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Chiral anomalies and Poincare invariance: I study variations of the fermionic determinant for a nonabelian Dirac
fermion with external vector and axial vector sources. I consider different
regularizations, leading to different chiral anomalies when the variations are
chiral transformations. For these different regularizations, I then consider
variations associated with Poincare transformations. I find that both Lorentz
and translational invariance are anomalously violated in general, but that they
are respected when the variations of the determinant are regularized to give a
Wess-Zumino consistent anomaly (the Bardeen anomaly). If the variations are
regularized to give a covariant anomaly, then Poincare invariance is not
respected. Following Manohar in an investigation of Poincare anomalies in a
chiral gauge theory, this gives an alternative way to understand the need for a
consistent regularization of the variations of the fermionic determinant.
|
Quantum (In)Stability of a Brane-World AdS$\bf_5$ Universe at Nonzero
Temperature: We consider the quantum effects of bulk matter (scalars, spinors) in the
Randall-Sundrum AdS$_5$ brane-world at nonzero temperature. The thermodynamic
energy (modulus potential) is evaluated at low and high temperatures. This
potential has an extremum which could be a minimum in some cases (for example,
for a single fermion). That suggests a new dynamical mechanism to stabilize the
thermal AdS$_5$ brane-world. It is shown that the brane separation required to
solve the hierarchy scale problem may occur at a quite low temperature. A
natural generalization in terms of the AdS/CFT correspondence (through the
supergravity thermal contribution) is also possible.
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Scrambling in nearly thermalized states at large central charge: We study $2d$ conformal field theory (CFT) at large central charge $c$ and
finite temperature $T$ with heavy operators inserted at spatial infinity. The
heavy operators produce a nearly thermalized steady state at an effective
temperature $T_{\rm eff}\leq T$. Under some assumptions, we find an effective
Schwarzian-like description of these states and, when they exist, their gravity
duals. We use this description to compute the Lyapunov exponents for light
operators to be $2\pi T_{\rm eff}$, so that scrambling is suppressed by the
heavy insertions.
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The LHC String Hunter's Companion: The mass scale of fundamental strings can be as low as few TeV/c^2 provided
that spacetime extends into large extra dimensions. We discuss the
phenomenological aspects of weakly coupled low mass string theory related to
experimental searches for physics beyond the Standard Model at the Large Hadron
Collider (LHC). We consider the extensions of the Standard Model based on open
strings ending on D-branes, with gauge bosons due to strings attached to stacks
of D-branes and chiral matter due to strings stretching between intersecting
D-branes. We focus on the model-independent, universal features of low mass
string theory. We compute, collect and tabulate the full-fledged string
amplitudes describing all 2->2 parton scattering subprocesses at the leading
order of string perturbation theory. We cast our results in a form suitable for
the implementation of stringy partonic cross sections in the LHC data analysis.
The amplitudes involving four gluons as well as those with two gluons plus two
quarks do not depend on the compactification details and are completely
model-independent. They exhibit resonant behavior at the parton center of mass
energies equal to the masses of Regge resonances. The existence of these
resonances is the primary signal of string physics and should be easy to
detect. On the other hand, the four-fermion processes like quark-antiquark
scattering include also the exchanges of heavy Kaluza-Klein and winding states,
whose details depend on the form of internal geometry. They could be used as
``precision tests'' in order to distinguish between various compactification
scenarios.
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Generalized Quantum Dynamics with Arrow of Time: It is shown, that quantum theory with complex evolutionary time parameter and
non-Hermitian Hamiltonian structure can be used for natural unification of
quantum and thermodynamic principles. The theory is postulated as analytical in
respect to the parameter of evolution, which real part is identified with the
`usual' physical time, whereas the imaginary one is understood as proportional
to the inverse absolute temperature. Also, the Hermitian part of the
Hamiltonian is put equal to conventional operator of energy. It is shown, that
the anti-Hermitian Hamiltonian part, which is taken as commuting with the
energy operator, is constructed from parameters of decay of the system. It is
established, that quantum dynamics, predicted by this theory, is integrable in
the same sense as the corresponding non-modified one, and that it possesses a
well defined arrow of time in isothermal and adiabatic regimes of the
evolution. It is proved, that average value of the decay operator decreases
monotonously (as the function of the physical time) in these important
thermodynamical regimes for the arbitrary initial data taken. We discuss
possible application of the general formalism developed to construction of
time-irreversible modification of a string theory.
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Supersymmetric 4D Rotating Black Holes from 5D Black Rings: We present supersymmetric solutions describing black holes with non-vanishing
angular momentum in four dimensional asymptotically flat space. The solutions
are obtained by Kaluza-Klein reduction of five-dimensional supersymmetric black
rings wrapped on the fiber of a Taub-NUT space. We show that in the
four-dimensional description the singularity of the nut can be hidden behind a
regular black hole event horizon and thereby obtain an explicit example of a
non-static multi-black hole solution in asymptotically flat four dimensions.
