reveals a quantum
anomaly. | Extended Connection in Yang-Mills Theory: The three fundamental geometric components of Yang-Mills theory -gauge field,
gauge fixing and ghost field- are unified in a new object: an extended
connection in a properly chosen principal fiber bundle. To do this, it is
necessary to generalize the notion of gauge fixing by using a gauge fixing
connection instead of a section. From the equations for the extended
connection's curvature, we derive the relevant BRST transformations without
imposing the usual horizontality conditions. We show that the gauge field's
standard BRST transformation is only valid in a local trivialization and we
obtain the corresponding global generalization. By using the Faddeev-Popov
method, we apply the generalized gauge fixing to the path integral quantization
of Yang-Mills theory. We show that the proposed gauge fixing can be used even
in the presence of a Gribov's obstruction. |
Stokes Phenomena and Non-perturbative Completion in the Multi-cut
Two-matrix Models: The Stokes multipliers in the matrix models are invariants in the
string-theory moduli space and related to the D-instanton chemical potentials.
They not only represent non-perturbative information but also play an important
role in connecting various perturbative string theories in the moduli space.
They are a key concept to the non-perturbative completion of string theory and
also expected to imply some remnant of strong coupling dynamics in M theory. In
this paper, we investigate the non-perturbative completion problem consisting
of two constraints on the Stokes multipliers. As the first constraint, Stokes
phenomena which realize the multi-cut geometry are studied in the Z_k symmetric
critical points of the multi-cut two-matrix models. Sequence of solutions to
the constraints are obtained in general k-cut critical points. A discrete set
of solutions and a continuum set of solutions are explicitly shown, and they
can be classified by several constrained configurations of the Young diagram.
As the second constraint, we discuss non-perturbative stability of backgrounds
in terms of the Riemann-Hilbert problem. In particular, our procedure in the
2-cut (1,2) case (pure-supergravity case) completely fixes the D-instanton
chemical potentials and results in the Hastings-McLeod solution to the
Painlev\'e II equation. It is also stressed that the Riemann-Hilbert approach
realizes an off-shell background independent formulation of non-critical string
theory. | Dynamical D-Terms in Supergravity: Most phenomenological models of supersymmetry breaking rely on nonzero
F-terms rather than nonzero D-terms. An important reason why D-terms are often
neglected is that it turns out to be very challenging to realize D-terms at
energies parametrically smaller than the Planck scale in supergravity. As we
demonstrate in this paper, all conventional difficulties may, however, be
overcome if the generation of the D-term is based on strong dynamics. To
illustrate our idea, we focus on a certain class of vector-like SUSY breaking
models that enjoy a minimal particle content and which may be easily embedded
into more complete scenarios. We are then able to show that, upon gauging a
global flavor symmetry, an appropriate choice of Yukawa couplings readily
allows to dynamically generate a D-term at an almost arbitrary energy scale.
This includes in particular the natural and consistent realization of D-terms
around, above and below the scale of grand unification in supergravity, without
the need for fine-tuning of any model parameters. Our construction might
therefore bear the potential to open up a new direction for model building in
supersymmetry and early universe cosmology. |
Self-field QED(1+1) with massless matter fields: Two-body problem: We consider two-body problem in the self-field (1+1)-dimensional quantum
electrodynamics on the circle. We present two formulations of the problem which
correspond to two different types of variational principles and prove that both
formulations lead to the same spectrum of the two-body Hamiltonian with
massless matter fields. We give the exact and complete solution of the
relativistic two-body equation in the massless case. | Expository Remarks on Three-Dimensional Gravity and Hyperbolic
Invariants: We consider complex invariants associated with compact real three-dimensional
hyperbolic spaces. The contribution of the Chern-Simons invariants of
irreducible U(n)-flat connections on hyperbolic fibered manifolds to the low
order expansion of the quantum gravitational path integral is analyzed. |
The Virtue of Defects in 4D Gauge Theories and 2D CFTs: We advance a correspondence between the topological defect operators in
Liouville and Toda conformal field theories - which we construct - and loop
operators and domain wall operators in four dimensional N=2 supersymmetric
gauge theories on S^4. Our computation of the correlation functions in
Liouville/Toda theory in the presence of topological defect operators, which
are supported on curves on the Riemann surface, yields the exact answer for the
partition function of four dimensional gauge theories in the presence of
various walls and loop operators; results which we can quantitatively
substantiate with an independent gauge theory analysis. As an interesting
outcome of this work for two dimensional conformal field theories, we prove
that topological defect operators and the Verlinde loop operators are different
descriptions of the same operators. | D=5 Einstein-Maxwell-Chern-Simons Black Holes: 5-dimensional Einstein-Maxwell-Chern-Simons theory with Chern-Simons
coefficient $\lambda=1$ has supersymmetric black holes with vanishing horizon
angular velocity, but finite angular momentum. Here supersymmetry is associated
with a borderline between stability and instability, since for $\lambda>1$ a
rotational instability arises, where counterrotating black holes appear, whose
horizon rotates in the opposite sense to the angular momentum. For $\lambda>2$
black holes are no longer uniquely characterized by their global charges, and
rotating black holes with vanishing angular momentum appear. |
The Epstein-Glaser causal approach to the Light-Front QED$_{4}$. II:
Vacuum Polarization tensor: In this work we show how to construct the one-loop vacuum polarization for
light-front QED$_{4}$ in the framework of the perturbative causal theory.
Usually, in the canonical approach, it is considered for the fermionic
propagator the so-called instantaneous term, but it is known in literature that
this term is controversial because it can be omitted by computational reasons;
for instance, by compensation or vanishing by dimensional regularization. In
this work we propose a solution to this paradox. First, in the perturbative
causal theory, it is shown that the fermionic propagator does not have
instantaneous terms, and with this propagator we calculate the one-loop vacuum
polarization, from the calculation it follows the same result as obtained by
the standard approach, but without reclaiming any extra assumptions. Moreover,
since the perturbative causal theory is defined in the distributional
framework, we can also show the reason behind we obtaining the same result
whether we consider or not the instantaneous fermionic propagator term. | Higher derivative corrections to DBI action at $ α'^2$ order: We use the compatibility of D-brane action with linear off-shell T-duality
and linear on-shell S-duality as guiding principles to find all world volume
couplings of one massless closed and three massless open strings at order
$\alpha'^2$ in type II superstring theories in flat space-time. |
Two-loop supergravity on AdS$_5\times$S$^5$ from CFT: We describe a construction of the two-loop amplitude of four graviton
supermultiplets in AdS$_5\times$S$^5$. We start from an ansatz for a
preamplitude from which we generate the full amplitude under the action of a
specific Casimir operator. The ansatz captures a recent ansatz of Huang and
Yuan and we confirm their result through similar constraints. The form of the
result suggests that all ambiguities are captured by the preamplitude which
determines the result up to tree-level ambiguities only. We identify a class of
four-dimensional `zigzag' integrals which are perfectly adapted to describing
the leading logarithmic discontinuity to all orders. We also observe that a
bonus crossing symmetry of the preamplitude follows from the transformation
properties of the Casimir operator. Combined with the zigzag integrals this
allows us to construct a crossing symmetric function with the correct leading
logarithmic discontinuities in all channels.
From the two-loop result we extract an explicit expression for the two-loop
correction to the anomalous dimensions of twist-four operators of generic spin
which includes dependence on (alternating) nested harmonic sums up to weight
three. We also revisit the prescription of the bulk-point limit of AdS
amplitudes and show how it recovers the full flat-space amplitude, not just its
discontinuity. With this extended notion of the bulk-point limit we reproduce
the scale-dependent logarithmic threshold terms of type IIB string theory in
flat-space. | On the harmonic superspace geometry of $(4,4)$ supersymmetric sigma
models with torsion: Starting from the dual action of $(4,4)$ $2D$ twisted multiplets in the
harmonic superspace with two independent sets of $SU(2)$ harmonic variables, we
present its generalization which hopefully provides an off-shell description of
general $(4,4)$ supersymmetric sigma models with torsion. Like the action of
the torsionless $(4,4)$ hyper-K\"ahler sigma models in the standard harmonic
superspace, it is characterized by a number of superfield potentials. They
depend on $n$ copies of a triple of analytic harmonic $(4,4)$ superfields. As
distinct from the hyper-K\"ahler case, the potentials prove to be severely
constrained by the self-consistency condition which stems from the
commutativity of the left and right harmonic derivatives. We show that for
$n=1$ these constraints reduce the general action to that of $(4,4)$ twisted
multiplet, while for $n\geq 2$ there exists a wide class of new actions which
cannot be written only via twisted multiplets. Their most striking feature is
the nonabelian and in general nonlinear gauge invariance which substitutes the
abelian gauge symmetry of the dual action of twisted multiplets and ensures the
correct number of physical degrees of freedom. We show, on a simple example,
that these actions describe sigma models with non-commuting left and right
complex structures on the bosonic target. |
The Canonical Partition Function for Quons: We calculate the canonical partition function $Z_N$ for a system of $N$ free
particles obeying so-called `quon' statistics where $q$ is real and satisfies
$|q|<1$ by using simple counting arguments. We observe that this system is
afflicted by the Gibbs paradox and that $Z_N$ is independent of $q$. We
demonstrate that such a system of particles obeys the ideal gas law and that
the internal energy $U$ ( and hence the specific heat capacity $C_V$ ) is
identical to that of a system of $N$ free particles obeying Maxwell-Boltzmann
statistics. | Affine Toda Solitons and Automorphisms of Dynkin Diagrams: Using Hirota's method, solitons are constructed for affine Toda field
theories based on the simply-laced affine algebras. By considering
automorphisms of the simply-laced Dynkin diagrams, solutions to the remaining
algebras, twisted as well as untwisted, are deduced. |
Universal Charge Diffusion and the Butterfly Effect: We study charge diffusion in holographic scaling theories with a
particle-hole symmetry. We show that these theories have a universal regime in
which the diffusion constant is given by $D_c = C v_B^2/ (2 \pi T)$ where $v_B$
is the velocity of the butterfly effect. The constant of proportionality, $C$,
depends only on the scaling exponents of the infra-red theory. Our results
suggest an unexpected connection between transport at strong coupling and
quantum chaos. | Beyond the WKB approximation in PT-symmetric quantum mechanics: The mergings of energy levels associated with the breaking of PT symmetry in
the model of Bender and Boettcher, and in its generalisation to incorporate a
centrifugal term, are analysed in detail. Even though conventional WKB
techniques fail, it is shown how the ODE/IM correspondence can be used to
obtain a systematic approximation scheme which captures all previously-observed
features. Nonperturbative effects turn out to play a crucial role, governing
the behaviour of almost all levels once the symmetry-breaking transition has
been passed. In addition, a novel treatment of the radial Schrodinger equation
is used to recover the values of local and non-local conserved charges in the
related integrable quantum field theories, without any need for resummation
even when the angular momentum is nonzero. |
Bosonisation of the Complex-boson realisation of $W_\infty$: We bosonise the complex-boson realisations of the $W_\infty$ and
$W_{1+\infty}$ algebras. We obtain nonlinear realisations of $W_\infty$ and
$W_{1+\infty}$ in terms of a pair of fermions and a real scalar. By further
bosonising the fermions, we then obtain realisations of $W_\infty$ in terms of
two scalars. Keeping the most non-linear terms in the scalars only, we arrive
at two-scalar realisations of classical $w_\infty$. | Orbifolds versus smooth heterotic compactifications: Following the recent exploration of smooth heterotic compactifications with
unitary bundles, orbifold compactifications in six dimensions can be shown to
correspond in the blow-up to compactifications with U(1) gauge backgrounds. A
powerful tool is the comparison of anomaly polynomials. The presentation here
focuses on heterotic SO(32) compactifications in six dimensions including
five-branes. Four dimensional and E8 x E8 models are briefly commented on. |
Yang-Mills Instanton Sheaves: The SL(2,C) Yang-Mills instanton solutions constructed recently by the
biquaternion method were shown to satisfy the complex version of the ADHM
equations and the Monad construction. Moreover, we discover that, in addition
to the holomorphic vector bundles on CP^3 similar to the case of SU(2) ADHM
construction, the SL(2,C) instanton solutions can be used to explicitly
construct instanton sheaves on CP^3. Presumably, the existence of these
instanton sheaves is related to the singularities of the SL(2,C) instantons on
S^4 which do not exist for SU(2) instantons. | Area Potentials and Deformation Quantization: Systems built out of N-body interactions, beyond 2-body interactions, are
formulated on the plane, and investigated classically and quantum mechanically
(in phase space). Their Wigner Functions--the density matrices in phase-space
quantization--are given and analyzed. |
A Semiclassical String Description of Wilson Loop with Local Operators: We discuss a semiclassical string description to circular Wilson loops
without/with local operator insertions. By considering a semiclassical
approximation of type IIB string theory on AdS_5 X S^5 around the corresponding
classical solutions, quadratic actions with respect to fluctuations are
computed. Then the dual corresponding operators describing the fluctuations are
discussed from the point of view of a small deformation of the Wilson loops.
The result gives new evidence for AdS/CFT correspondence. | Thermal duality and non-singular cosmology in d-dimensional superstrings: We are presenting the basic ingredients of a stringy mechanism able to
resolve both the Hagedorn instabilities of finite temperature superstrings as
well as the initial singularity of the induced cosmology in arbitrary
dimensions. These are shown to be generic in a large class of (4,0) type II
superstring vacua, where non-trivial "gravito-magnetic" fluxes lift the
Hagedorn instabilities of the thermal ensemble and the temperature duality
symmetry is restored. This symmetry implies a universal maximal critical
temperature. In all such models there are three characteristic regimes, each
with a distinct effective field theory description: Two dual asymptotically
cold regimes associated with the light thermal momentum and light thermal
winding states, and the intermediate regime where additional massless thermal
states appear. The partition function exhibits a conical structure as a
function of the thermal modulus, irrespective of the space-time dimension.
Thanks to asymptotic right-moving supersymmetry, the genus-1 partition function
is well-approximated by that of massless thermal radiation in all of the three
effective field theory regimes. The resulting time-evolution describes a
bouncing cosmology connecting, via spacelike branes, a contracting thermal
"winding" Universe to an expanding thermal "momentum" Universe, free of any
essential curvature singularities. The string coupling remains perturbative
throughout the cosmological evolution. Bouncing cosmologies are presented for
both zero and negative spatial curvature. |
Monopole-Instanton Type Solutions In 3D Gravity: Three dimensional Euclidean gravity in the dreibein-spin connection formalism
is investigated. We use the monopole-instanton ansatz for the dreibein and the
spin connection. The equations of motion are solved. We point out a two
dimensional solution with a vanishing action. | Multiple Mellin-Barnes integrals and triangulations of point
configurations: We present a novel technique for the analytic evaluation of multifold
Mellin-Barnes (MB) integrals, which commonly appear in physics, as for instance
in the calculations of multi-loop multi-scale Feynman integrals. Our approach
is based on triangulating a set of points which can be assigned to a given MB
integral, and yields the final analytic results in terms of linear combinations
of multiple series, each triangulation allowing the derivation of one of these
combinations. When this technique is applied to the computation of Feynman
integrals, the involved series are of the (multivariable) hypergeometric type.