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On-shell Recursion in String Theory: We prove that all open string theory disc amplitudes in a flat background
obey Britto-Cachazo-Feng-Witten (BCFW) on-shell recursion relations, up to a
possible reality condition on a kinematic invariant. Arguments that the same
holds for tree level closed string amplitudes are given as well. Non-adjacent
BCFW-shifts are related to adjacent shifts through monodromy relations for
which we provide a novel CFT based derivation. All possible recursion relations
are related by old-fashioned string duality. The field theory limit of the
analysis for amplitudes involving gluons is explicitly shown to be smooth for
both the bosonic string as well as the superstring. In addition to a proof a
less rigorous but more powerful argument based on the underlying CFT is
presented which suggests that the technique may extend to a much more general
setting in string theory. This is illustrated by a discussion of the open
string in a constant B-field background and the closed string on the level of
the sphere.
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On Diff(S^1) Covariantization Of Pseudodifferential Operator: A study of diff($S^1$) covariant properties of pseudodifferential operator of
integer degree is presented. First, it is shown that the action of diff($S^1$)
defines a hamiltonian flow defined by the second Gelfand-Dickey bracket if and
only if the pseudodifferential operator transforms covariantly. Secondly, the
covariant form of a pseudodifferential operator of degree n not equal to 0, 1,
-1 is constructed by exploiting the inverse of covariant derivative. This, in
particular, implies the existence of primary basis for W_{KP}^{(n)} (n not
equal to 0, 1, -1).
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From Spinning Conformal Blocks to Matrix Calogero-Sutherland Models: In this paper we develop further the relation between conformal four-point
blocks involving external spinning fields and Calogero-Sutherland quantum
mechanics with matrix-valued potentials. To this end, the analysis of
\cite{Schomerus:2016epl} is extended to arbitrary dimensions and to the case of
boundary two-point functions. In particular, we construct the potential for any
set of external tensor fields. Some of the resulting Schr\"{o}dinger equations
are mapped explicitly to the known Casimir equations for 4-dimensional seed
conformal blocks. Our approach furnishes solutions of Casimir equations for
external fields of arbitrary spin and dimension in terms of functions on the
conformal group. This allows us to reinterpret standard operations on conformal
blocks in terms of group-theoretic objects. In particular, we shall discuss the
relation between the construction of spinning blocks in any dimension through
differential operators acting on seed blocks and the action of left/right
invariant vector fields on the conformal group.
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High-speed Contraction of Transverse Rotations to Gauge Transformations: The Inonu-Wigner contraction is applied to special relativity and the little
groups of the Lorentz group. If the O(3) symmetry group for massive particle is
boosted to an infinite-momentum frame, it becomes contracted to a combination
of the cylindrical group and the two-dimensional Euclidean group. The Euclidean
component becomes the Lorentz condition applicable to the electromagnetic
four-potential, and the cylindrical component leads to the helicity and gauge
degrees of freedom. The rotation around the cylindrical axis corresponds to the
helicity, while the translation parallel to the axis on the cylindrical surface
leads to a gauge transformation.
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Deviations from the Area Law for Supersymmetric Black Holes: We review modifications of the Bekenstein-Hawking area law for black hole
entropy in the presence of higher-derivative interactions. In four-dimensional
N=2 compactifications of string theory or M-theory these modifications are
crucial for finding agreement between the macroscopic entropy obtained from
supergravity and the microscopic entropy obtained by counting states in string
or M-theory. Our discussion is based on the effective Wilsonian action, which
in the context of N=2 supersymmetric theories is defined in terms of
holomorphic quantities. At the end we briefly indicate how to incorporate
non-holomorphic corrections.
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Accelerated detectors in Dirac vacuum: the effects of horizon
fluctuations: We consider an Unruh-DeWitt detector interacting with a massless Dirac field.
Assuming that the detector is moving along an hyperbolic trajectory, we modeled
the effects of fluctuations in the event horizon using a Dirac equation with
random coefficients. First, we develop the perturbation theory for the
fermionic field in a random media. Further we evaluate corrections due to the
randomness in the response function associated to different model detectors.
|
Hidden Conformal Symmetry of Warped AdS_3 Black Holes: We show that for a certain low frequency limit the wave equation of a generic
massive scalar field in the background of the spacelike warped AdS_3 black hole
can be written as the Casimir of an SL(2,R) symmetry. Two sets of SL(2,R)
generators are found which uncover the hidden SL(2,R)\times SL(2,R) symmetry of
the solution. This symmetry is only locally defined and is spontaneously broken
to U(1)\times U(1) by a periodic identification of the \phi coordinate. By
using the generator of the identification we read the left and right
temperatures (T_L,T_R) of the proposed dual conformal field theory which are in
complete agreement with the WAdS/CFT conjecture. Moreover, under the above
condition of the scalar wave frequency, absorption cross section of the scalar
field is consistent with the two-point function of the dual CFT.
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SU$(2|1)$ supersymmetric spinning models of chiral superfields: We construct SU$(2|1)$, $d=1$ supersymmetric models based on the coupling of
dynamical and semi-dynamical (spin) multiplets, where the interaction term of
both multiplets is defined on the generalized chiral superspace. The dynamical
multiplet is defined as a chiral multiplet ${\bf (2,4,2)}$, while the
semi-dynamical multiplet is associated with a multiplet ${\bf (4,4,0)}$ of the
mirror type.
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SYM on Quotients of Spheres and Complex Projective Spaces: We introduce a generic procedure to reduce a supersymmetric Yang-Mills (SYM)
theory along the Hopf fiber of squashed $S^{2r-1}$ with $U(1)^r$ isometry, down
to the $\mathbb{CP}^{r-1}$ base. This amounts to fixing a Killing vector $v$
generating a $U(1)\subset U(1)^r$ rotation and dimensionally reducing either
along $v$ or along another direction contained in $U(1)^r$. To perform such
reduction we introduce a $\mathbb{Z}_p$ quotient freely acting along one of the
two fibers. For fixed $p$ the resulting manifolds $S^{2r-1}/\mathbb{Z}_p\equiv
L^{2r-1}(p,\pm 1)$ are a higher dimensional generalization of lens spaces. In
the large $p$ limit the fiber shrinks and effectively we find theories living
on the base manifold. Starting from $\mathcal{N}=2$ SYM on $S^3$ and
$\mathcal{N}=1$ SYM on $S^5$ we compute the perturbative partition functions on
$L^{2r-1}(p,\pm 1)$ and, in the large $p$ limit, on $\mathbb{CP}^{r-1}$,
respectively for $r=2$ and $r=3$. We show how the reductions along the two
inequivalent fibers give rise to two distinct theories on the base. Reducing
along $v$ gives an equivariant version of Donaldson-Witten theory while the
other choice leads to a supersymmetric theory closely related to Pestun's
theory on $S^4$. We use our technique to reproduce known results for $r=2$ and
we provide new results for $r=3$. In particular we show how, at large $p$, the
sum over fluxes on $\mathbb{CP}^2$ arises from a sum over flat connections on
$L^{5}(p,\pm 1)$. Finally, for $r=3$, we also comment on the factorization of
perturbative partition functions on non simply connected manifolds.
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Branches of the Black Hole Wave Function Need Not Contain Firewalls: We discuss the branching structure of the quantum-gravitational wave function
that describes the evaporation of a black hole. A global wave function which
initially describes a classical Schwarzschild geometry is continually decohered
into distinct semiclassical branches by the emission of Hawking radiation. The
laws of quantum mechanics dictate that the wave function evolves unitarily, but
this unitary evolution is only manifest when considering the global description
of the wave function; it is not implemented by time evolution on a single
semiclassical branch. Conversely, geometric notions like the position or
smoothness of a horizon only make sense on the level of individual branches. We
consider the implications of this picture for probes of black holes by
classical observers in definite geometries, like those involved in the AMPS
construction. We argue that individual branches can describe semiclassical
geometries free of firewalls, even as the global wave function evolves
unitarily. We show that the pointer states of infalling detectors that are
robust under Hamiltonian evolution are distinct from, and incompatible with,
those of exterior detectors stationary with respect to the black hole horizon,
in the sense that the pointer bases are related to each other via nontrivial
transformations that mix the system, apparatus, and environment. This result
describes a Hilbert-space version of black hole complementarity.
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${\cal N}=4$ supersymmetric Yang-Mills thermodynamics from effective
field theory: The free energy density of ${\cal N}=4$ supersymmetric Yang-Mills theory in
four space-time dimensions is derived through second order in the 't Hooft
coupling $\lambda$ at finite temperature using effective-field theory methods.
The contributions to the free energy density at this order come from the hard
scale $T$ and the soft scale $\sqrt{\lambda} T$. The effects of the scale $T$
are encoded in the coefficients of an effective three-dimensional field theory
that is obtained by dimensional reduction at finite temperature. The effects of
the electric scale $\sqrt{\lambda} T$ are taken into account by perturbative
calculations in the effective theory.
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Clean Time-Dependent String Backgrounds from Bubble Baths: We consider the set of controlled time-dependent backgrounds of general
relativity and string theory describing ``bubbles of nothing'', obtained via
double analytic continuation of black hole solutions. We analyze their quantum
stability, uncover some novel features of their dynamics, identify their causal
structure and observables, and compute their particle production spectrum. We
present a general relation between squeezed states, such as those arising in
cosmological particle creation, and nonlocal theories on the string worldsheet.
The bubble backgrounds have various aspects in common with de Sitter space,
Rindler space, and moving mirror systems, but constitute controlled solutions
of general relativity and string theory with no external forces. They provide a
useful theoretical laboratory for studying issues of observables in systems
with cosmological horizons, particle creation, and time-dependent string
perturbation theory.
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Dynamics of Antimembranes in the Maximally Supersymmetric
Eleven-Dimensional pp Wave: We study a spherical antimembrane in the eleven dimensional pp wave. In this
background, a single antimembrane breaks all the supersymmetries because its
dipole is misaligned with the background flux. Using the BMN matrix theory we
compute the one-loop potential for the antimembrane. Then we put the
antimembrane in the field produced by a source spherical membrane and compute
the velocity-dependent part of the interaction between them on both the
supergravity side and the BMN matrix theory side. Despite the aforementioned
nonsupersymmetry of the antimembrane, it is found that the results on the two
sides completely agree.