We implement our method in the Mathematica package MBConicHulls.wl, an already
existing software dedicated to the analytic evaluation of multiple MB
integrals, based on a recently developed computational approach using
intersections of conic hulls. The triangulation method is remarkably faster
than the conic hulls approach and can thus be used for the calculation of
higher-fold MB integrals as we show here by computing triangulations for highly
complicated objects such as the off-shell massless scalar one-loop 15-point
Feynman integral whose MB representation has 104 folds. As other applications
we show how this technique can provide new results for the off-shell massless
conformal hexagon and double box Feynman integrals, as well as for the hard
diagram of the two loop hexagon Wilson loop. |
Causal Poisson Brackets of the SL(2,R) WZNW Model and its Coset Theories: From the basic chiral and anti-chiral Poisson bracket algebra of the SL(2,R)
WZNW model, non-equal time Poisson brackets are derived. Through Hamiltonian
reduction we deduce the corresponding brackets for its coset theories. | Symmetries of N=4 supersymmetric CP(n) mechanics: We explicitly constructed the generators of $SU(n+1)$ group which commute
with the supercharges of N=4 supersymmetric $\mathbb{CP}^n$ mechanics in the
background U(n) gauge fields. The corresponding Hamiltonian can be represented
as a direct sum of two Casimir operators: one Casimir operator on $SU(n+1)$
group contains our bosonic and fermionic coordinates and momenta, while the
second one, on the SU(1,n) group, is constructed from isospin degrees of
freedom only. |
How many surface modes does one see on the boundary of a Dirac material?: We present full expressions for the surface part of polarization tensor of a
Dirac fermion confined in a half-space in $3+1$ dimensions. We compare this
tensor to the polarization tensor of eventual surface mode (which is a $2+1$
dimensional Dirac fermion) and find essential differences in the conductivities
in both Hall and normal sectors. Thus, the interaction with electromagnetic
field near the boundary differs significantly in the full model and in the
effective theory for the surface mode. | Structure constants of twist-two light-ray operators in the triple Regge
limit: The structure constants of twist-two operators with spin $j$ in the BFKL
limit $g^2\rightarrow 0, j\rightarrow 1$ but ${g^2\over j-1}\sim 1$ are
determined from the calculation of the three-point correlator of twist-two
light-ray operators in the triple Regge limit. It is well known that the
anomalous dimensions of twist-two operators in this limit are determined by the
BFKL intercept. Similarly, the obtained structure constants are determined by
an analytic function of three BFKL intercepts. |
Baryons from instantons in holographic QCD: We consider aspects of dynamical baryons in a holographic dual of QCD that is
proposed on the basis of a D4/D8-brane configuration. We construct a soliton
solution carrying a unit baryon number and show that it is given by an
instanton solution of four-dimensional Yang-Mills theory with fixed size. The
Chern-Simons term on the flavor D8-branes plays a crucial role of protecting
the instanton from collapsing to zero size. By quantizing the collective
coordinates of the soliton, we work out the baryon spectra. Negative-parity
baryons as well as baryons with higher spins and isospins can be obtained in a
simple manner. | String-theory Realization of Modular Forms for Elliptic Curves with
Complex Multiplication: It is known that the L-function of an elliptic curve defined over Q is given
by the Mellin transform of a modular form of weight 2. Does that modular form
have anything to do with string theory? In this article, we address a question
along this line for elliptic curves that have complex multiplication defined
over number fields. So long as we use diagonal rational N=(2,2) superconformal
field theories for the string-theory realizations of the elliptic curves, the
weight-2 modular form turns out to be the Boltzmann-weighted
(q^{L_0-c/24}-weighted) sum of U(1) charges with F e^{ \pi i F} insertion
computed in the Ramond sector. |
A Matrix Big Bang: The light-like linear dilaton background represents a particularly simple
time-dependent 1/2 BPS solution of critical type IIA superstring theory in ten
dimensions. Its lift to M-theory, as well as its Einstein frame metric, are
singular in the sense that the geometry is geodesically incomplete and the
Riemann tensor diverges along a light-like subspace of codimension one. We
study this background as a model for a big bang type singularity in string
theory/M-theory. We construct the dual Matrix theory description in terms of a
(1+1)-d supersymmetric Yang-Mills theory on a time-dependent world-sheet given
by the Milne orbifold of (1+1)-d Minkowski space. Our model provides a
framework in which the physics of the singularity appears to be under control. | First Law, Counterterms and Kerr-AdS_5 Black Holes: We apply the counterterm subtraction technique to calculate the action and
other quantities for the Kerr--AdS black hole in five dimensions using two
boundary metrics; the Einstein universe and rotating Einstein universe with
arbitrary angular velocity. In both cases, the resulting thermodynamic
quantities satisfy the first law of thermodynamics. We point out that the
reason for the violation of the first law in previous calculations is that the
rotating Einstein universe, used as a boundary metric, was rotating with an
angular velocity that depends on the black hole rotation parameter. Using a new
coordinate system with a boundary metric that has an arbitrary angular
velocity, one can show that the resulting physical quantities satisfy the first
law. |
Relativistic two-fluid hydrodynamics with quantized vorticity from the
nonlinear Klein-Gordon equation: We consider a relativistic two-fluid model of superfluidity, in which the
superfluid is described by an order parameter that is a complex scalar field
satisfying the nonlinear Klein-Gordon equation (NLKG). The coupling to the
normal fluid is introduced via a covariant current-current interaction, which
results in the addition of an effective potential, whose imaginary part
describes particle transfer between superfluid and normal fluid. Quantized
vorticity arises in a class of singular solutions and the related vortex
dynamics is incorporated in the modified NLKG, facilitating numerical analysis
which is usually very complicated in the phenomenology of vortex filaments. The
dual transformation to a string theory description (Kalb-Ramond) of quantum
vorticity, the Magnus force and the mutual friction between quantized vortices
and normal fluid are also studied. | Wake Potential in Strong Coupling Plasma from AdS/CFT Correspondence: With the dielectric function computed from AdS/CFT correspondence, we studied
the wake potential induced by a fast moving charge in strong coupling plasma,
and compared it with the weak coupling wake potential for different particle
velocities as $v=0.55c$ and $v=0.99c$. The most prominent difference between
strong and weak wake potential is that when $v=0.99c$ the remarkable
oscillation due to Cerenkov-like radiation and Mach cone in weak coupling
disappears in strong coupling, which implies that the plasmon mode with phase
velocity lower than the speed of light dose not exist in strong coupling
plasma. |
Gravitational action for a massive Majorana fermion in 2d quantum
gravity: We compute the gravitational action of a free massive Majorana fermion
coupled to two-dimensional gravity on compact Riemann surfaces of arbitrary
genus. The structure is similar to the case of the massive scalar. The
small-mass expansion of the gravitational yields the Liouville action at zeroth
order, and we can identify the Mabuchi action at first order. While the massive
Majorana action is a conformal deformation of the massless Majorana CFT, we
find an action different from the one given by the David-Distler-Kawai (DDK)
ansatz. | Optimized post Gaussian approximation in the background field method: We have extended the variational perturbative theory based on the back ground
field method to include the optimized expansion of Okopinska and the post
Gaussian effective potential of Stansu and Stevenson. This new method provides
much simpler way to compute the correction terms to the Gausssian effective
action (or potential). We have also renormalized the effective potential in 3+1
dimensions by introducing appropriate counter terms in the lagrangian |
Nilpotent Symmetries For A Free Relativistic Particle In Augmented
Superfield Formalism: In the framework of the augmented superfield formalism, the local, covariant,
continuous and off-shell (as well as on-shell) nilpotent (anti-)BRST symmetry
transformations are derived for a $(0 + 1)$-dimensional free scalar
relativistic particle that provides a prototype physical example for the more
general reparametrization invariant string- and gravitational theories. The
trajectory (i.e. the world-line) of the free particle, parametrized by a
monotonically increasing evolution parameter $\tau$, is embedded in a
$D$-dimensional flat Minkowski target manifold. This one-dimensional system is
considered on a $(1 + 2)$-dimensional supermanifold parametrized by an even
element $\tau$ and a couple of odd elements ($\theta$ and $\bar\theta$) of a
Grassmannian algebra. The horizontality condition and the invariance of the
conserved (super)charges on the (super)manifolds play very crucial roles in the
above derivations of the nilpotent symmetries. The geometrical interpretations
for the nilpotent (anti-)BRST charges are provided in the framework of
augmented superfield approach. | Mirror Symmetry of Minimal Calabi-Yau Manifolds: We perform the mirror transformations of Calabi-Yau manifolds with one moduli
whose Hodge numbers $(h^{11}, h^{21})$ are minimally small. Since the
difference of Hodge numbers is the generation of matter fields in superstring
theories made of compactifications, minimal Hodge numbers of the model of
phenomenological interest are (1,4). Genuine minimal Calabi-Yau manifold which
has least degrees of freedom for K\"ahler and complex deformation is (1,1)
model. With help of {\it Mathematica} and {\it Maple}, we derive Picard-Fuchs
equations for periods, and determine their monodromy behaviors completely such
that all monodromy matrices are consistent in the mirror prescription of the
model (1,4), (1,3) and (1,1). We also discuss to find the description for each
mirror of (1,3) and (1,1) by combining invariant polynomials of variety on
which (1,5) model is defined. The genus 0 instanton numbers coming from mirror
transformations in above models look reasonable. We propose the weighted
discriminant for genus 1 instanton calculus which makes all instanton numbers
integral, except (1,1) case. |
Casimir Energy for a Spherical Cavity in a Dielectric: Applications to
Sonoluminescence: In the final few years of his life, Julian Schwinger proposed that the
``dynamical Casimir effect'' might provide the driving force behind the
puzzling phenomenon of sonoluminescence. Motivated by that exciting suggestion,
we have computed the static Casimir energy of a spherical cavity in an
otherwise uniform material. As expected the result is divergent; yet a
plausible finite answer is extracted, in the leading uniform asymptotic
approximation. This result agrees with that found using zeta-function
regularization. Numerically, we find far too small an energy to account for the
large burst of photons seen in sonoluminescence. If the divergent result is
retained, it is of the wrong sign to drive the effect. Dispersion does not
resolve this contradiction. In the static approximation, the Fresnel drag term
is zero; on the mother hand, electrostriction could be comparable to the
Casimir term. It is argued that this adiabatic approximation to the dynamical
Casimir effect should be quite accurate. | Microstructure in matrix elements: We investigate the simple model of Pennington, Shenker, Stanford and Yang for
modeling the density matrix of Hawking radiation, but further include dynamics
for EOW branes behind the horizon. This allows interactions that scatter one
interior state to another, and also allows EOW loops. At strong coupling, we
find that EOW states are no longer random; the ensemble has collapsed, and
coupling constants encode the microscopic matrix elements of Hawking radiation.
This suggests strong interior dynamics are important for understanding
evaporating black holes, without any ensemble average. In this concrete model
the density matrix of the radiation deviates from the thermal state, small
off-diagonal fluctuations encode equivalences between naively orthogonal
states, and bound the entropy from above. For almost evaporated black holes the
off-diagonal terms become as large as the diagonal ones, eventually giving a
pure state. We also find the unique analytic formula for all Renyi entropies. |
Graviton scattering in matrix theory and supergravity: I briefly review recent work on the comparison between two and three graviton
scattering in supergravity and matrix theory | Hopf Term, Fractional Spin and Soliton Operators in the O(3) Nonlinear
Sigma Model: We re-examine three issues, the Hopf term, fractional spin and the soliton
operators, in the 2+1 dimensional O(3) nonlinear sigma model based on the
adjoint orbit parameterization (AOP) introduced earlier. It is shown that the
Hopf Term is well-defined for configurations of any soliton charge $Q$ if we
adopt a time independent boundary condition at spatial infinity. We then
develop the Hamiltonian formulation of the model in the AOP and thereby argue
that the well-known $Q^2$-formula for fractional spin holds only for a
restricted class of configurations. Operators which create states of given
classical configurations of any soliton number in the (physical) Hilbert space
are constructed. Our results clarify some of the points which are crucial for
the above three topological issues and yet have remained obscure in the
literature. |
Goldstone multiplet for partially broken superconformal symmetry: The bosonic parts of D3-brane actions in AdS(5) backgrounds are known to have
symmetries which are field-dependent extensions of conformal transformations of
the worldvolume coordinates. Using the coset space SU(2,2|1)/SO(4,1), we apply
the method of nonlinear realizations to construct a four-dimensional N = 1
off-shell supersymmetric action which has a generalized field-dependent
superconformal invariance. The Goldstone fields for broken scale, chiral and
S-supersymmetry transformations form a chiral supermultiplet. | Generating the curvature perturbation with instant preheating: A new mechanism for generating the curvature perturbation at the end of
inflaton has been investigated. The dominant contribution to the primordial
curvature perturbation may be generated during the period of instant
preheating. The mechanism converts isocurvature perturbation related to a light
field into curvature perturbation, where the ``light field'' is not the
inflaton field. This mechanism is important in inflationary models where
kinetic energy is significant at the end of inflaton. We show how one can apply
this mechanism to various brane inflationary models. |
Entropic Corrections to Coulomb's Law: Two well-known quantum corrections to the area law have been introduced in
the literatures, namely, logarithmic and power-law corrections. Logarithmic
corrections, arises from loop quantum gravity due to thermal equilibrium
fluctuations and quantum fluctuations, while, power-law correction appears in
dealing with the entanglement of quantum fields in and out the horizon.