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Anisotropic Power-law Inflation: We study an inflationary scenario in supergravity model with a gauge kinetic
function. We find exact anisotropic power-law inflationary solutions when both
the potential function for an inflaton and the gauge kinetic function are
exponential type. The dynamical system analysis tells us that the anisotropic
power-law inflation is an attractor for a large parameter region.
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On the Time Dependence of Adiabatic Particle Number: We consider quantum field theoretic systems subject to a time-dependent
perturbation, and discuss the question of defining a time dependent particle
number not just at asymptotic early and late times, but also during the
perturbation. Naively, this is not a well-defined notion for such a
non-equilibrium process, as the particle number at intermediate times depends
on a basis choice of reference states with respect to which particles and
anti-particles are defined, even though the final late-time particle number is
independent of this basis choice. The basis choice is associated with a
particular truncation of the adiabatic expansion. The adiabatic expansion is
divergent, and we show that if this divergent expansion is truncated at its
optimal order, a universal time dependence is obtained, confirming a general
result of Dingle and Berry. This optimally truncated particle number provides a
clear picture of quantum interference effects for perturbations with
non-trivial temporal sub-structure. We illustrate these results using several
equivalent definitions of adiabatic particle number: the Bogoliubov, Riccati,
Spectral Function and Schrodinger picture approaches. In each approach, the
particle number may be expressed in terms of the tiny deviations between the
exact and adiabatic solutions of the Ermakov-Milne equation for the associated
time-dependent oscillators.
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Physical Resurgent Extrapolation: Expansions of physical functions are controlled by their singularities, which
have special structure because they themselves are physical, corresponding to
instantons, caustics or saddle configurations. Resurgent asymptotics formalizes
this idea mathematically, and leads to significantly more powerful
extrapolation methods to extract physical information from a finite number of
terms of an expansion, including precise decoding of non-perturbative effects.
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The RN/CFT Correspondence: Recently it has been shown in 0901.0931 [hep-th] that the approach to
extremality for the non-extremal Reissner-Nordstrom black hole is not
continuous. The non-extremal RN black hole splits into two spacetimes at the
extremality: an extremal black hole and a disconnected $AdS_2\times S^2$ space
which has been called the "compactification solution". As a possible resolution
for understanding the entropy of extremal RN black hole, it has been speculated
that the entropy of the non-extremal black hole may be carried by the latter
solution. By uplifting the four dimensional "compactification solution" with
electric charge $Q_e$ to a five dimensional solution, we show that this
solution is dual to a CFT with central charge $c=6Q_e^3$. The Cardy formula
then shows that the microscopic entropy of the CFT is the same as the
macroscopic entropy of the "compactification solution".
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Goldstone Superfield Actions for Partially Broken AdS5 Supersymmetry: We explicitly construct N=1 worldvolume supersymmetric minimal off-shell
Goldstone superfield actions for two options of 1/2 partial spontaneous
breaking of AdS5 supersymmetry SU(2,2|1) corresponding to its nonlinear
realizations in the supercosets with the AdS5 and AdS5 X S1 bosonic parts. The
relevant Goldstone supermultiplets are comprised, respectively, by improved
tensor and chiral N=1 superfields. The second action is obtained from the first
one by duality transformation. In the bosonic sectors they yield static-gauge
Nambu-Goto actions for L3-brane on AdS5 and scalar 3-brane on AdS5 X S1.
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Effective electromagnetic actions for Lorentz violating theories
exhibiting the axial anomaly: The CPT odd contribution to the effective electromagnetic action deriving
from the vacuum polarization tensor in a large class of fermionic systems
exhibiting Lorentz invariance violation (LIV) is calculated using thermal field
theory methods, focusing upon corrections depending on the chemical potential.
The systems considered exhibit the axial anomaly and their effective actions
are described by axion electrodynamics whereby all the LIV parameters enter in
the coupling $\Theta(x)$ to the unmodified Pontryagin density. A preliminary
application to type-I tilted Weyl semimetals is briefly presented.
|
Strong Coupling Quantum Gravity and Physics beyond the Planck Scale: We propose a renormalization prescription for the Wheeler-DeWitt equation of
(3+1)-dimensional Einstein gravity and also propose a strong coupling expansion
as an approximation scheme to probe quantum geometry at length scales much
smaller than the Planck length. We solve the Wheeler-DeWitt equation to the
second order in the expansion in a class of local solutions and discuss
problems arising in our approach.
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D-branes, Quivers, and ALE Instantons: Effective field theories in type I and II superstring theories for D-branes
located at points in the orbifold C^2/Z_n are supersymmetric gauge theories
whose field content is conveniently summarized by a `quiver diagram,' and whose
Lagrangian includes non-metric couplings to the orbifold moduli: in particular,
twisted sector moduli couple as Fayet-Iliopoulos terms in the gauge theory.
These theories describe D-branes on resolved ALE spaces. Their spaces of vacua
are moduli spaces of smooth ALE metrics and Yang-Mills instantons, whose
metrics are explicitly computable. For U(N) instantons, the construction
exactly reproduces results of Kronheimer and Nakajima.
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A Deformation Theory of Self-Dual Einstein Spaces: The self-dual Einstein equations on a compact Riemannian 4-manifold can be
expressed as a quadratic condition on the curvature of an $SU(2)$ (spin)
connection which is a covariant generalization of the self-dual Yang-Mills
equations. Local properties of the moduli space of self-dual Einstein
connections are described in the context of an elliptic complex which arises in
the linearization of the quadratic equations on the $SU(2)$ curvature. In
particular, it is shown that the moduli space is discrete when the cosmological
constant is positive; when the cosmological constant is negative the moduli
space can be a manifold the dimension of which is controlled by the
Atiyah-Singer index theorem.
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BC_n Ruijsenaars-Schneider models: R-Matrix structure and hamiltonians: This paper is replaced and superseded by nlin.SI/0106015 (Title: Structures
in BC_N Ruijsenaars-Schneider models)
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U-duality and Network Configurations of Branes: We explicitly write down the invariant supersymmetry conditions for branes
with generic values of moduli and U-duality charges in various space-time
dimensions $D \leq 10$. We then use these results to obtain new BPS states,
corresponding to network type structure of such branes.
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On Unconstrained SU(2) Gluodynamics with Theta Angle: The Hamiltonian reduction of classical SU(2) Yang-Mills field theory to the
equivalent unconstrained theory of gauge invariant local dynamical variables is
generalized to the case of nonvanishing theta angle. It is shown that for any
theta angle the elimination of the pure gauge degrees of freedom leads to a
corresponding unconstrained nonlocal theory of self-interacting second rank
symmetric tensor fields, and that the obtained classical unconstrained
gluodynamics with different theta angles are canonically equivalent as on the
original constrained level.
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Neutrinos, Axions and Conformal Symmetry: We demonstrate that radiative breaking of conformal symmetry (and
simultaneously electroweak symmetry) in the Standard Model with right-chiral
neutrinos and a minimally enlarged scalar sector induces spontaneous breaking
of lepton number symmetry, which naturally gives rise to an axion-like particle
with some unusual features. The couplings of this `axion' to Standard Model
particles, in particular photons and gluons, are entirely determined (and
computable) via the conformal anomaly, and their smallness turns out to be
directly related to the smallness of the masses of light neutrinos.
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10D Massive Type IIA Supergravities as the uplift of Parabolic M2-brane
Torus bundles: We remark that the two 10D massive deformations of the $N=2$ maximal type IIA
supergravity (Romans and HLW supergravity) are associated to the low energy
limit of the uplift to 10D of M2-brane torus bundles with parabolic monodromy
linearly and non-linearly realized respectively. Romans supergravity
corresponds to M2-brane compactified on a twice-punctured torus bundle.
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Duality between Noncommutative Yang-Mills-Chern-Simons and Non-Abelian
Self-Dual Models: By introducing an appropriate parent action and considering a perturbative
approach, we establish, up to fourth order terms in the field and for the full
range of the coupling constant, the equivalence between the noncommutative
Yang-Mills-Chern-Simons theory and the noncommutative, non-Abelian Self-Dual
model. In doing this, we consider two different approaches by using both the
Moyal star-product and the Seiberg-Witten map.
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One-loop effective action for Einstein gravity in special background
gauge: The one-loop effective action for Einstein gravity in a special one-parameter
background gauge is calculated up to first order in a gauge parameter. It is
shown that the effective action does not depend upon the gauge parameter on
shell.
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Embedded Defects: We give a prescription for embedding classical solutions and, in particular,
topological defects in field theories which are invariant under symmetry groups
that are not necessarily simple. After providing examples of embedded defects
in field theories based on simple groups, we consider the electroweak model and
show that it contains the $Z$ string and a one parameter family of strings
called the $W(\alpha )$ string. It is argued that, although the members of this
family are gauge equivalent when considered in isolation, each member should be
considered distinct when multi-string solutions are considered. We then turn to
the issue of stability of embedded defects and demonstrate the instability of a
large class of such solutions in the absence of bound states or condensates.
The $Z$ string is shown to be unstable when the Weinberg angle ($\theta_w$) is
$\pi /4$ for all values of the Higgs mass. The $W$ strings are also shown to be
unstable for a large range of parameters. Embedded monopoles suffer from the
Brandt-Neri-Coleman instability. A simple physical understanding of this
instability is provided in terms of the phenomenon of W-condensation. Finally,
we connect the electroweak string solutions to the sphaleron: ``twisted'' loops
of W string and finite segments of W and Z strings collapse into the sphaleron
configuration, at least, for small values of $\theta_w$.
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From $r$-Spin Intersection Numbers to Hodge Integrals: Generalized Kontsevich Matrix Model (GKMM) with a certain given potential is
the partition function of $r$-spin intersection numbers. We represent this GKMM
in terms of fermions and expand it in terms of the Schur polynomials by
boson-fermion correspondence, and link it with a Hurwitz partition function and
a Hodge partition by operators in a $\widehat{GL}(\infty)$ group. Then, from a
$W_{1+\infty}$ constraint of the partition function of $r$-spin intersection
numbers, we get a $W_{1+\infty}$ constraint for the Hodge partition function.
The $W_{1+\infty}$ constraint completely determines the Schur polynomials
expansion of the Hodge partition function.