Inspired by Verlinde's argument on the entropic force, and assuming the quantum
corrected relation for the entropy, we propose the entropic origin for the
Coulomb's law in this note. Also we investigate the Uehling potential as a
radiative correction to Coulomb potential in 1-loop order and show that for
some value of distance the entropic corrections of the Coulomb's law is
compatible with the vacuum-polarization correction in QED. So, we derive
modified Coulomb's law as well as the entropy corrected Poisson's equation
which governing the evolution of the scalar potential $\phi$. Our study further
supports the unification of gravity and electromagnetic interactions based on
the holographic principle. | Magnetic Monopole in Noncommutative Space-Time and Wu-Yang
Singularity-Free Gauge Transformations: We investigate the validity of the Dirac Quantization Condition (DQC) for
magnetic monopoles in noncommutative space-time. We use an approach which is
based on an extension of the method introduced by Wu and Yang. To study the
effects of noncommutativity of space-time, we consider the gauge
transformations of $U_\star(1)$ gauge fields and use the corresponding deformed
Maxwell's equations. Using a perturbation expansion in the noncommutativity
parameter $\theta$, we show that the DQC remains unmodified up to the first
order in the expansion parameter. The result is obtained for a class of
noncommutative source terms, which reduce to the Dirac delta function in the
commutative limit. |
The Holographic dark energy reexamined: We have reexamined the holographic dark energy model by considering the
spatial curvature. We have refined the model parameter and observed that the
holographic dark energy model does not behave as phantom model. Comparing the
holographic dark energy model to the supernova observation alone, we found that
the closed universe is favored. Combining with the Wilkinson Microwave
Anisotropy Probe (WMAP) data, we obtained the reasonable value of the spatial
curvature of our universe. | Scattering and Thermodynamics of Integrable N=2 Theories: We study $N$=2 supersymmetric integrable theories with spontaneously-broken
\Zn\ symmetry. They have exact soliton masses given by the affine $SU(n)$ Toda
masses and fractional fermion numbers given by multiples of $1/n$. The basic
such $N$=2 integrable theory is the $A_n$-type $N$=2 minimal model perturbed by
the most relevant operator. The soliton content and exact S-matrices are
obtained using the Landau-Ginzburg description. We study the thermodynamics of
these theories and calculate the ground-state energies exactly, verifying that
they have the correct conformal limits. We conjecture that the soliton content
and S-matrices in other integrable \Zn\ $N$=2 theories are given by the tensor
product of the above basic $N$=2 \Zn\ scattering theory with various $N$=0
theories. In particular, we consider integrable perturbations of $N$=2
Kazama-Suzuki models described by generalized Chebyshev potentials, $CP^{n-1}$
sigma models, and $N$=2 sine-Gordon and its affine Toda generalizations. |
Finite Factorization equations and Sum Rules for BPS correlators in N=4
SYM theory: A class of exact non-renormalized extremal correlators of half-BPS operators
in N=4 SYM, with U(N) gauge group, is shown to satisfy finite factorization
equations reminiscent of topological gauge theories. The finite factorization
equations can be generalized, beyond the extremal case, to a class of
correlators involving observables with a simple pattern of SO(6) charges. The
simple group theoretic form of the correlators allows equalities between ratios
of correlators in N=4 SYM and Wilson loops in Chern-Simons theories at
k=\infty, correlators of appropriate observables in topological G/G models and
Wilson loops in two-dimensional Yang-Mills theories. The correlators also obey
sum rules which can be generalized to off-extremal correlators. The simplest
sum rules can be viewed as large k limits of the Verlinde formula using the
Chern-Simons correspondence. For special classes of correlators, the saturation
of the factorization equations by a small subset of the operators in the large
N theory is related to the emergence of semiclassical objects like KK modes and
giant gravitons in the dual ADS \times S background. We comment on an
intriguing symmetry between KK modes and giant gravitons. | Thermodynamical properties of interacting holographic dark energy model
with apparent horizon: We have investigated the thermodynamical properties of the universe with dark
energy. It is demonstrated that in a universe with spacial curvature the
natural choice for IR cutoff could be the apparent horizon radius. We shown
that any interaction of pressureless dark matter with holographic dark energy,
whose infrared cutoff is set by the apparent horizon radius, implying a
constant effective equation of state of dark component in a universe. In
addition we found that for the static observer in space, the comoving distance
has a faster expansion than the apparent horizon radius with any spatial
curvature. We also verify that in some conditions the modified first law of
thermodynamics could return to the classic form at apparent horizon for a
universe filled with dark energy and dark matter. Besides, the generalized
second law of thermodynamics is discussed in a region enclosed by the apparent
horizon. |
Instantons and Entanglement Entropy: We would like to put the area law -- believed to by obeyed by entanglement
entropies in the ground state of a local field theory -- to scrutiny in the
presence of non-perturbative effects. We study instanton corrections to
entanglement entropy in various models whose instanton effects are well
understood, including $U(1)$ gauge theory in 2+1 dimensions and false vacuum
decay in $\phi^4$ theory, and we demonstrate that the area law is indeed obeyed
in these models. We also perform numerical computations for toy wavefunctions
mimicking the theta vacuum of the (1+1)-dimensional Schwinger model. Our
results indicate that such superpositions exhibit no more violation of the area
law than the logarithmic behavior of a single Fermi surface. | A new supersymmetry: We propose a new supersymmetry in field theory that generalizes standard
supersymmetry and we construct field theoretic models that provide some of its
representations. This symmetry combines a finite number of standard 4D
supersymmetry multiplets into a single multiplet with a new type of
Kaluza-Klein embedding in higher dimensions. We suggest that this mechanism may
have phenomenological applications in understanding family unification. The
algebraic structure, which has a flavor of W-algebras, is directly motivated by
S-theory and its application in black holes. We show connections to previous
proposals in the literature for 12 dimensional supergravity, Yang-Mills, (2,1)
heterotic superstrings and Matrix models that attempt to capture part of the
secret theory behind string theory. |
String (In)Stability Issues with Broken Supersymmetry: We review the main results of our investigations motivated by the tadpole
potentials of ten-dimensional strings with broken supersymmetry. While these
are at best partial indications, it is hard to resist the feeling that they do
capture some lessons of String Theory. For example, these very tadpole
potentials lead to weak-string-coupling cosmologies that appear to provide
clues on the onset of the inflation from an initial fast roll. The transition,
if accessible to us, would offer a natural explanation for the lack of power
manifested by the CMB at large angular scales. In addition, the same tadpole
potentials can drive spontaneous compactifications to lower-dimensional
Minkowski spaces at corresponding length scales. Furthermore, the cosmological
solutions exhibit an intriguing "instability of isotropy" that, if taken at
face value, would point to an accidental origin of compactification. Finally,
symmetric static AdS x S solutions driven by the tadpole potentials also exist,
but they are unstable due to mixings induced by their internal fluxes. On the
other hand, the original Dudas-Mourad solution is perturbatively stable, and we
have gathered some detailed evidence that instabilities induced by internal
fluxes can be held under control in a similar class of weak-coupling type-IIB
compactifications to Minkowski space. | Quantum integrability of a massive anisotropic SU(N) fermionic model: We consider a general anisotropic massive SU(N) fermionic model, and
investigate its quantum integrability. In particular, by regularizing singular
operator products, we derive a system of equations resulting in the S-matrix
and find some non-trivial solutions. We illustrate our findings on the example
of a SU(3) model, and show that the Yang-Baxter equation is satisfied in the
massless limit for all coupling constants, while in the massive case the
solutions are parameterized in terms of the exceptional solutions to the
eight-vertex model. |
Sailing from Warped AdS_3 to Warped dS_3 in Topologically Massive
Gravity: Three-dimensional warped anti-de Sitter space in topologically massive
gravity with a negative cosmological constant has been proposed to be
holographically dual to a two-dimensional conformal field theory. We extend
this proposal to both positive and vanishing values of the cosmological
constant where stretched warped anti-de Sitter space is found to be a solution.
For positive cosmological constant, another class of warped solutions is
obtained by a spacelike (timelike) line fibration over Lorentzian (Euclidean)
two-dimensional de Sitter space. These solutions exhibit a cosmological horizon
and Hawking temperature much like de Sitter space. Global identifications of
this warped de Sitter space may contain a horizon in addition to the
cosmological one. At a degenerate point, warped de Sitter space becomes a
fibration over two-dimensional flat space. Finally, we study scalar waves in
these backgrounds. Scalars in stretched warped anti-de Sitter space exhibit
superradiance which can be interpreted as Schwinger pair production of charged
particles in two-dimensional anti-de Sitter space. | A Walk Through Superstring Theory With an Application to Yang-Mills
Theory: K-strings and D-branes as Gauge/Gravity Dual Objects: Superstring theory is one current, promising attempt at unifying gravity with
the other three known forces: the electromagnetic force, and the weak and
strong nuclear forces. Though this is still a work in progress, much effort has
been put toward this goal. A set of specific tools which are used in this
effort are gauge/gravity dualities. This thesis consists of a specific
implementation of gauge/gravity dualities to describe k-strings of strongly
coupled gauge theories as objects dual to Dp-branes embedded in confining
supergravity backgrounds from low energy superstring field theory. Along with
superstring theory, k-strings are also commonly investigated with lattice gauge
theory and Hamiltonian methods. A k-string is a colorless combination of
quark-antiquark source pairs, between which a color flux tube develops. The two
most notable terms of the k-string energy are, for large quark anti-quark
separation L, the tension term, proportional to L, and the Coulombic 1/L
correction, known as the Luscher term. This thesis provides an overview of
superstring theories and how gauge/gravity dualities emerge from them. It shows
in detail how these dualities can be used for the specific problem of
calculating the k-string energy in 2 + 1 and 3 + 1 space-time dimensions as the
energy of Dp-branes in the dual gravitational theory. A detailed review of
k-string tension calculations is given where good agreement is found with
lattice gauge theory and Hamiltonian methods. In reviewing the k-string
tension, we also touch on how different representations of k-strings can be
described with Dp-branes through gauge/gravity dualities. The main result of
this thesis is how the Luscher term is found to emerge as the one loop quantum
corrections to the Dp-brane energy. In 2+1 space-time dimensions, we have
Luscher term data to compare with from lattice gauge theory, where we find good
agreement. |
Extended phase space thermodynamics for hairy black holes: We expand our results in \cite{Astefanesei:2019ehu} to investigate a general
class of exact hairy black hole solutions in Einstein-Maxwell-dilaton gravity.
The dilaton is endowed with a potential that originates from an electromagnetic
Fayet-Iliopoulos term in $\mathcal{N} = 2$ extended supergravity in four
spacetime dimensions. We present the usual thermodynamics by using the
counterterm method supplemented with boundary terms for a scalar field with
mixed boundary conditions. We then extend our analysis by considering a
dynamical cosmological constant and verify the isoperimetric inequality. We
obtain a very rich phase diagram and criticality in both the canonical and
grand canonical ensembles. Within string theory, the cosmological constant is
related to the radius of the external sphere (of the compactification) and can
be interpreted as a modulus. In this context, the existence of a critical value
hints to the fact that the thermodynamic properties of black holes in lower
dimensions depend on the size of the compactification. | Discrete Hirota's equation in quantum integrable models: The recent progress in revealing classical integrable structures in quantum
models solved by Bethe ansatz is reviewed. Fusion relations for eigenvalues of
quantum transfer matrices can be written in the form of classical Hirota's
bilinear difference equation. This equation is also known as the completely
discretized version of the 2D Toda lattice. We explain how one obtains the
specific quantum results by solving the classical equation. The auxiliary
linear problem for the Hirota equation is shown to generalize Baxter's T-Q
relation. |
Emergent strings at infinite distance with broken supersymmetry: We investigate the infinite-distance properties of families of unstable flux
vacua in string theory with broken supersymmetry. To this end, we employ a
generalized notion of distance in the moduli space and we build a holographic
description for the non-perturbative regime of the tunneling cascade in terms
of a renormalization group flow. In one limit we recover an exponentially light
tower of Kaluza-Klein states, while in the opposite limit we find a tower of
higher-spin excitations of D1-branes, realizing the emergent string proposal.
In particular, the holographic description includes a free sector, whose
emergent superconformal symmetry resonates with supersymmetric stability, the
CFT distance conjecture and S-duality. We compute the anomalous dimensions of
scalar vertex operators and single-trace higher-spin currents, finding an
exponential suppression with the distance which is not generic from the
renormalization group perspective, but appears specific to our settings. | An Extension of Distribution Theory Related to Gauge Field Theory: We show that a considerable part of the theory of (ultra)distributions and
hyperfunctions can be extended to more singular generalized functions, starting
from an angular localizability notion introduced previously. Such an extension
is needed to treat gauge quantum field theories with indefinite metric in a
generic covariant gauge. Prime attention is paid to the generalized functions
defined on the Gelfand-Shilov spaces $S_\alpha^0$ which gives the widest
framework for construction of gauge-like models. We associate a similar test
function space with every open and every closed cone, show that these spaces
are nuclear and obtain the required formulas for their tensor products. The
main results include the generalization of the Paley--Wiener--Schwartz theorem
to the case of arbitrary singularity and the derivation of the relevant theorem
on holomorphic approximation. |
Quasitriangularity of quantum groups at roots of 1: An important property of a Hopf algebra is its quasitriangularity and it is
useful various applications. This property is investigated for quantum groups
$sl_2$ at roots of 1. It is shown that different forms of the quantum group
$sl_2$ at roots of 1 are either quasitriangular or have similar structure which
will be called autoquasitriangularity. In the most interesting cases this
property means that "braiding automorphism" is a combination of some Poisson
transformation and an adjoint transformation with certain element of the tensor
square of the algebra. | The one-legged K-theoretic vertex of fourfolds from 3d gauge theory: We present formulas for the K-theoretic Pandharipande-Thomas vertex of
fourfolds, for the case of one non-trivial leg. They are obtained from
computations in a three-dimensional supersymmetric gauge theory, where we
identify the field content and boundary conditions that correspond to the
vertex with tautological insertions. |
PT Symmetry and QCD: Finite Temperature and Density: The relevance of PT symmetry to quantum chromodynamics (QCD), the gauge
theory of the strong interactions, is explored in the context of finite
temperature and density. Two significant problems in QCD are studied: the sign
problem of finite-density QCD, and the problem of confinement. It is proven
that the effective action for heavy quarks at finite density is PT-symmetric.
For the case of 1+1 dimensions, the PT-symmetric Hamiltonian, although not
Hermitian, has real eigenvalues for a range of values of the chemical potential
$\mu$, solving the sign problem for this model. The effective action for heavy
quarks is part of a potentially large class of generalized sine-Gordon models
which are non-Hermitian but are PT-symmetric. Generalized sine-Gordon models
also occur naturally in gauge theories in which magnetic monopoles lead to
confinement. We explore gauge theories where monopoles cause confinement at
arbitrarily high temperatures. Several different classes of monopole gases
exist, with each class leading to different string tension scaling laws. For
one class of monopole gas models, the PT-symmetric affine Toda field theory
emerges naturally as the effective theory. This in turn leads to sine-law
scaling for string tensions, a behavior consistent with lattice simulations. | Electric-magnetic Duality of Abelian Gauge Theory on the Four-torus,
from the Fivebrane on T2 x T4, via their Partition Functions: We compute the partition function of four-dimensional abelian gauge theory on
a general four-torus T4 with flat metric using Dirac quantization. In addition
to an SL(4, Z) symmetry, it possesses SL(2,Z) symmetry that is electromagnetic
S-duality. We show explicitly how this SL(2, Z) S-duality of the 4d abelian
gauge theory has its origin in symmetries of the 6d (2,0) tensor theory, by
computing the partition function of a single fivebrane compactified on T2 x T4,
which has SL(2,Z) x SL(4,Z) symmetry. If we identify the couplings of the
abelian gauge theory \tau = {\theta\over 2\pi} + i{4\pi\over e^2} with the
complex modulus of the T2 torus, \tau = \beta^2 + i {R_1\over R_2}, then in the
small T2 limit, the partition function of the fivebrane tensor field can be
factorized, and contains the partition function of the 4d gauge theory. In this
way the SL(2,Z) symmetry of the 6d tensor partition function is identified with
the S-duality symmetry of the 4d gauge partition function. Each partition
function is the product of zero mode and oscillator contributions, where the
SL(2,Z) acts suitably. For the 4d gauge theory, which has a Lagrangian, this
product redistributes when using path integral quantization. |
A discrete history of the Lorentzian path integral: In these lecture notes, I describe the motivation behind a recent formulation
of a non-perturbative gravitational path integral for Lorentzian (instead of
the usual Euclidean) space-times, and give a pedagogical introduction to its
main features. At the regularized, discrete level this approach solves the
problems of (i) having a well-defined Wick rotation, (ii) possessing a
coordinate-invariant cutoff, and (iii) leading to_convergent_ sums over
geometries. Although little is known as yet about the existence and nature of
an underlying continuum theory of quantum gravity in four dimensions, there are
already a number of beautiful results in d=2 and d=3 where continuum limits
have been found. They include an explicit example of the inequivalence of the
Euclidean and Lorentzian path integrals, a non-perturbative mechanism for the
cancellation of the conformal factor, and the discovery that causality can act
as an effective regulator of quantum geometry. | Dirac operators on quantum two spheres: We investigate the spin $1/2$ fermions on quantum two spheres. It is shown
that the wave functions of fermions and a Dirac Operator on quantum two spheres
can be constructed in a manifestly covariant way under the quantum group
$SU(2)_q$. The concept of total angular momentum and chirality can be expressed
by using $q$-analog of Pauli-matrices and appropriate commutation relations. |
Dressing the Giant Magnon II: We extend our earlier work by demonstrating how to construct classical string
solutions describing arbitrary superpositions of scattering and bound states of
dyonic giant magnons on S^5 using the dressing method for the SU(4)/Sp(2) coset
model. We present a particular scattering solution which generalizes solutions
found in hep-th/0607009 and hep-th/0607044 to the case of arbitrary magnon
momenta. We compute the classical time delay for the scattering of two dyonic
magnons carrying angular momenta with arbitrary relative orientation on the
S^5. | Crossing versus locking: Bit threads and continuum multiflows: Bit threads are curves in holographic spacetimes that manifest boundary
entanglement, and are represented mathematically by continuum analogues of
network flows or multiflows. Subject to a density bound, the maximum number of
threads connecting a boundary region to its complement computes the
Ryu-Takayanagi entropy. When considering several regions at the same time, for
example in proving entropy inequalities, there are various inequivalent density
bounds that can be imposed. We investigate for which choices of bound a given
set of boundary regions can be "locked", in other words can have their
entropies computed by a single thread configuration. We show that under the
most stringent bound, which requires the threads to be locally parallel,
non-crossing regions can in general be locked, but crossing regions cannot,
where two regions are said to cross if they partially overlap and do not cover
the entire boundary. We also show that, under a certain less stringent density
bound, a crossing pair can be locked, and conjecture that any set of regions
not containing a pairwise crossing triple can be locked, analogously to the
situation for networks. |
The decay of massive closed superstrings with maximum angular momentum: We study the decay of a very massive closed superstring (i.e. \alpha' M^2>>
1) in the unique state of maximum angular momentum. This is done in flat
ten-dimensional spacetime and in the regime of weak string coupling, where the
dominant decay channel is into two states of masses M_1, M_2. We find that the
lifetime surprisingly grows with the first power of the mass M: T =c \alpha' M.