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A Causal Alternative to Feynman's Propagator: The Feynman propagator used in the conventional in-out formalism in quantum
field theory is not a causal propagator as wave packets are propagated
virtually instantaneously outside the causal region of the initial state. We
formulate a causal in-out formalism in quantum field theory by making use of
the Wheeler propagator, the time ordered commutator propagator, which is
manifestly causal. Only free scalar field theories and their first quantization
are considered. We identify the real Klein Gordon field itself as the wave
function of a neutral spinless relativistic particle. Furthermore, we derive a
probability density for our relativistic wave packet using the inner product
between states that live on a suitably defined Hilbert space of real quantum
fields. We show that the time evolution of our probability density is governed
by the Wheeler propagator, such that it behaves causally too.
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BMS Algebra, Double Soft Theorems, and All That: The Lie algebra generated by supertranslation and superrotation vector fields
at null infinity, known as the extended BMS (eBMS) algebra is expected to be a
symmetry algebra of the quantum gravity S matrix. However, the algebra of
commutators of the quantized eBMS charges has been a thorny issue in the
literature. On the one hand, recent developments in celestial holography point
towards a symmetry algebra which is a closed Lie algebra with no central
extension or anomaly, and on the other hand, work of Distler, Flauger and Horn
has shown that when these charges are quantized at null infinity, the
commutator of a supertranslation and a superrotation charge does not close into
a supertranslation but gets deformed by a 2 cocycle term, which is consistent
with the original proposal of Barnich and Troessaert.
In this paper, we revisit this issue in light of recent developments in the
classical understanding of superrotation charges. We show that, for extended
BMS symmetries, a phase space at null infinity is an extension of hitherto
considered phase spaces which also includes a mode associated to the spin
memory and its conjugate partner. We also show that for holomorphic vector
fields on the celestial plane, quantization of the eBMS charges in the new
phase space leads to an algebra which closes without a 2 cocycle. The
degenerate vacua are labelled by the soft news and a Schwarzian mode which
corresponds to deformations of the celestial metric by superrotations. The
closed eBMS quantum algebra may also lead to a convergence between two
manifestations of asymptotic symmetries, one via asymptotic quantization at
null infinity and the other through celestial holography.
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Sine-Gordon Theory with Higher Spin $N=2$ Supersymmetry and the Massless
Limit: The Sine-Gordon theory at $\frac{\beta^{2}}{8\pi} = \frac{2}{(2n+3)},\; n=
1,2,3 \cdots $ has a higher spin generalization of the $N=2$ supersymmetry with
the central terms which arises from the affine quantum group $U_{q}( \hat{s
\ell} (2))$. Observing that the algebraic determination of $S$ matrices $(
\approx {\rm quantum~ integrability })$ requires the saturation of the
generalized Bogomolny bound, we construct a variant of the Sine-Gordon theory
at this value of the coupling in the framework of $S$ matrix theory. The
spectrum consists of a doublet of fractionally charged solitons as well as that
of anti-solitons in addition to the ordinary breathers. The construction
demonstrates the existence of the theory other than the one by the truncation
to the breathers considered by Smirnov. The allowed values for the fractional
part of the fermion number is also determined. The central charge in the
massless limit is found to be $c= 1$ from the TBA calculation for nondiagonal S
matrices. The attendant $c=1$ conformal field theory is the gaussian model with
${\bf Z_{2}}$ graded chiral algebra at the radius parameter $r= \sqrt{2n+3}$.
In the course of the calculation, we find $4n+2$ zero modes from the
(anti-)soliton distributions.
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Infrared singularities in the null-plane bound-state equation when going
to 1+1 dimensions: In this paper we first consider the null-plane bound-state equation for a $q
\bar q$ pair in 1+3 dimensions and in the lowest-order Tamm-Dancoff
approximation. Light-cone gauge is chosen with a causal prescription for the
gauge pole in the propagator. Then we show that this equation, when
dimensionally reduced to 1+1 dimensions, becomes 't Hooft's bound-state
equation, which is characterized by an $x^+$-instantaneous interaction. The
deep reasons for this coincidence are carefully discussed.
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Alternative approaches to the Casalbuoni-Brink-Schwarz Superparticle: Wigner's method of induced representations is applied to the N=1
super-Poincare group, and by using a state corresponding to the basic vector of
the little group as a Clifford vacuum we show that the spin operator of a
supersymmetric point particle obeys Wigner's constraints. As dynamical
variables for the particle we use canonical coordinates on the symmetry group
manifold. The physical phase space is then constructed using a vielbein
formalism. We find that the Casalbuoni-Brink-Schwarz superparticle appears as a
special case of our general construction. Finally, the theory is reformulated
as a gauge theory where the gauge freedom corresponds to the choice of spin
constraints or, equivalently, the free choice of relativistic center of mass.
In a special case the gauge symmetry reduces to the well known kappa-symmetry.
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Generalized Randall-Sundrum model with a single thick brane: A generalized version of the Randall-Sundrum model-2 with different
cosmological constants on each side of a brane has been discussed. A
possibility of replacing the singular brane by a configuration of a scalar
field has been also considered, the Einstein equations for this setup were
solved and stability of the solution discussed. It has been shown that under
mild assumptions the relation between cosmological constants and the brane
tension obtained in the brane limit does not depend on the particular choice of
the regularizing profile of the scalar field.
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Zero-Branes, Quantum Mechanics and the Cosmological Constant: We analyse some dynamical issues in a modified type IIA supergravity,
recently proposed as an extension of M-theory that admits de Sitter space. In
particular we find that this theory has multiple zero-brane solutions. This
suggests a microscopic quantum mechanical matrix description which yields a
massive deformation of the usual M(atrix) formulation of M-theory and type IIA
string theory.
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Radiation and the classical double copy for color charges: We construct perturbative classical solutions of the Yang-Mills equations
coupled to dynamical point particles carrying color charge. By applying a set
of color to kinematics replacement rules first introduced by Bern, Carrasco and
Johansson (BCJ), these are shown to generate solutions of d-dimensional dilaton
gravity, which we also explicitly construct. Agreement between the gravity
result and the gauge theory double copy implies a correspondence between
non-Abelian particles and gravitating sources with dilaton charge. When the
color sources are highly relativistic, dilaton exchange decouples, and the
solutions we obtain match those of pure gravity. We comment on possible
implications of our findings to the calculation of gravitational waveforms in
astrophysical black hole collisions, directly from computationally simpler
gluon radiation in Yang-Mills theory.
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Quantum Mechanics and the Continuum Limit of an Emergent Geometry: Recent advances in emergent geometry have identified a new class of models
that represent spacetime as the graph obtained as the ground state of
interacting Ising spins. These models have many desirable features, including
stable excitations possessing many of the characteristics of a quantum
particle. We analyze the dynamics of such excitations, including a detailed
treatment of the edge states not previously addressed. Using a minimal
prescription for the interaction of defects we numerically investigate
approximate bounds to the speed of propagation of such a `particle'. We
discover, using numerical simulations, that there may be a Lieb-Robinson bound
to propagation that could point the way to how a causal structure could be
accommodated in this class of emergent geometry models.
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F-term uplifted racetrack inflation: It is shown that two classes of racetrack inflation models, saddle point and
inflection point ones, can be constructed in a fully supersymmetric framework
with the matter field F-term as a source of supersymmetry (SUSY) breaking and
uplifting. Two models of F-term SUSY breaking are considered: the Polonyi model
and the quantum corrected O'Raifeartaigh model. In the former case, both
classes of racetrack inflation models differ significantly from the
corresponding models with non-SUSY uplifting. The main difference is a quite
strong dominance of the inflaton by the matter field. In addition, fine-tuning
of the parameters is relaxed as compared to the original racetrack models. In
the case of the racetrack inflation models coupled to the O'Raifeartaigh model,
the matter field is approximately decoupled from the inflationary dynamics.
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The heat kernel for deformed spheres: We derive the asymptotic expansion of the heat kernel for a Laplace operator
acting on deformed spheres. We calculate the coefficients of the heat kernel
expansion on two- and three-dimensional deformed spheres as functions of
deformation parameters. We find that under some deformation the conformal
anomaly for free scalar fields on $R^4\times \tilde S^2$ and $R^6\times \tilde
S^2$ is canceled.
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The Giant Inflaton: We investigate a new mechanism for realizing slow roll inflation in string
theory, based on the dynamics of p anti-D3 branes in a class of mildly warped
flux compactifications. Attracted to the bottom of a warped conifold throat,
the anti-branes then cluster due to a novel mechanism wherein the background
flux polarizes in an attempt to screen them. Once they are sufficiently close,
the M units of flux cause the anti-branes to expand into a fuzzy NS5-brane,
which for rather generic choices of p/M will unwrap around the geometry,
decaying into D3-branes via a classical process. We find that the effective
potential governing this evolution possesses several epochs that can
potentially support slow-roll inflation, provided the process can be arranged
to take place at a high enough energy scale, of about one or two orders of
magnitude below the Planck energy; this scale, however, lies just outside the
bounds of our approximations.
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Vacuum Polarization of a Charged Massless Scalar Field on Cosmic String
Spacetime in the Presence of a Magnetic Field: In this paper we consider a charged massless scalar quantum field operator in
the spacetime of an idealized cosmic string, i.e., an infinitely long, straight
and static cosmic string, which presents a magnetic field confined in a
cylindrical tube of finite radius. Three distinct situations are taking into
account in this analysis: {\it{i)}} a homogeneous field inside the tube,
{\it{ii)}} a magnetic field proportional to $1/r$ and {\it{iii)}} a cylindrical
shell with $\delta$-function. In these three cases the axis of the infinitely
long tube of radius $R$ coincides with the cosmic string. In order to study the
vacuum polarization effects outside the tube, we explicitly calculate the
Euclidean Green function associated with this system for the three above
situations, considering points in the region outside the tube.
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Geometrical Structures of M-Theory: N=(2,1) heterotic string theory provides clues about hidden structure in
M-theory related to string duality; in effect it geometrizes some aspects of
duality. The program whereby one may deduce this hidden structure is outlined,
together with the results obtained to date. Speculations are made as to the
eventual shape of the theory. Talk presented at Strings '96 (Santa Barbara,
July 20-25, 1996).