We also compute the decay rate for each values of M_1, M_2. We find that, for
large M, the dynamics selects only special channels of decay: modulo processes
which are exponentially suppressed, for every decay into a state of given mass
M_1, the mass M_2 of the other state is uniquely determined. | Sequences of Bubbles and Holes: New Phases of Kaluza-Klein Black Holes: We construct and analyze a large class of exact five- and six-dimensional
regular and static solutions of the vacuum Einstein equations. These solutions
describe sequences of Kaluza-Klein bubbles and black holes, placed alternately
so that the black holes are held apart by the bubbles. Asymptotically the
solutions are Minkowski-space times a circle, i.e. Kaluza-Klein space, so they
are part of the (\mu,n) phase diagram introduced in hep-th/0309116. In
particular, they occupy a hitherto unexplored region of the phase diagram,
since their relative tension exceeds that of the uniform black string. The
solutions contain bubbles and black holes of various topologies, including
six-dimensional black holes with ring topology S^3 x S^1 and tuboid topology
S^2 x S^1 x S^1. The bubbles support the S^1's of the horizons against
gravitational collapse. We find two maps between solutions, one that relates
five- and six-dimensional solutions, and another that relates solutions in the
same dimension by interchanging bubbles and black holes. To illustrate the
richness of the phase structure and the non-uniqueness in the (\mu,n) phase
diagram, we consider in detail particular examples of the general class of
solutions. |
Completeness and consistency of renormalisation group flows: We study different renormalisation group flows for scale dependent effective
actions, including exact and proper-time renormalisation group flows. These
flows have a simple one loop structure. They differ in their dependence on the
full field-dependent propagator, which is linear for exact flows. We
investigate the inherent approximations of flows with a non-linear dependence
on the propagator. We check explicitly that standard perturbation theory is not
reproduced. We explain the origin of the discrepancy by providing links to
exact flows both in closed expressions and in given approximations. We show
that proper-time flows are approximations to Callan-Symanzik flows. Within a
background field formalism, we provide a generalised proper-time flow, which is
exact. Implications of these findings are discussed. | Pulse shape dependence in the dynamically assisted Sauter-Schwinger
effect: While the Sauter-Schwinger effect describes nonperturbative electron-positron
pair creation from vacuum by a strong and slowly varying electric field
$E_{\mathrm{strong}}$ via tunneling, the dynamically assisted Sauter-Schwinger
effect corresponds to a strong (exponential) enhancement of the pair-creation
probability by an additional weak and fast electric or electromagnetic pulse
$E_{\mathrm{weak}}$. Using the WKB and worldline instanton method, we find that
this enhancement mechanism strongly depends on the shape of the fast pulse. For
the Sauter profile $1/\cosh^2(\omega t)$ considered previously, the threshold
frequency $\omega_{\mathrm{crit}}$ (where the enhancement mechanism sets in) is
basically independent of the magnitude $E_{\mathrm{weak}}$ of the weak
pulse---whereas for a Gaussian pulse $\exp(-\omega^2t^2)$, an oscillating
profile $\cos(\omega t)$ or a standing wave $\cos(\omega t)\cos(kx)$, the value
of $\omega_{\mathrm{crit}}$ does depend (logarithmically) on
$E_{\mathrm{weak}}/E_{\mathrm{strong}}$. |
On the Matter of N=2 Matter: We introduce a variety of four-dimensional N = 2 matter multiplets which have
not previously appeared explicitly in the literature. Using these, we develop a
class of supersymmetric actions supplying a context for a systematic
exploration of N = 2 matter theories, some of which include Hypermultiplet
sectors in novel ways. We construct an N = 2 supersymmetric field theory in
which the propagating fields are realized off-shell exclusively as Lorentz
scalars and Weyl spinors and which involves a sector with precisely the
R-charge assignments characteristic of Hypermultiplets. | Symmetry Factors of Feynman Diagrams and the Homological Perturbation
Lemma: We discuss the symmetry factors of Feynman diagrams of scalar field theories
with polynomial potential. After giving a concise general formula for them, we
present an elementary and direct proof that when computing scattering
amplitudes using the homological perturbation lemma, each contributing Feynman
diagram is indeed included with the correct symmetry factor. |
Perturbative classical conformal blocks as Steiner trees on the
hyperbolic disk: We consider the Steiner tree problem in hyperbolic geometry in the context of
the AdS/CFT duality between large-$c$ conformal blocks on the boundary and
particle motions in the bulk. The Steiner trees are weighted graphs on the
Poincare disk with a number of endpoints and trivalent vertices connected to
each other by edges in such a way that an overall length is minimum. We specify
a particular class of Steiner trees that we call holographic. Their
characteristic property is that a holographic Steiner tree with $N$ endpoints
can be inscribed into an $N$-gon with $N-1$ ideal vertices. The holographic
Steiner trees are dual to large-$c$ conformal blocks. Particular examples of
$N=2,3,4$ Steiner trees as well as their dual conformal blocks are explicitly
calculated. We discuss geometric properties of the holographic Steiner trees
and their realization in CFT terms. It is shown that connectivity and cuts of
the Steiner trees encode the factorization properties of large-$c$ conformal
blocks. | Study of the "Non-Abelian" Current Algebra of a Non-linear
$σ$-Model: A particular form of non-linear $\sigma$-model, having a global gauge
invariance, is studied. The detailed discussion on current algebra structures
reveals the non-abelian nature of the invariance, with {\it{field dependent
structure functions}}. Reduction of the field theory to a point particle
framework yields a non-linear harmonic oscillator, which is a special case of
similar models studied before in \cite{car}. The connection with noncommutative
geometry is also established. |
Quasinormal Modes of C-metric from SCFTs: We study the quasinormal modes (QNM) of the charged C-metric, which
physically stands for a charged accelerating black hole, with the help of
Nekrasov's partition function of 4d $\mathcal{N}=2$ superconformal field
theories (SCFTs). The QNM in the charged C-metric are classified into three
types: the photon-surface modes, the accelerating modes and the near-extremal
modes, and it is curious how the single quantization condition proposed in
arXiv:2006.06111 can reproduce all the different families. We show that the
connection formula encoded in terms of Nekrasov's partition function captures
all these families of QNM numerically and recovers the asymptotic behavior of
the accelerating and the near-extremal modes analytically. Using the connection
formulae of different 4d $\mathcal{N}=2$ SCFTs, one can solve both the radial
and the angular part of the scalar perturbation equation respectively. The same
algorithm can be applied to the de Sitter (dS) black holes to calculate both
the dS modes and the photon-sphere modes. | Smeared BTZ Black Hole from Space Noncommutativity: We study a novel phenomena of smearing of black hole horizons from the effect
of space noncommutativity. We present an explicit example in $AdS_3$ space,
using the Chern-Simons formulation of gravity. This produces a smeared BTZ
black hole which goes beyond the classical spacetime unexpectedly and there is
{\it no} reality problem in our approach with the gauge group $U(1,1) \times
U(1,1)$. The horizons are smeared, due to a splitting of the Killing horizon
and the apparent horizon, and there is a metric signature change to Euclidean
in the smeared region. The inner boundary of the smeared region acts as a
trapped surface for timelike particles but the outer as a classical barrier for
ingoing particles. The lightlike signals can escape from or reach the smeared
region in a {\it finite} time, which indicates that {\it the black hole is not
so dark, even classically.} In addition, it is remarked that the Hawking
temperature can {\it not} be defined by the regularity in the Euclidean
geometry except in the non-rotating case, and the origin can be smeared by a
{\it new} (apparent) horizon. |
Background independence in a background dependent renormalization group: Within the derivative expansion of conformally reduced gravity, the modified
split Ward identities are shown to be compatible with the flow equations if and
only if either the anomalous dimension vanishes or the cutoff profile is chosen
to be power law. No solutions exist if the Ward identities are incompatible. In
the compatible case, a clear reason is found for why Ward identities can still
forbid the existence of fixed points; however, for any cutoff profile, a
background independent (and parametrisation independent) flow equation is
uncovered. Finally, expanding in vertices, the combined equations are shown
generically to become either over-constrained or highly redundant beyond the
six-point level. | Consequences of Deformation of the Heisenberg Algebra: In this paper we will demonstrate that like the existence of a minimum
measurable length, the existence of a maximum measurable momentum, also
influence all quantum mechanical systems. Beyond the simple one dimensional
case, the existence of a maximum momentum will induce non-local corrections to
the first quantized Hamiltonian. However, these non-local corrections can be
effectively treated as local corrections by using the theory of harmonic
extensions of functions. We will also analyses the second quantization of this
deformed first quantized theory. Finally, we will analyses the gauge symmetry
corresponding to this deformed theory. |
Extensions of 2D Gravity: After reviewing some aspects of gravity in two dimensions, it is shown that
non-trivial embeddings of sl(2) in a semi-simple (super) Lie algebra give rise
to a very large class of extensions of 2D gravity. The induced action is
constructed as a gauged WZW model and an exact expression for the effective
action is given. (Talk presented at the Journees Relativistes '93, Brussels,
April, 1993). | Clifford Algebras, Spinors and $Cl(8,8)$ Unification: It is shown how the vector space $V_{8,8}$ arises from the Clifford algebra
$Cl(1,3)$ of spacetime. The latter algebra describes fundamental objects such
as strings and branes in terms of their $r$-volume degrees of freedom,
$x^{\mu_1 \mu_2 ...\mu_r}$ $\equiv x^M$, $r=0,1,2,3$, that generalizethe
concept of center of mass. Taking into account that there are sixteen $x^M$,
$M=1,2,3,...,16$, and in general $16 \times 15/2 = 120$ rotations of the form
$x'^M = {R^M}_N x^N$, we can consider $x^M$ as components of a vector $X=x^M
q_M$, where $q_M$ are generators of the Clifford algebra $Cl(8,8)$. The vector
space $V_{8,8}$ has enough room for the unification of the fundamental
particles and forces of the standard model. The rotations in $V_{8,8}\otimes
\mathbb{C}$ contain the grand unification group $SO(10)$ as a subgroup, and
also the Lorentz group $SO(1,3)$. It is shown how the Coleman-Mandula no go
theorem can be avoided. Spinors in $V_{8,8}\otimes \mathbb{C}$ are constructed
in terms of the wedge products of the basis vectors rewritten in the Witt
basis. They satisfy the massless Dirac equation in $M_{8,8}$ with the internal
part of the Dirac operator giving the non vanishing masses in four dimensions. |
Time-Space Noncommutativity And Symmetries For A Massive Relativistic
Particle: We show the existence of a time-space noncommutativity (NC) for the physical
system of a massive relativistic particle by exploiting the underlying symmetry
properties of this system. The space-space NC is eliminated by the
consideration of the exact symmetry properties and their consistency with the
equations of motion for the above system. The symmetry corresponding to the
noncommutative geometry turns out to be the special case of the gauge symmetry
such that the mass parameter of the above system becomes noncommutative with
the space and time variables. The possible deformations of the gauge algebra
between the spacetime variables and the angular momenta are discussed in
detail. These modifications owe their origin to the NC of the mass parameter
with the space and time variables. The cohomological origin for the above NC is
addressed in the language of the off-shell nilpotent Becchi-Rouet-Stora-Tyutin
(BRST) symmetry transformations. | Peculiarities of String Theory on AdS(4) x CP(3): We review peculiar features of type IIA string theory compactified on AdS(4)
x CP(3) superspace, in particular, the structure of the Green-Schwarz action,
issues with fixing its kappa-symmetry, classical integrability and the string
instanton on CP(3) |
Supersymmetry in the Half-Oscillator - Revisited: Following a recent study by Das and Pernice [Nucl. Phys. B561, (1999) 357],
we have carefully analyzed the half-harmonic oscillator. In contrast to their
observations, our analysis reveals that the spectrum does not allow for a zero
energy ground state and hence the supersymmetry is broken when the domain is
restricted to the positive half of the real axis. | A Matrix Model for 2D Quantum Gravity defined by Causal Dynamical
Triangulations: A novel continuum theory of two-dimensional quantum gravity, based on a
version of Causal Dynamical Triangulations which incorporates topology change,
has recently been formulated as a genuine string field theory in
zero-dimensional target space (arXiv:0802.0719). Here we show that the
Dyson-Schwinger equations of this string field theory are reproduced by a cubic
matrix model. This matrix model also appears in the so-called Dijkgraaf-Vafa
correspondence if the superpotential there is required to be renormalizable. In
the spirit of this model, as well as the original large-N expansion by 't
Hooft, we need no special double-scaling limit involving a fine tuning of
coupling constants to obtain the continuum quantum-gravitational theory. Our
result also implies a matrix model representation of the original, strictly
causal quantum gravity model. |
Deforming tachyon kinks and tachyon potentials: In this paper we investigate deformation of tachyon potentials and tachyon
kink solutions. We consider the deformation of a DBI type action with gauge and
tachyon fields living on D1-brane and D3-brane world-volume. We deform tachyon
potentials to get other consistent tachyon potentials by using properly a
deformation function depending on the gauge field components. Resolutions of
singular tachyon kinks via deformation and applications of deformed tachyon
potentials to scalar cosmology scenario are discussed. | Flow-oriented perturbation theory: We introduce a new diagrammatic approach to perturbative quantum field
theory, which we call flow-oriented perturbation theory (FOPT). Within it,
Feynman graphs are replaced by strongly connected directed graphs (digraphs).
FOPT is a coordinate space analogue of time-ordered perturbation theory and
loop-tree duality, but it has the advantage of having combinatorial and
canonical Feynman rules, combined with a simplified $i\varepsilon$ dependence
of the resulting integrals. Moreover, we introduce a novel digraph-based
representation for the S-matrix. The associated integrals involve the Fourier
transform of the flow polytope. Due to this polytope's properties, our S-matrix
representation exhibits manifest infrared singularity factorization on a
per-diagram level. Our findings reveal an interesting interplay between
spurious singularities and Fourier transforms of polytopes. |
De Sitter Holography with a Finite Number of States: We investigate the possibility that, in a combined theory of quantum
mechanics and gravity, de Sitter space is described by finitely many states.
The notion of observer complementarity, which states that each observer has
complete but complementary information, implies that, for a single observer,
the complete Hilbert space describes one side of the horizon. Observer
complementarity is implemented by identifying antipodal states with outgoing
states. The de Sitter group acts on S-matrix elements. Despite the fact that
the de Sitter group has no nontrivial finite-dimensional unitary
representations, we show that it is possible to construct an S-matrix that is
finite-dimensional, unitary, and de Sitter-invariant. We present a class of
examples that realize this idea holographically in terms of spinor fields on
the boundary sphere. The finite dimensionality is due to Fermi statistics and
an `exclusion principle' that truncates the orthonormal basis in which the
spinor fields can be expanded. | Vectorial AdS_5/CFT_4 duality for spin-one boundary theory: We consider an example of vectorial AdS_5/CFT_4 duality when the boundary
theory is described by N free complex or real Maxwell fields. It is dual to a
particular ("type C") higher spin theory in AdS_5 containing fields in special
mixed-symmetry representations. We extend the study of this theory in
arXiv:1410.3273 by deriving the expression for the large N limit of the
corresponding singlet-sector partition function on S^1 x S^3. We find that in
both complex U(N) and real O(N) invariant cases the form of the one-particle
partition function is as required by the AdS/CFT duality. We also demonstrate
the matching of the Casimir energy on S^3 by assuming an integer shift in the
bulk theory coupling. |
A New Approach for Bosonization of Massive Thirring Model in Three
Dimensions: We develop a new approach for bosonization based on the direct comparison of
current correlation functions and apply it to the case of the Massive Thirring
Model in three dimensions in the weak coupling regime, but with an arbitrary
mass. Explicit bosonized forms for the lagrangian and the current are obtained
in terms of a vector gauge field. Exact results for the corresponding
expressions are also obtained in the case of a free massive fermion. Finally, a
comment on the derivation of the current algebra directly from the bosonized
expressions is included. | The metric on field space, functional renormalization, and
metric-torsion quantum gravity: Searching for new non-perturbatively renormalizable quantum gravity theories,
functional renormalization group (RG) flows are studied on a theory space of
action functionals depending on the metric and the torsion tensor, the latter
parameterized by three irreducible component fields. A detailed comparison with
Quantum Einstein-Cartan Gravity (QECG), Quantum Einstein Gravity (QEG), and
"tetrad-only" gravity, all based on different theory spaces, is performed. It
is demonstrated that, over a generic theory space, the construction of a
functional RG equation (FRGE) for the effective average action requires the
specification of a metric on the infinite-dimensional field manifold as an
additional input. A modified FRGE is obtained if this metric is
scale-dependent, as it happens in the metric-torsion system considered. |
Scattering amplitudes and electromagnetic horizons: We consider the scattering of charged particles on particular electromagnetic
fields which have properties analogous to gravitational horizons. Classically,
particles become causally excluded from regions of spacetime beyond a null
surface which we identify as the `electromagnetic horizon'. In the quantum
theory there is pair production at the horizon via the Schwinger effect, but
only one particle from the pair escapes the field. Furthermore, unitarity
appears to be violated when crossing the horizon, and there is no well-defined
S-matrix. Despite this, we show how to use the perturbiner method to construct
`amplitudes' which contain all the dynamical information required to construct
observables related to pair creation, and to radiation from particles
scattering on the background. | Casimir Energy of 5D Electromagnetism and New Regularization Based on
Minimal Area Principle: We examine the Casimir energy of 5D electromagnetism in the recent
standpoint. The bulk geometry is flat. Z$_2$ symmetry and the periodic
property, for the extra coordinate, are taken into account. After confirming
the consistency with the past result, we do new things based on a {\it new
regularization}. In the treatment of the divergences, we introduce IR and UV
cut-offs and {\it restrict} the (4D momentum, extra coordinate)-integral
region. The regularized configuration is the {\it sphere lattice}, in the 4D
continuum space, which changes along the extra coordinate. The change
(renormalization flow) is specified by the {\it minimal area principle}, hence
this regularization configuration is string-like. We do the analysis not in the
Kaluza-Klein expanded form but in a {\it closed} form. We do {\it not} use any
perturbation. The formalism is based on the heat-kernel approach using the {\it
position/momentum propagator}. Interesting relations between the heat-kernels
and the P/M propagators are obtained, where we introduce the {\it generalized}
P/M propagators. A useful expression of the Casimir energy, in terms of the P/M
propagator, is obtained. The restricted-region approach is replaced by the
weight-function approach in the latter-half description. Its meaning, in
relation to the {\it space-time quantization}, is argued. {\it Finite} Casimir
energy is numerically obtained. The compactification-size parameter
(periodicity) suffers from the renormalization effect. Numerical evaluation is
exploited. Especially the minimal surface lines in the 5D flat space are
obtained both numerically using the Runge-Kutta method and analytically using
the general solution. |
Hairy Black holes in General Minimal Massive Gravity: In this work, we investigate the near horizon and asymptotic symmetries of
static and rotating hairy$-$AdS black hole in the framework of general minimal
massive gravity. We obtain energy, angular momentum and entropy of the
solutions. Then we show that our results for these quantities are consistent
with the first law of black hole thermodynamics. By considering the near
horizon geometry of black hole, we find near horizon conserved charges and
their algebra. By writing the algebra of conserved charges in terms of Fourier
modes we have obtained the conserved charges in terms of zero modes. | Charged Particles: A Builder's Guide: It is sometimes claimed that one cannot describe charged particles in gauge
theories. We identify the root of the problem and present an explicit
construction of charged particles. This is shown to have good perturbative
properties and, asymptotically before and after scattering, to recover particle
modes. |
The SU(2) X U(1) Electroweak Model based on the Nonlinearly Realized
Gauge Group. II. Functional Equations and the Weak Power-Counting: In the present paper, that is the second part devoted to the construction of
an electroweak model based on a nonlinear realization of the gauge group SU(2)
X U(1), we study the tree-level vertex functional with all the sources
necessary for the functional formulation of the relevant symmetries (Local
Functional Equation, Slavnov-Taylor identity, Landau Gauge Equation) and for
the symmetric removal of the divergences. The Weak Power Counting criterion is
proven in the presence of the novel sources. The local invariant solutions of
the functional equations are constructed in order to represent the counterterms
for the one-loop subtractions. The bleaching technique is fully extended to the
fermion sector. The neutral sector of the vector mesons is analyzed in detail
in order to identify the physical fields for the photon and the Z boson. The
identities necessary for the decoupling of the unphysical modes are fully
analyzed. These latter results are crucially bound to the Landau gauge used
throughout the paper. | Homolumo Gap from Dynamical Energy Levels: We introduce a dynamical matrix model where the matrix $X$ is interpreted as
a Hamiltonian representing interaction of a bosonic system with a single
fermion. We show how a system of second-quantized fermions influences the
ground state of the whole system by producing a gap between the highest
occupied eigenvalue and the lowest unoccupied eigenvalue. We describe the
development of the gap in both, strong and weak coupling regime, while for the
intermediate coupling strength we expect formation of homolumo "kinks". |
Massive gravitons as dark matter and gravitational waves: We consider the possibility that the massive graviton is a viable candidate
of dark matter in the context of bimetric gravity. We first derive the
energy-momentum tensor of the massive graviton and show that it indeed behaves
as that of dark matter fluid. We then discuss a production mechanism and the
present abundance of massive gravitons as dark matter. Since the metric to
which ordinary matter fields couple is a linear combination of the two mass
eigenstates of bigravity, production of massive gravitons, i.e. the dark matter
particles, is inevitably accompanied by generation of massless gravitons, i.e.
the gravitational waves. Therefore, in this scenario some information about
dark matter in our universe is encoded in gravitational waves. For instance, if
LIGO detects gravitational waves generated by the preheating after inflation
then the massive graviton with the mass of $\sim 0.01$ GeV is a candidate of
the dark matter. | K-homology in algebraic geometry and D-branes: In this article, we study how the Grothendieck group of coherent sheaves can
be used to describe D-branes. We show how global bound state construction in
topological $K$-theory can be adapted to our context, showing that D-branes
wrapping a subvariety are holomorphically classified by a relative $K$-group.
By taking the duality between the relative $K$-groups and the $K$-homologies,
we show that D-brane charge of type IIB superstrings is properly classified by
the $K$-homology. |
On Metastable Vacua and the Warped Deformed Conifold: Analytic Results: Continuing the programme of constructing the backreacted solution
corresponding to smeared anti-D3 branes in the warped deformed conifold, we
solve analytically the equations governing the space of first-order
deformations around this solution. We express the results in terms of at most
three nested integrals. These are the simplest expressions for the space of
$SU(2) \times SU(2) \times \ZZ_2$-invariant deformations, in which the putative
solution for smeared anti-D3 branes must live. We also explain why one cannot
claim to identify this solution without fully relating the coefficients of the
infrared and ultraviolet expansions of the deformation modes. The analytic
solution we find is the first step in this direction. | The holographic entropy arrangement: We develop a convenient framework for characterizing multipartite
entanglement in composite systems, based on relations between entropies of
various subsystems. This continues the program initiated in arXiv:1808.07871,
of using holography to effectively recast the geometric problem into an
algebraic one. We prove that, for an arbitrary number of parties, our procedure
identifies a finite set of entropic information quantities that we conveniently
represent geometrically in the form of an arrangement of hyperplanes. This
leads us to define the holographic entropy arrangement, whose algebraic and
combinatorial aspects we explore in detail. Using the framework, we derive
three new information quantities for four parties, as well as a new infinite
family for any number of parties. A natural construct from the arrangement is
the holographic entropy polyhedron which captures holographic entropy
inequalities describing the physically allowed region of entropy space. We
illustrate how to obtain the polyhedron by winnowing down the arrangement
through a sieve to pick out candidate sign-definite information quantities.
Comparing the polyhedron with the holographic entropy cone, we find perfect
agreement for 4 parties and corroborating evidence for the conjectured 5-party
entropy cone. We work with explicit configurations in arbitrary
(time-dependent) states leading to both simple derivations and an intuitive
picture of the entanglement pattern. |
Black Hole Bound on the Number of Species and Quantum Gravity at LHC: In theories with a large number N of particle species, black hole physics
imposes an upper bound on the mass of the species equal to M_{Planck}/\sqrt{N}.
This bound suggests a novel solution to the hierarchy problem in which there
are N \approx 10^{32} gravitationally coupled species, for example 10^{32}
copies of the Standard Model. The black hole bound forces them to be at the
weak scale, hence providing a stable hierarchy. We present various arguments,
that in such theories the effective gravitational cutoff is reduced to
\Lambda_G \approx M_{Planck}/\sqrt{N} and a new description is needed around
this scale. In particular black-holes smaller than \Lambda_G^{-1} are already
no longer semi-classical. The nature of the completion is model dependent. One
natural possibility is that \Lambda_G is the quantum gravity scale. We provide
evidence that within this type of scenarios, contrary to the standard
intuition, micro black holes have a (slowly-fading) memory of the species of
origin. Consequently the black holes produced at LHC, will predominantly decay
into the Standard Model particles, and negligibly into the other species. | Modified Chaplygin Gas as Scalar Field and Holographic Dark Energy Model: We study the correspondence between field theoretic and holographic dark
energy density of the universe with the modified Chaplygin gas (MCG)
respectively both in a flat and non-flat FRW universe. We present an equivalent
representation of the MCG with a homogeneous minimally coupled scalar field by
constructing the corresponding potential. A new scalar field potential is
obtained here which is physically realistic and important for cosmological
model building. In addition we also present holographic dark energy model
described by the MCG. The dynamics of the corresponding holographic dark energy
field is determined by reconstructing the potential in a non-flat universe. The
stability of the holographic dark energy in this case in a non-flat universe is
also discussed. |
Improved Holographic QCD and the Quark-gluon Plasma: We review construction of the improved holographic models for QCD-like
confining gauge theories and their applications to the physics of the
Quark-gluon plasma. We also review recent progress in this area of research.
The lecture notes start from the vacuum structure of these theories, then
develop thermodynamic and hydrodynamic observables and end with more advanced
topics such as the holographic QCD in the presence of external magnetic fields.
This is a summary of the lectures presented at the 56th Cracow School of
Theoretical Physics in Spring 2016 at Zakopane, Poland. | Superconnection in the spin factor approach to particle physics: The notion of superconnection devised by Quillen in 1985 and used in
gauge-Higgs field theory in the 1990's is applied to the spin factors
(finite-dimensional euclidean Jordan algebras) recently considered as
representing the finite quantum geometry of one generation of fermions in the
Standard Model of particle physics. |
Page Curve of AdS-Vaidya Model for Evaporating Black Holes: We study an evaporating black hole in the boundary conformal field theory
(BCFT) model. We show that a new BCFT solution that acts as a time-dependent
brane which we call the moving end-of-the-radiation (METR) brane leads to a new
type of Hubeny-Rangamani-Takayanagi surface. We further examine the island
formulation in this particular time-dependent spacetime. The Page curve is
calculated by using Holographic Entanglement Entropy (HEE) in the context of
double holography. | Holographic Order from Modular Chaos: We argue for an exponential bound characterizing the chaotic properties of
modular Hamiltonian flow of QFT subsystems. In holographic theories, maximal
modular chaos is reflected in the local Poincare symmetry about a
Ryu-Takayanagi surface. Generators of null deformations of the bulk extremal
surface map to modular scrambling modes -positive CFT operators saturating the
bound- and their algebra probes the bulk Riemann curvature, clarifying the
modular Berry curvature proposal of arXiv:1903.04493. |
Thermodynamics of charged rotating black branes in Brans-Dicke theory
with quadratic scalar field potential: We construct a class of charged rotating solutions in $(n+1)$-dimensional
Maxwell-Brans-Dicke theory with flat horizon in the presence of a quadratic
potential and investigate their properties. These solutions are neither
asymptotically flat nor (anti)-de Sitter. We find that these solutions can
present black brane, with inner and outer event horizons, an extreme black
brane or a naked singularity provided the parameters of the solutions are
chosen suitably. We compute the finite Euclidean action through the use of
counterterm method, and obtain the conserved and thermodynamic quantities by
using the relation between the action and free energy in grand-canonical
ensemble. We find that these quantities satisfy the first law of
thermodynamics, and the entropy does not follow the area law. | Open M-branes on AdS_{4/7} x S^{7/4} Revisited: We proceed further with a study of open supermembrane on the AdS_{4/7} x
S^{7/4} backgrounds. Open supermembrane can have M5-brane and 9-brane as
Dirichlet branes. In AdS and pp-wave cases the configurations of Dirichlet
branes are restricted. A classification of possible Dirichlet branes, which is
given up to and including the fourth order of fermionic variable \th in
hep-th/0310035, is shown to be valid even at full order of \th. We also discuss
open M5-brane on the AdS_{4/7} x S^{7/4}. |
Topological and Nontopological Solitons in a Gauged O(3) Sigma Model
with Chern-Simons term: The $O(3)$ nonlinear sigma model with its $U(1)$ subgroup gauged, where the
gauge field dynamics is solely governed by a Chern-Simons term, admits both
topological as well as nontopological self-dual soliton solutions for a
specific choice of the potential. It turns out that the topological solitons
are infinitely degenerate in any given sector. | Resonances in sinh- and sine-Gordon models and higher equations of
motion in Liouville theory: The notion of operator resonances was introduced earlier by Al. Zamolodchikov
within the framework of the conformal perturbation theory. The resonances are
related to logarithmic divergences of integrals in the perturbation expansion,
and manifest themselves in poles of the correlation functions and form factors
of local operators considered as functions of conformal dimensions. The
residues of the poles can be computed by means of some operator identities.
Here we study the resonances in the Liouville, sinh- and sine-Gordon models,
considered as perturbations of a massless free boson. We show that the
well-known higher equations of motion discovered by Al. Zamolodchikov in the
Liouville field theory are nothing but resonance identities for some descendant
operators. The resonance expansion in the vicinity of a resonance point
provides a regularized version of the corresponding operators. We try to
construct the corresponding resonance identities and resonance expansions in
the sinh- and sine-Gordon theories. In some cases it can be done explicitly,
but in most cases we are only able to obtain a general form so far. We show
nevertheless that the resonances are perturbatively exact, which means that
each of them only appears in a single term of the perturbation theory. |
Balanced metrics and noncommutative Kaehler geometry: In this paper we show how Einstein metrics are naturally described using the
quantization of the algebra of functions on a Kahler manifold M. In this setup
one interprets M as the phase space itself, equipped with the Poisson brackets
inherited from the Kahler 2-form. We compare the geometric quantization
framework with several deformation quantization approaches. We find that the
balanced metrics appear naturally as a result of setting the vacuum energy to
be the constant function on the moduli space of semiclassical vacua. In the
classical limit these metrics become Kahler-Einstein (when M admits such
metrics). Finally, we sketch several applications of this formalism, such as
explicit constructions of special Lagrangian submanifolds in compact Calabi-Yau
manifolds. | A Superstring Field Theory for Supergravity: A covariant closed superstring field theory, equivalent to classical
ten-dimensional Type II supergravity, is presented. The defining conformal
field theory is the ambitwistor string worldsheet theory of Mason and Skinner.
This theory is known to reproduce the scattering amplitudes of Cachazo, He and
Yuan in which the scattering equations play an important role and the string
field theory naturally incorporates these results. We investigate the operator
formalism description of the ambitwsitor string and propose an action for the
string field theory of the bosonic and supersymmetric theories. The correct
linearised gauge symmetries and spacetime actions are explicitly reproduced and
evidence is given that the action is correct to all orders. The focus is on the
Neveu-Schwarz sector and the explicit description of tree level perturbation
theory about flat spacetime. Application of the string field theory to general
supergravity backgrounds and the inclusion of the Ramond sector are briefly
discussed. |
Free Field Dynamics in the Generalized AdS (Super)Space: Pure gauge representation for general vacuum background fields (Cartan forms)
in the generalized $AdS$ superspace identified with $OSp(L,M)$ is found. This
allows us to formulate dynamics of free massless fields in the generalized
$AdS$ space-time and to find their (generalized) conformal and higher spin
field transformation laws. Generic solution of the field equations is also
constructed explicitly. The results are obtained with the aid of the star
product realization of ortosymplectic superalgebras. | Integrable deformations of CFTs and the discrete Hirota equations: We solve the discrete Hirota equations (Kirillov-Reshetikhin Q-systems) for
$A_r$, and their analogue for $D_r$, for the cases where the second variable
ranges over either a finite set or over all integers. Until now only special
solutions were known. We find all solutions for which no component vanishes, as
required in the known applications. As an introduction we present the known
solution where the second variable ranges over the natural numbers. |
Charged Black Rings at large D: We study the charged slowly rotating black holes in the Einstein-Maxwell
theory in the large dimensions. By using the 1/D expansion in the near region
of the black hole we obtain the effective equations for the charged slowly
rotating black holes. The effective equations describe the charged black ring,
the charged slowly rotating Myers-Perry black hole and the charged slowly
boosted black string as stationary solutions. By embedding the solution of the
effective equations into the flat spacetime background in the ring coordinate
we obtain the charged black ring solution at large D analytically. We find that
the charge lowers the angular momentum of the black ring due to the regular
condition on the solution. By the perturbation analysis of the effective
equations, we obtain the quasinormal modes of the charge perturbation and the
gravitational perturbation analytically. Like the neutral case the charged thin
black ring suffers from the Gregory-Laflamme-like instability under
non-axisymmetric perturbations, but the charge helps weaken the instability.
Besides, we find that the large D analysis always respect the cosmic
censorship. | Elliptical and Purely NS Superstrata: We analyze the BPS equations in the ``superstratum sector'' of
three-dimensional gauged supergravity. We obtain multi-parameter supersymmetric
solutions that include elliptical deformations of the supertubes that underlie
standard superstrata. We uplift the three-dimensional solutions to obtain the
corresponding six-dimensional geometries. This yields new families of
elliptically-deformed, ambi-bolar hyper-K\"ahler geometries in four dimensions
with a non-tri-holomorphic $U(1)$ isometry. We also find a new family of
scaling superstrata whose S-dual lives entirely within the NS-sector of
supergravity, and will thus be more amenable to exact analysis using string
probes. In all these new superstrata, including the scaling ones, if the
momentum charge is non-zero we find that the ellipse stays away from the
degeneration locus in which the ellipse becomes flat. |
Vacuum interpolation in supergravity via super p-branes: We show that many of the recently proposed supersymmetric p-brane solutions
of d=10 and d=11 supergravity have the property that they interpolate between
Minkowski spacetime and a compactified spacetime, both being supersymmetric
supergravity vacua. Our results imply that the effective worldvolume action for
small fluctuations of the super p-brane is a supersingleton field theory for
$(adS)_{p+2}$, as has been often conjectured in the past. | Twisted indices, Bethe ideals and 3d $\mathcal{N}=2$ infrared dualities: We study the topologically twisted index of 3d $\mathcal{N}=2$ supersymmetric
gauge theories with unitary gauge groups. We implement a Gr\"obner basis
algorithm for computing the $\Sigma_g\times S^1$ index explicitly and exactly
in terms of the associated Bethe ideal, which is defined as the algebraic ideal
associated with the Bethe equations of the corresponding 3d $A$-model. We then
revisit recently discovered infrared dualities for unitary SQCD with gauge
group $U(N_c)_{k, k +l N_c}$ with $l\neq 0$, namely the Nii duality that
generalises the Giveon-Kutasov duality, the Amariti-Rota duality that
generalises the Aharony duality, and their further generalisations in the case
of arbitrary numbers of fundamental and antifundamental chiral multiplets. In
particular, we determine all the flavour Chern-Simons contact terms needed to
make these dualities work. This allows us to check that the twisted indices of
dual theories match exactly. We also initiate the study of the Witten index of
unitary SQCD with $l\neq 0$. |
On the effective lagrangian in spinor electrodynamics with added
violation of Lorentz and CPT symmetries: We consider quantum electrodynamics with additional coupling of spinor fields
to the space-time independent axial vector violating both Lorentz and CPT
symmetries. The Fock-Schwinger proper time method is used to calculate the
one-loop effective action up to the second order in the axial vector and to all
orders in the space-time independent electromagnetic field strength. We find
that the Chern-Simons term is not radiatively induced and that the effective
action is CPT invariant in the given approximation. | Holography and off-center collisions of localized shock waves: Using numerical holography, we study the collision, at non-zero impact
parameter, of bounded, localized distributions of energy density chosen to
mimic relativistic heavy ion collisions, in strongly coupled N = 4
supersymmetric Yang-Mills theory. Both longitudinal and transverse dynamics in
the dual field theory are properly described. Using the gravitational
description we solve 5D Einstein equations, without dimensionality reducing
symmetry restrictions, to find the asymptotically anti-de Sitter spacetime
geometry. Implications of our results on the understanding of early stages of
heavy ion collisions, including the development of transverse radial flow, are
discussed. |
Chiral Symmetry Breaking in a Uniform External Magnetic Field: Using the nonperturbative Schwinger-Dyson equation, we show that chiral
symmetry is dynamically broken in QED at weak couplings when an external
magnetic field is present, and that chiral symmetry is restored at temperatures
above $T_c \simeq \alpha\pi^2/\sqrt{2 \pi |eH|}$, where $\alpha$ is the fine
structure constant and $H$ is the magnetic field strength. | Asymptotically flat black holes and gravitational waves in
three-dimensional massive gravity: Different classes of exact solutions for the BHT massive gravity theory are
constructed and analyzed. We focus in the special case of the purely quadratic
Lagrangian, whose field equations are irreducibly of fourth order and are known
to admit asymptotically locally flat black holes endowed with gravitational
hair. The first class corresponds to a Kerr-Schild deformation of Minkowski
spacetime along a covariantly constant null vector. As in the case of General
Relativity, the field equations linearize so that the solution can be easily
shown to be described by four arbitrary functions of a single null coordinate.
These solutions can be regarded as a new sort of pp-waves. The second class is
obtained from a deformation of the static asymptotically locally flat black
hole, that goes along the spacelike (angular) Killing vector. Remarkably,
although the deformation is not of Kerr-Schild type, the field equations also
linearize, and hence the generic solution can be readily integrated. It is
neither static nor spherically symmetric, being described by two integration
constants and two arbitrary functions of the angular coordinate. In the static
case it describes "black flowers" whose event horizons break the spherical
symmetry. The generic time-dependent solution appears to describe a graviton
that moves away from a black flower. Despite the asymptotic behaviour of these
solutions at null infinity is relaxed with respect to the one for General
Relativity, the asymptotic symmetries coincide. However, the algebra of the
conserved charges corresponds to BMS$_{3}$, but devoid of central extensions.
The "dynamical black flowers" are shown to possess a finite energy. The surface
integrals that define the global charges also turn out to be useful in the
description of the thermodynamics of solutions with event horizons. |
Exact N=2 Supergravity Solutions With Polarized Branes: We construct several classes of exact supersymmetric supergravity solutions
describing D4 branes polarized into NS5 branes and F-strings polarized into D2
branes. These setups belong to the same universality class as the perturbative
solutions used by Polchinski and Strassler to describe the string dual of N=1*
theories. The D4-NS5 setup can be interpreted as a string dual to a confining
4+1 dimensional theory with 8 supercharges, whose properties we discuss. By
T-duality, our solutions give Type IIB supersymmetric backgrounds with
polarized branes. | Sphalerons, Antisphalerons and Vortex Rings: We present new classical solutions of Weinberg-Salam theory in the limit of
vanishing Weinberg angle. In these static axially symmetric solutions, the
Higgs field vanishes either on isolated points on the symmetry axis, or on
rings centered around the symmetry axis. The solutions represent systems of
sphalerons, antisphalerons, and vortex rings. |
Small cosmological constant in seesaw mechanism with breaking down SUSY: The observed small value of cosmological constant can be naturally related
with the scale of breaking down supersymmetry in agreement with other
evaluations in particle physics. | Gribov horizon and i-particles: about a toy model and the construction
of physical operators: Restricting the functional integral to the Gribov region $\Omega$ leads to a
deep modification of the behavior of Euclidean Yang-Mills theories in the
infrared region. For example, a gluon propagator of the Gribov type,
$\frac{k^2}{k^4+{\hat \gamma}^4}$, can be viewed as a propagating pair of
unphysical modes, called here $i$-particles, with complex masses $\pm i{\hat
\gamma}^2$. From this viewpoint, gluons are unphysical and one can see them as
being confined. We introduce a simple toy model describing how a suitable set
of composite operators can be constructed out of $i$-particles whose
correlation functions exhibit only real branch cuts, with associated positive
spectral density. These composite operators can thus be called physical and are
the toy analogy of glueballs in the Gribov-Zwanziger theory. |
Spacing of the entropy spectrum for KS Black hole in Horava-Lifshitz
gravity: In this paper we present the spectrum of entropy/area for Kehagias-Sfetsos
(KS) black hole in Ho$\check{\textbf{r}}$ava-Lifshitz (HL)gravity via
quasi-normal modes (QNM) approach. We show that in the massive case the mass
parameter $\mu$ disappears in the entropy spectrum and only the quasinormal
modes modified by a term which is proportional to the mass square term. Our
calculations show that the charge like parameter $\frac{1}{2\omega}=Q^{2}$
appears in the surface gravity and our calculations can be applied to any
spherically symmetric spacetime which has only one physically acceptable
horizon. Our main difference between our calculations and what was done in
\cite{1} is that the portion of charge and mass is included explicitly in the
surface gravity and consequently in the QNM expression. Since the imaginary
part of the QNM is related to the adiabatic invariance of the system and also
to the entropy, surprisingly the mass parameter do not appear in the entropy
spectrum. Our conclusion supported by some acclaims about that the scalar field
parameters (charges) can not change the fundamental parameters in the
4-dimensional black holes. | A Computer Algorithm For Engineering Off-Shell Multiplets With Four
Supercharges On The World Sheet: We present an adinkra-based computer algorithm implemented in a Mathematica
code and use it in a limited demonstration of how to engineer off-shell,
arbitrary N-extended world-sheet supermultiplets. Using one of the outputs from
this algorithm, we present evidence for the unexpected discovery of a
previously unknown 8 - 8 representation of N = 2 world sheet supersymmetry. As
well, we uncover a menagerie of (p, q) = (3, 1) world sheet supermultiplets. |
The rank-2 classification problem III: curves with additional
automorphisms: This is the third in a series of papers which outlines an approach to the
classification of $\mathcal{N}{=}2$ superconformal field theories at rank 2 via
the study of their Coulomb branch geometries. Here we use the fact that the
encoding of a Coulomb branch geometry as a Seiberg-Witten curve and 1-form
enjoys a large reparametrisation invariance. While there is always a unique way
to fix this invariance such that the curve and 1-form are single-valued over
the Coulomb branch -- the "canonical frame" of the curve used in the first two
papers in this series -- there are other useful frames in which the curve is
single-valued but the 1-form is allowed to be multi-valued. In these frames,
which we call "automorphism frames", the 1-form is periodic up to an
automorphism twist. We argue that the multi-valuedness of the automorphism
frame can simplify the computational complexity of finding new consistent scale
invariant solutions. We demonstrate this in an example by using the
automorphism frame to construct for the first time a genus 2 Seiberg-Witten
curve for the $\mathcal{N}{=}4$ SU(3) superYang-Mills theory, a solution that
is hard to find by other approaches. | Scattering and bound states of Dirac Equation in presence of cosmic
string for Hulthén potential: In this work we study the Dirac equation with vector and scalar potentials in
the spacetime generated by a cosmic string. Using an approximation for the
centrifugal term, a solution for the radial differential equation is obtained.
We consider the scattering states under the Hulth\'{e}n potential and obtain
the phase shifts. From the poles of the scattering $S$-matrix the states
energies are determined as well. |
Rényi Entropy for a $\bf 2d$ CFT with a gauge field: $\bf \widehat{\rm
SU}(N)_1$ WZW theory on a branched torus: The R\'enyi entropy for the $\widehat{\rm SU}(N)_1$ WZW model as described by
$N$ free fermions coupled to a $U(1)$ constraint field is computed on an
$n$-sheeted branched torus. The boundary condition of the harmonic component of
the gauge field on the homology cycles of the genus $g$ Riemann surface is
central to the final result. This calculation is complementary to that of
arXiv:$1510.05993$, which presents the bose side of the bose-fermi equivalence. | Quark Mass Correction to Chiral Separation Effect and Pseudoscalar
Condensate: We derived an analytic structure of the quark mass correction to chiral
separation effect (CSE) in small mass regime. We confirmed this structure by a
D3/D7 holographic model study in a finite density, finite magnetic field
background. The quark mass correction to CSE can be related to correlators of
pseudo-scalar condensate, quark number density and quark condensate in static
limit. We found scaling relations of these correlators with spatial momentum in
the small momentum regime. They characterize medium responses to electric
field, inhomogeneous quark mass and chiral shift. Beyond the small momentum
regime, we found existence of normalizable mode, which possibly leads to
formation of spiral phase. The normalizable mode exists beyond a critical
magnetic field, whose magnitude decreases with quark chemical potential. |
Ruijsenaars-Schneider three-body models with N=2 supersymmetry: The Ruijsenaars-Schneider models are conventionally regarded as relativistic
generalizations of the Calogero integrable systems. Surprisingly enough, their
supersymmetric generalizations escaped attention. In this work, N=2
supersymmetric extensions of the rational and hyperbolic Ruijsenaars-Schneider
three-body models are constructed within the framework of the Hamiltonian
formalism. It is also known that the rational model can be described by the
geodesic equations associated with a metric connection. We demonstrate that the
hyperbolic systems are linked to non-metric connections. | The imaginary time Path Integral and non-time-reversal-invariant- saddle
points of the Euclidean Action: We discuss new bounce-like (but non-time-reversal-invariant-) solutions to
Euclidean equations of motion, which we dub boomerons. In the Euclidean path
integral approach to quantum theories, boomerons make an imaginary contribution
to the vacuum energy. The fake vacuum instabilty can be removed by cancelling
boomeron contributions against contributions from time reversed boomerons
(anti-boomerons). The cancellation rests on a sign choice whose significance is
not completely understood in the path integral method. |
Restrictions of Pfaffian Systems for Feynman Integrals: This work studies limits of Pfaffian systems, a class of first-order PDEs
appearing in the Feynman integral calculus. Such limits appear naturally in the
context of scattering amplitudes when there is a separation of scale in a given
set of kinematic variables. We model these limits, which are often singular,
via restrictions of D-modules. We thereby develop two different restriction
algorithms: one based on gauge transformations, and another relying on the
Macaulay matrix. These algorithms output Pfaffian systems containing fewer
variables and of smaller rank. We show that it is also possible to retain
logarithmic corrections in the limiting variable. The algorithms are showcased
in many examples involving Feynman integrals and hypergeometric functions
coming from GKZ systems. | Braneworld sum rules and positive tension branes in a massive gravity: By taking advantage of the braneworld sum rules, we explore the feasibility
of constructing a braneworld scenario consisting solely of positive tension
branes in a 5D extension of the Lorentz-violating massive gravity. It is found
that the theory supports three distinct brane configurations, one of which is
exactly what we expected, consisting solely of two positive tension branes. The
cosmological problem of Randall-Sundrum-1 model and the gauge hierarchy problem
can be solved in this model simultaneously. Furthermore, the analysis of linear
perturbations reveals that the tensor, vector and scalar modes are all massive
and share the same mass spectrum, except that the ground state of vector mode
is absent. Moreover, the tensor and vector modes are robust, but the scalar
mode is ghost-like. Interestingly, even though the Kaluza-Klein gravitons have
an extremely small mass splitting scale, an estimation of the effective
gravitational potential and production of these gravitons on the brane
indicates that the phenomenology of the present model is equivalent to that of
the 6D ADD model. |
Tensionless Strings, WZW Models at Critical Level and Massless Higher
Spin Fields: We discuss the notion of tensionless limit in quantum bosonic string theory,
especially in flat Minkowski space, noncompact group manifolds (e.g., SL(2,R))
and coset manifolds (e.g., AdS). We show that in curved space typically there
exists a critical value of the tension which is related to the critical value
of the level of the corresponding affine algebra. We argue that at the critical
level the sring theory becomes tensionless and that there exists a huge new
symmetry of the theory. We dicuss the appearence of the higher spin massless
states at the critical level. | Gauge fields in (anti)-de Sitter space and Connections of its symmetry
algebra: The generalized connections of the (anti)-de Sitter space symmetry algebra,
which are differential forms of arbitrary degree with values in any irreducible
(spin)-tensor representation of the (anti)-de Sitter algebra, are studied. It
is shown that arbitrary-spin gauge field in (anti)-de Sitter space, massless or
partially-massless, can be described by a single connection. A 'one-to-one'
correspondence between the connections of the (anti)-de Sitter algebra and the
gauge fields is established. The gauge symmetry is manifest and auxiliary
fields are automatically included in the formalism. |
Some three-point correlation functions in the eta-deformed AdS_5 x S^5: We compute some normalized structure constants in the $\eta$-deformed
$AdS_5\times S^5$ in the framework of the semiclassical approach. This is done
for the cases when the "heavy" string states are finite-size giant magnons
carrying one angular momentum and for three different choices of the "light"
state: primary scalar operators, dilaton operator with nonzero momentum,
singlet scalar operators on higher string levels. Since the dual field theory
is still unknown, the results obtained here must be considered as conjectures
or as predictions from the string theory side.
Keywords: Gauge/string duality, Correlation functions
PACS:11.25.-w, 11.25.Tq | NS Branes in Type I Theory: We consider novel nonperturbative effects of type I theories compactified on
singular ALE spaces obtained by adding NS branes. Such effects include a
description of small $E_8$ instantons at singularities. |
Mirror symmetry and new approach to constructing orbifolds of Gepner
models: Motivated by the principles of the conformal bootstrap, primarily the
principle of Locality, simultaneously with the requirement of space-time
supersymmetry, we reconsider constructions of compactified superstring models.
Starting from requirements of space-time supersymmetry and mutual locality, we
construct a complete set of physical fields of orbifolds of Gepner models. To
technically implement this, we use spectral flow generators to construct all
physical fields from the chiral primary fields. The set of these spectral flow
operators forms a so-called admissible group $G_{adm}$, which defines a given
orbifold. The action of these operators produces a collection of physical
fields consistent with the action of supersymmetry generators. The selection of
mutually local fields from this collection is carried out using the mirror
group $G^*_{adm}$. The permutation of $G_{adm}$ and $G^*_{adm}$ replaces the
original orbifold with a mirror one that satisfies the same conditions as the
original one. This also implies that the resulting model is modular invariant. | String Cosmology and Chaos: We briefly review three aspects of string cosmology: (1) the ``stochastic''
approach to the pre-big bang scenario, (2) the presence of chaos in the generic
cosmological solutions of the tree-level low-energy effective actions coming
out of string theory, and (3) the remarkable link between the latter chaos and
the Weyl groups of some hyperbolic Kac-Moody algebras. Talk given at the
Francqui Colloquium ``Strings and Gravity: Tying the Forces Together''
(Brussels, October 2001). |
Note on Mutual Information between Two Intervals of Extremal BTZ: In this note we compute mutual information between two intervals in CFTs dual
to extremal BTZ (UV CFT) and near horizon limit of extremal BTZ (IR CFT) using
the replica technique in some limiting regimes, which can be compared with
holographic description. | Spectral Covers, Charged Matter and Bundle Cohomology: We consider four dimensional heterotic compactifications on smooth elliptic
Calabi-Yau threefolds. Using spectral cover techniques, we study bundle
cohomology groups corresponding to charged matter multiplets. The analysis
shows that in generic situations, the resulting charged matter spectrum is
stable under deformations of the vector bundle. |
Gauge Symmetry Breaking through Soft Masses in Supersymmetric Gauge
Theories: We analyze the effects of soft supersymmetry breaking terms on N=1
supersymmetric QCD with $N_f$ flavors and color gauge group $SU(N_c)$. The mass
squared of some squarks may be negative, as long as vacuum stability is ensured
by a simple mass inequality. For $N_f<N_c$, we include the dynamics of the
non-perturbative superpotential and use the original (s)quark and gauge fields,
while for $N_f>N_c+1$, we formulate the dynamics in terms of dual (s)quarks and
a dual gauge group $SU(N_f-N_c)$. The presence of negative squark mass squared
terms leads to spontaneous breakdown of flavor and color symmetry. We determine
this breaking pattern, derive the spectrum, and argue that the masses vary
smoothly as one crosses from the Higgs phase into the confining phase. | Hiding Anomalies: Anomalies can be anticipated at the classical level without changing the
classical cohomology, by introducing extra degrees of freedom. In the process,
the anomaly does not quite disappear. We show that, in fact, it is shifted to
new symmetries that come with the extra fields. |
Hamiltonian derivation of dual gravitational charges: We provide a Hamiltonian derivation of recently discovered dual BMS charges.
In order to do so, we work in the first order formalism and add to the usual
Palatini action, the Holst term, which does not contribute to the equations of
motion. We give a method for finding the leading order integrable dual charges
\`a la Wald-Zoupas and construct the corresponding charge algebra. We argue
that in the presence of fermions, the relevant term that leads to dual charges
is the topological Nieh-Yan term. | An Operator Valued Extension of the Super KdV Equations: An extension of the Super KdV integrable system in terms of operator valued
functions is obtained. Following the ideas of Gardner, a general algebraic
approach for finding the infinitely many conserved quantities of integrable
systems is presented. The approach is applied to the above described system and
infinitely many conserved quantities are constructed. In a particular case they
reduce to the corresponding conserved quantities of Super KdV. |
Classical solutions for the Carroll-Field-Jackiw-Proca electrodynamics: In the present work, we investigate classical solutions of the
Maxwell-Carroll-Field-Jackiw-Proca (MCFJP) electrodynamics for the cases a
purely timelike and spacelike Lorentz-violating (LV) background. Starting from
the MCFJP Lagrangian and the associated wave equations written for the
potential four-vector, the tensor form of the Green function is achieved. In
the timelike case, the components of the stationary Green function are
explicitly written. The classical solutions for the electric and magnetic field
strengths are then evaluated, being observed that the electric sector is not
modified by the LV background, keeping the Maxwell-Proca behavior. The magnetic
field associated with a charge in uniform motion presents an oscillating
behavior that also provides an oscillating MCFJ solution (in the limit of a
vanishing Proca mass), but does not recover the Maxwell-Proca solution in the
limit of vanishing background. In the spacelike case, the stationary Green
function is written and also explicitly carried out in the regime of a small
background. The electric and magnetic fields reveal to possess an exponentially
decaying behavior, that recover the Maxwell-Proca solutions. | Soft Scalars and the Geometry of the Space of Celestial CFTs: Known examples of the holographic dictionary in asymptotically Anti-de Sitter
spacetimes equate moduli spaces of bulk vacua with conformal manifolds in the
dual quantum field theory. We demonstrate that the same identification holds
for gravity in asymptotically flat spacetimes in any dimension, in accord with
expectations derived from the celestial conformal field theory (CCFT)
formalism. Soft limits of moduli scalars described by the sigma model are
universal, and relate to parallel transport of $S$-matrix observables over the
moduli space of bulk vacua. The leading "soft moduli operator" is the shadow
transform of a dimension $\Delta=d$ marginal operator $M(x)$. The universal
form of the soft limit guarantees that $M(x)$ acts as a marginal deformation in
the CCFT$_d$, and coherent states of the soft scalars correspond to finite
deformations along the conformal manifold. This manifold typically has
curvature, which is captured by the antisymmetric double-soft theorem and which
reflects the Berry curvature in CCFT$_d$. We also compute the
Mellin-transformed four-point function in the sigma model and compare to a
formula of Kutasov for the curvature of the conformal manifold. |
Searching for gauge theories with the conformal bootstrap: Infrared fixed points of gauge theories provide intriguing targets for the
modern conformal bootstrap program. In this work we provide some preliminary
evidence that a family of gauged fermionic CFTs saturate bootstrap bounds and
can potentially be solved with the conformal bootstrap. We start by considering
the bootstrap for $SO(N)$ vector 4-point functions in general dimension $D$. In
the large $N$ limit, upper bounds on the scaling dimensions of the lowest
$SO(N)$ singlet and traceless symmetric scalars interpolate between two
solutions at $\Delta =D/2-1$ and $\Delta =D-1$ via generalized free field
theory. In 3D the critical $O(N)$ vector models are known to saturate the
bootstrap bounds and correspond to the kinks approaching $\Delta =1/2$ at large
$N$. We show that the bootstrap bounds also admit another infinite family of
kinks ${\cal T}_D$, which at large $N$ approach solutions containing free
fermion bilinears at $\Delta=D-1$ from below. The kinks ${\cal T}_D$ appear in
general dimensions with a $D$-dependent critical $N^*$ below which the kink
disappears. We also study relations between the bounds obtained from the
bootstrap with $SO(N)$ vectors, $SU(N)$ fundamentals, and $SU(N)\times SU(N)$
bi-fundamentals. We provide a proof for the coincidence between bootstrap
bounds with different global symmetries. We show evidence that the proper
symmetries of the underlying theories of ${\cal T}_D$ are subgroups of $SO(N)$,
and we speculate that the kinks ${\cal T}_D$ relate to the fixed points of
gauge theories coupled to fermions. | General-relativistic spin system: The models of spin systems defined on Euclidean space provide powerful
machinery for studying a broad range of condensed matter phenomena. While the
non-relativistic effective description is sufficient for most of the
applications, it is interesting to consider special and general relativistic
extensions of such models. Here, we introduce a framework that allows us to
construct theories of continuous spin variables on a curved spacetime. Our
approach takes advantage of the results of the non-linear field space theory,
which shows how to construct compact phase space models, in particular for the
spherical phase space of spin. Following the methodology corresponding to a
bosonization of spin systems into the spin wave representations, we postulate a
representation having the form of the Klein-Gordon field. This representation
is equivalent to the semi-classical version of the well-known
Holstein-Primakoff transformation. The general-relativistic extension of the
spin wave representation is then performed, leading to the
general-relativistically motivated modifications of the Ising model coupled to
a transversal magnetic field. The advantage of our approach is its off-shell
construction, while the popular methods of coupling fermions to general
relativity usually depend on the form of Einstein field equations with matter.
Furthermore, we show equivalence between the considered spin system and the
Dirac-Born-Infeld type scalar field theory with a specific potential, which is
also an example of k-essence theory. Based on this, the cosmological
consequences of the introduced spin field matter content are preliminarily
investigated. |
Looking for a Matrix model of ABJM: Encouraged by the recent construction of fuzzy sphere solutions in the ABJM
theory, we re-analyze the latter from the perspective of a Matrix-like model.
In particular, we argue that a vortex solution exhibits properties of a
supergraviton, while a kink represents a 2-brane. Other solutions are also
consistent with the Matrix-type interpretation. We study vortex scattering and
compare with graviton scattering in the massive ABJM background, however our
results are inconclusive. We speculate on how to extend our results to
construct a Matrix theory of ABJM. | The thermoelectric properties of inhomogeneous holographic lattices: We consider inhomogeneous, periodic, holographic lattices of D=4
Einstein-Maxwell theory. We show that the DC thermoelectric conductivity matrix
can be expressed analytically in terms of the horizon data of the corresponding
black hole solution. We numerically construct such black hole solutions for
lattices consisting of one, two and ten wave-numbers. We numerically determine
the AC electric conductivity which reveals Drude physics as well as resonances
associated with sound modes. No evidence for an intermediate frequency scaling
regime is found. All of the monochromatic lattice black holes that we have
constructed exhibit scaling behaviour at low temperatures which is consistent
with the appearance of $AdS_2\times\mathbb{R}^2$ in the far IR at T=0. |
Qubit Heating Near a Hotspot: Effective theories describing black hole exteriors contain many open-system
features due to the large number of gapless degrees of freedom that lie beyond
reach across the horizon. A simple solvable Caldeira-Leggett type model of a
quantum field interacting within a small area with many unmeasured thermal
degrees of freedom was recently proposed in arXiv:2106.09854 to provide a toy
model of this kind of dynamics against which more complete black hole
calculations might be compared. We here compute the response of a simple
Unruh-DeWitt detector (or qubit) interacting with a massless quantum field
$\phi$ coupled to such a hotspot. Our treatment differs from traditional
treatments of Unruh-DeWitt detectors by using Open-EFT tools to reliably
calculate the qubit's late-time behaviour. We use these tools to determine the
efficiency with which the qubit thermalizes as a function of its proximity to
the hotspot. We identify a Markovian regime in which thermalization does occur,
though only for qubits closer to the hotspot than a characteristic distance
scale set by the $\phi$-hotspot coupling. We compute the thermalization time,
and find that it varies inversely with the $\phi$-qubit coupling strength in
the standard way. | On subdivision invariant actions for random surfaces: We consider a subdivision invariant action for dynamically triangulated
random surfaces that was recently proposed (R.V. Ambartzumian et. al., Phys.
Lett. B 275 (1992) 99) and show that it is unphysical: The grand canonical
partition function is infinite for all values of the coupling constants. We
conjecture that adding the area action to the action of Ambartzumian et. al.
leads to a well-behaved theory. |
tt* Geometry in 3 and 4 Dimensions: We consider the vacuum geometry of supersymmetric theories with 4
supercharges, on a flat toroidal geometry. The 2 dimensional vacuum geometry is
known to be captured by the $tt^*$ geometry. In the case of 3 dimensions, the
parameter space is $(T^{2}\times {\mathbb R})^N$ and the vacuum geometry turns
out to be a solution to a generalization of monopole equations in $3N$
dimensions where the relevant topological ring is that of line operators. We
compute the generalization of the 2d cigar amplitudes, which lead to $S^2\times
S^1$ or $S^3$ partition functions which are distinct from the supersymmetric
partition functions on these spaces, but reduce to them in a certain limit. We
show the sense in which these amplitudes generalize the structure of 3d
Chern-Simons theories and 2d RCFT's. In the case of 4 dimensions the parameter
space is of the form $(T^3\times {\mathbb R})^M\times T^{3N}$, and the vacuum
geometry is a solution to a mixture of generalized monopole equations and
generalized instanton equations (known as hyper-holomorphic connections). In
this case the topological rings are associated to surface operators. We discuss
the physical meaning of the generalized Nahm transforms which act on all of
these geometries. | Chaos in CFT dual to rotating BTZ: We compute out-of-time-order correlators (OTOCs) in two-dimensional
holographic conformal field theories (CFTs) with different left- and
right-moving temperatures. Depending on whether the CFT lives on a spatial line
or circle, the dual bulk geometry is a boosted BTZ black brane or a rotating
BTZ black hole. In the case when the spatial direction is non-compact, we
generalise a computation of Roberts and Stanford and show that to reproduce the
correct bulk answer a maximal channel contribution needs to be selected when
using the identity block approximation. We use the correspondence between
global conformal blocks and geodesic Witten diagrams to extend our results to
CFTs on a spatial circle.
In arXiv:1908.03574 it was shown that the OTOC for a rotating BTZ black hole
exhibits a periodic modulation about an average exponential decay with Lyapunov
exponent $2\pi/\beta$. In the extremal limit where the black hole is maximally
rotating, it was shown in arXiv:2009.08518 that the OTOC exhibits an average
cubic growth, on which is superposed a sawtooth pattern which has small periods
of Lyapunov growth due to the non-zero temperature of left-movers in the dual
CFT. Our computations explain these results from a dual CFT perspective. |
Laughlin type wave function for two-dimensional anyon fields in a
KMS-state: The correlation functions of two-dimensional anyon fields in a KMS-state are
studied. For T=0 the $n$-particle wave functions of noncanonical fermions of
level $\alpha$, $\alpha$ odd, are shown to be of Laughlin type of order
$\alpha$. For $T>0$ they are given by a simple finite-temperature
generalization of Laughlin's wave function. This relates the first and second
quantized pictures of the fractional quantum Hall effect. | Theory of Cosmological Perturbations with Cuscuton: This paper presents the first derivation of the quadratic action for
curvature perturbations, $\zeta$, within the framework of cuscuton gravity. We
study the scalar cosmological perturbations sourced by a canonical single
scalar field in the presence of cuscuton field. We identify $\zeta$ as comoving
curvature with respect to the source field and we show that it retains its
conservation characteristic on super horizon scales. The result provides an
explicit proof that cuscuton modification of gravity around
Friedmann-Lemaitre-Robertson-Walker (FLRW) metric is ghost free. We also
investigate the potential development of other instabilities in cuscuton
models. We find that in a large class of these models, there is no generic
instability problem. However, depending on the details of slow-roll parameters,
specific models may display gradient instabilities. |
The Amplituhedron from Momentum Twistor Diagrams: We propose a new diagrammatic formulation of the all-loop scattering
amplitudes/Wilson loops in planar N=4 SYM, dubbed the "momentum-twistor
diagrams". These are on-shell-diagrams obtained by gluing trivalent black and
white vertices defined in momentum twistor space, which, in the reduced diagram
case, are known to be related to diagrams in the original twistor space. The
new diagrams are manifestly Yangian invariant, and they naturally represent
factorization and forward-limit contributions in the all-loop BCFW recursion
relations in momentum twistor space, in a fashion that is completely different
from those in momentum space. We show how to construct and evaluate
momentum-twistor diagrams, and how to use them to obtain tree-level amplitudes
and loop-level integrands; in particular for the latter we identify an isolated
bubble-structure for each loop variable, arising from a forward limit, or
entangled removal of particles. From a given diagram one can directly read off
the C, D matrices via a generalized "boundary measurement"; this in turn
determines a cell in the amplituhedron associated with the amplitude, and our
diagrammatic representations of the amplitude can provide triangulations of the
amplituhedron with generally very intricate geometries. To demonstrate the
computational power of the formalism, we give explicit results for general
two-loop integrands, and the cells of the complete amplituhedron for two-loop
MHV amplitudes. | A Lagrangian Formulation of 2-Dimensional Topological Gravity and
Čech-De-Rham Cohomology: We present a very simplified analysis of how one can overcome the Gribov
problem in a non-abelian gauge theory. Our formulae, albeit quite simplified,
show that possible breakdowns of the Slavnov-Taylor identity could in principle
come from singularities in space of gauge orbits. To test these ideas we
exhibit the calculation of a very simple correlation function of 2-dimensional
topological gravity and we show how in this model the singularities of the
moduli space induce a breakdown of the Slavnov-Taylor identity. We comment on
the technical relevance of the possibility of including the singularities into
a finite number of cells of the moduli space. |
The planar limit of integrated 4-point functions: We compute the planar limit, as all-order power series in the 't Hooft
coupling, of various integrated 4-point functions of chiral primary operators
of ${\cal N}=4$ SU(N) super Yang-Mills, and of moment map operators of ${\cal
N}=2$ SU(N) SQCD. We do so by computing the planar free energy on $S^4$ of the
respective massive deformations of these theories, and then taking advantage of
the exact relation between these free energies and the integrated 4-point
functions. | Stringy Unification of Type IIA and IIB Supergravities under N=2 D=10
Supersymmetric Double Field Theory: To the full order in fermions, we construct D=10 type II supersymmetric
double field theory. We spell the precise N=2 supersymmetry transformation
rules as for 32 supercharges. The constructed action unifies type IIA and IIB
supergravities in a manifestly covariant manner with respect to O(10,10)
T-duality and a pair of local Lorentz groups, or Spin(1,9) \times Spin(9,1),
besides the usual general covariance of supergravities or the generalized
diffeomorphism. While the theory is unique, the solutions are twofold. Type IIA
and IIB supergravities are identified as two different types of solutions
rather than two different theories. |
Giant Leaps and Minimal Branes in Multi-Dimensional Flux Landscapes: There is a standard story about decay in multi-dimensional flux landscapes:
that from any state, the fastest decay is to take a small step, discharging one
flux unit at a time; that fluxes with the same coupling constant are
interchangeable; and that states with N units of a given flux have the same
decay rate as those with -N. We show that this standard story is false. The
fastest decay is a giant leap that discharges many different fluxes in unison;
this decay is mediated by a 'minimal' brane that wraps the internal manifold
and exhibits behavior not visible in the effective theory. We discuss the
implications for the cosmological constant. | 4-dimensional dilaton black holes with cosmological constant: Static and spherically symmetric black hole solutions with non-zero
cosmological constant are investigated. A formal power series solution is
found. It is proved that the number of regular horizons is less than or equal
to 2 for positive cosmological constant and is less than or equal to 1 for
negative cosmological constant. This shows a striking contrast to the fact that
the Reissner-Nordstr{\o}m-de Sitter black hole with positive cosmological
horizon has 3 regular horizons. |
New Directions in Non-Relativistic and Relativistic Rotational and
Multipole Kinematics for N-Body and Continuous Systems: In non-relativistic mechanics the center of mass of an isolated system is
easily separated out from the relative variables. For a N-body system these
latter are usually described by a set of Jacobi normal coordinates, based on
the clustering of the centers of mass of sub-clusters. The Jacobi variables are
then the starting point for separating {\it orientational} variables, connected
with the angular momentum constants of motion, from {\it shape} (or {\it
vibrational}) variables. Jacobi variables, however, cannot be extended to
special relativity. We show by group-theoretical methods that two new sets of
relative variables can be defined in terms of a {\it clustering of the angular
momenta of sub-clusters} and directly related to the so-called {\it dynamical
body frames} and {\it canonical spin bases}. The underlying group-theoretical
structure allows a direct extension of such notions from a non-relativistic to
a special- relativistic context if one exploits the {\it rest-frame instant
form of dynamics}. The various known definitions of relativistic center of mass
are recovered. The separation of suitable relative variables from the so-called
{\it canonical internal} center of mass leads to the correct kinematical
framework for the relativistic theory of the orbits for a N-body system with
action -at-a-distance interactions. The rest-frame instant form is also shown
to be the correct kinematical framework for introducing the Dixon multi-poles
for closed and open N-body systems, as well as for continuous systems,
exemplified here by the configurations of the Klein-Gordon field that are
compatible with the previous notions of center of mass. | A 3d-3d appetizer: We test the 3d-3d correspondence for theories that are labelled by Lens
spaces. We find a full agreement between the index of the 3d ${\cal N}=2$ "Lens
space theory" $T[L(p,1)]$ and the partition function of complex Chern-Simons
theory on $L(p,1)$. In particular, for $p=1$, we show how the familiar $S^3$
partition function of Chern-Simons theory arises from the index of a free
theory. For large $p$, we find that the index of $T[L(p,1)]$ becomes a constant
independent of $p$. In addition, we study $T[L(p,1)]$ on the squashed
three-sphere $S^3_b$. This enables us to see clearly, at the level of partition
function, to what extent $G_\mathbb{C}$ complex Chern-Simons theory can be
thought of as two copies of Chern-Simons theory with compact gauge group $G$. |
Unitary Matrix Models with a topological term and discrete time Toda
equation: We study the full unitary matrix models. Introducing a new term $l log U$, l
plays the role of the discrete time. On the other hand, the full unitary matrix
model contains a topological term. In the continuous limit it gives rise to a
phase transition at $\theta=\pi$. The ground state is characterize by the
discrete time l. The discrete time l plays like the instanton number. | Dynamically flavored description of holographic QCD in the presence of a
magnetic field: We construct the gravitational solution of the Witten-Sakai-Sugimoto model by
introducing a magnetic field on the flavor brane. With taking into account
their backreaction, we re-solve the type IIA supergravity in the presence of
the magnetic field. Our calculation shows the gravitational solutions are
magnetic-dependent and analytic both in the bubble (confined) and black brane
(deconfined) case. We study the dual field theory at the leading order in the
ratio of the number of flavors and colors, also in the Veneziano limit. Some
physical properties related to the hadronic physics in an external magnetic
field are discussed by using our confined backreaction solution
holographically. We also investigate the thermodynamics and holographic
renormalization of this model in both phases by our solution. Since the
backreaction of the magnetic field is considered in our gravitational solution,
it allows us to study the Hawking-Page transition with flavors and colors of
this model in the presence of the magnetic field. Finally we therefore obtain
the holographic phase diagram with the contributions from the flavors and the
magnetic field. Our holographic phase diagram is in agreement with lattice QCD
result qualitatively, which thus can be interpreted as the inhibition of
confinement or chirally broken symmetry by the magnetic field. |
Why Aren't Black Holes Infinitely Produced?: Unitarity and locality imply a remnant solution to the information problem,
and also imply that Reissner-Nordstrom black holes have infinite numbers of
internal states. Pair production of such black holes is reexamined including
the contribution of these states. It is argued that the rate is proportional to
the thermodynamic quantity Tr e^{-beta H}, where the trace is over the internal
states of a black hole; this is in agreement with estimates from an effective
field theory for black holes. This quantity, and the rate, is apparently
infinite due to the infinite number of states. One obvious out is if the number
of internal states of a black hole is finite. | Skyrmions with massive pions: In the Skyrme model with massless pions, the minimal energy multi-Skyrmions
are shell-like, with the baryon density localized on the edges of a polyhedron
that is approximately spherical and generically of the fullerene-type. In this
paper we show that in the Skyrme model with massive pions these configurations
are unstable for sufficiently large baryon number. Using numerical simulations
of the full nonlinear field theory, we show that these structures collapse to
form qualitatively different stable Skyrmion solutions. These new Skyrmions
have a flat structure and display a clustering phenomenon into lower charge
components, particularly components of baryon numbers three and four. These new
qualitative features of Skyrmions with massive pions are encouraging in
comparison with the expectations based on real nuclei. |
Higher Dimensional Dilaton Black Holes with Cosmological Constant: The metric of a higher-dimensional dilaton black hole in the presence of a
cosmological constant is constructed. It is found that the cosmological
constant is coupled to the dilaton in a non-trivial way. The dilaton potential
with respect to the cosmological constant consists of three Liouville-type
potentials. | On the renormalization of non-polynomial field theories: A class of scalar models with non-polynomial interaction, which naturally
admits an analytical resummation of the series of tadpole diagrams is studied
in perturbation theory. In particular, we focus on a model containing only one
renormalizable coupling that appear as a multiplicative coefficient of the
squared field. A renormalization group analysis of the Green functions of the
model shows that these are only approximated solutions of the flow equations,
with errors proportional to powers of the coupling, therefore smaller in the
region of weak coupling. The final output of the perturbative analysis is that
the renormalized model is non-interacting with finite mass and vanishing
vertices or, in an effective theory limited by an ultraviolet cut-off, the
vertices are suppressed by powers of the inverse cut-off. The relation with
some non-polynomial interactions derived long ago, as solutions of the
linearized functional renormalization group flow equations, is also discussed. |
Black hole radiance, short distances, and TeV gravity: Using a derivation of black hole radiance in terms of two-point functions one
can provide a quantitative estimate of the contribution of short distances to
the spectrum. Thermality is preserved for black holes with $\kappa l_P <<1$.
However, deviations from the Planckian spectrum can be found for mini black
holes in TeV gravity scenarios, even before reaching the Planck phase. | Supersymmetric Rotating Black Holes and Attractors: Five-dimensional stringy rotating black holes are embedded into N=2
supergravity interacting with one vector multiplet. The existence of an
unbroken supersymmetry of the rotating solution is proved directly by solving
the Killing spinor equations. The asymptotic enhancement of supersymmetry near
the horizon in the presence of rotation is established via the calculation of
the super-curvature. The area of the horizon of the rotating supersymmetric
black holes is found to be $\sqrt {Z_{fix}^{3 }- J^2}$, where $Z_{fix}$ is the
extremal value of the central charge in moduli space. |
Proof of universality of electrical conductivity at finite chemical
potential: It was proposed in arXiv:1008.2944 that, for certain gauge theories with
gravity duals, electrical conductivity at finite chemical potential is
universal. Here we provide a general proof that, when matter stress tensor
satisfies a compact constraint, electrical conductivity is universal. We
further elaborate our result with several conformal as well as non-conformal
gauge theories. We also discuss how boundary conductivity and universal
conductivity of stretched horizon are related. | Astrophysics in relative units as the theory of a conformal brane: The latest astrophysical data on the Supernova luminosity--distance --
redshift relations, primordial nucleosynthesis, value of Cosmic Microwave
Background--temperature, and baryon asymmetry are considered as an evidence of
relative measurement standard, field nature of time, and conformal symmetry of
the physical world. We show how these principles of description of the universe
help modern quantum field theory to explain the creation of the universe, time,
and matter from the physical vacuum as a state with the lowest energy. |
Open string modes at brane intersections: We study systematically the open string modes of a general class of BPS
intersections of branes. We work in the approximation in which one of the
branes is considered as a probe embedded in the near-horizon geometry generated
by the other type of branes. We mostly concentrate on the D3-D5 and D3-D3
intersections, which are dual to defect theories with a massive hypermultiplet
confined to the defect. In these cases we are able to obtain analytical
expressions for the fluctuation modes of the probe and to compute the
corresponding mass spectra of the dual operators in closed form. Other BPS
intersections are also studied and their fluctuation modes and spectra are
found numerically. | The effective action of warped M-theory reductions with
higher-derivative terms - Part II: We study the three-dimensional effective action obtained by reducing
eleven-dimensional supergravity with higher-derivative terms on a background
solution including a warp-factor, an eight-dimensional compact manifold, and
fluxes. The dynamical fields are K\"ahler deformations and vectors from the
M-theory three-form. We show that the potential is only induced by fluxes and
the naive contributions obtained from higher-curvature terms on a Calabi-Yau
background vanish once the back-reaction to the full solution is taken into
account. For the resulting three-dimensional action we analyse the K\"ahler
potential and complex coordinates and show compatibility with N=2
supersymmetry. We argue that the higher-order result is also compatible with a
no-scale condition. We find that the complex coordinates should be formulated
as divisor integrals for which a non-trivial interplay between the warp-factor
terms and the higher-curvature terms allow a derivation of the moduli space
metric. This leads us to discuss higher-derivative corrections to the M5-brane
action. |
Deconstructing Noncommutativity with a Giant Fuzzy Moose: We argue that the worldvolume theories of D-branes probing orbifolds with
discrete torsion develop, in the large quiver limit, new non-commutative
directions. This provides an explicit `deconstruction' of a wide class of
noncommutative theories. This also provides insight into the physical meaning
of discrete torsion and its relation to the T-dual B field. We demonstrate that
the strict large quiver limit reproduces the matrix theory construction of
higher-dimensional D-branes, and argue that finite `fuzzy moose' theories
provide novel regularizations of non-commutative theories and explicit string
theory realizations of gauge theories on fuzzy tori. We also comment briefly on
the relation to NCOS, (2,0) and little string theories. | Generalized geometry and nonlinear realization of generalized
diffeomorphism on D-brane effective action: The characterization of the DBI action of a Dp-brane using the generalized
geometry is discussed. It is shown that the DBI action is invariant under the
diffeomorphism and B-transformation of the generalized tangent bundle of the
target space. The symmetry is realized non-linearly on the fluctuation of the
D-brane. |
Chaos in a many-string scattering amplitude: String theory provides a compact integral expression for the tree-level
scattering amplitude of an arbitrary number of light strings. We focus on
amplitudes involving a few tachyons and many photons, with a special choice of
polarizations and kinematics. We pick out a particular pole in the amplitude --
one corresponding to successive photon scatterings, which lead to an
intermediate state with a highly excited string in a definite state. This
provides a physical process which creates a highly excited string. The observed
erratic behavior of the amplitude suggests that this may serve as a simple and
explicit illustration of chaos in many-particle scattering. | Space-filling D3-brane within coset approach: We derive the component on-shell action of the space-filling D3-brane, {\it
i.e.} $N=1$ supersymmetric Born-Infeld action, within the nonlinear realization
approach. The covariant Bianchi identity defining the $N=1$, $d=4$ vector
supermultiplet has been constructed by introducing a new bosonic Goldstone
superfield associated with the generator of the $U(1)$ group, which transforms
to each other the spinor generators of unbroken and spontaneously broken $N=1$,
$d=4$ supersymmetries. The first component of this Goldstone superfield is the
auxiliary field of the vector supermultiplet and, therefore, the Bianchi
identity can be properly defined. The component action of the D3-brane has a
very simple form, being written in terms of derivatives covariant with respect
to spontaneously broken supersymmetry - it just mimics its bosonic counterpart. |
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