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Supersymmetric Generalizations of Matrix Models: In this thesis generalizations of matrix and eigenvalue models involving
supersymmetry are discussed. Following a brief review of the Hermitian one
matrix model, the c=-2 matrix model is considered. Built from a matrix valued
superfield this model displays supersymmetry on the matrix level. We stress the
emergence of a Nicolai-map of this model to a free Hermitian matrix model and
study its diagrammatic expansion in detail. Correlation functions for quartic
potentials on arbitrary genus are computed, reproducing the string
susceptibility of c=-2 Liouville theory in the scaling limit. The results may
be used to perform a counting of supersymmetric graphs.
We then turn to the supereigenvalue model, today's only successful discrete
approach to 2d quantum supergravity. The model is constructed in a
superconformal field theory formulation by imposing the super-Virasoro
constraints. The complete solution of the model is given in the moment
description, allowing the calculation of the free energy and the multi-loop
correlators on arbitrary genus and for general potentials. The solution is
presented in the discrete case and in the double scaling limit. Explicit
results up to genus two are stated.
Finally the supersymmetric generalization of the external field problem is
addressed. We state the discrete super-Miwa transformations of the
supereigenvalue model on the eigenvalue and matrix level. Properties of
external supereigenvalue models are discussed, although the model corresponding
to the ordinary supereigenvalue model could not be identified so far.
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Solving Four Dimensional Field Theories with the Dirichlet Fivebrane: The realization of ${\cal N}=2$ four dimensional super Yang-Mills theories in
terms of a single Dirichlet fivebrane in type IIB string theory is considered.
A classical brane computation reproduces the full quantum low energy effective
action. This result has a simple explanation in terms of mirror symmetry.
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On-Shell Methods for the Two-Loop Dilatation Operator and Finite
Remainders: We compute the two-loop minimal form factors of all operators in the SU(2)
sector of planar N=4 SYM theory via on-shell unitarity methods. From the UV
divergence of this result, we obtain the two-loop dilatation operator in this
sector. Furthermore, we calculate the corresponding finite remainder functions.
Since the operators break the supersymmetry, the remainder functions do not
have the property of uniform transcendentality. However, the leading
transcendentality part turns out to be universal and is identical to the
corresponding BPS expressions. The remainder functions are shown to satisfy
linear relations which can be explained by Ward identities of form factors
following from R-symmetry.
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Mass Gap without Confinement: We revisit a one-parameter family of three-dimensional gauge theories with
known supergravity duals. We show that three infrared behaviors are possible.
For generic values of the parameter, the theories exhibit a mass gap but no
confinement, meaning no linear quark-antiquark potential; for one limiting
value of the parameter the theory flows to an infrared fixed point; and for
another limiting value it exhibits both a mass gap and confinement. Theories
close to these limiting values exhibit quasi-conformal and quasi-confining
dynamics, respectively. Eleven-dimensional supergravity provides a simple,
geometric explanation of these features.
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Exotic instantons in eight dimensions: In this paper, we study the (anti-)self-duality equations $\ast F\wedge F=\pm
F\wedge F$ in the eight-dimensional Euclidean space. Using properties of the
Clifford algebra $Cl_{0,8}(\mathbb{R})$, we find a new solution to these
equations.
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Gauge-invariant fields in the temporal gauge, Coulomb-gauge fields, and
the Gribov ambiguity: We examine the relation between Coulomb-gauge fields and the gauge-invariant
fields constructed in the temporal gauge for two-color QCD by comparing a
variety of properties, including their equal-time commutation rules and those
of their conjugate chromoelectric fields. We also express the temporal-gauge
Hamiltonian in terms of gauge-invariant fields and show that it can be
interpreted as a sum of the Coulomb-gauge Hamiltonian and another part that is
important for determining the equations of motion of temporal-gauge fields, but
that can never affect the time evolution of ``physical'' state vectors. We also
discuss multiplicities of gauge-invariant temporal-gauge fields that belong to
different topological sectors and that, in previous work, were shown to be
based on the same underlying gauge-dependent temporal-gauge fields. We argue
that these multiplicities of gauge-invariant fields are manifestations of the
Gribov ambiguity. We show that the differential equation that bases the
multiplicities of gauge-invariant fields on their underlying gauge-dependent
temporal-gauge fields has nonlinearities identical to those of the ``Gribov''
equation, which demonstrates the non-uniqueness of Coulomb-gauge fields. These
multiplicities of gauge-invariant fields --- and, hence, Gribov copies ---
appear in the temporal gauge, but only with the imposition of Gauss's law and
the implementation of gauge invariance; they do not arise when the theory is
represented in terms of gauge-dependent fields and Gauss's law is left
unimplemented.
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Falling D0-Branes in 2D Superstring Theory: In N=1, 2D superstring theory in the linear dilaton background, there exists
falling D0-branes that are described by time-dependent boundary states. These
falling D0-brane boundary states can be obtained by adapting the FZZT boundary
states of N=2 Super Liouville Field Theory (SLFT) to the case of the N=1, 2D
superstring. In particular, we find that there are four stable, falling
D0-branes (two branes and two anti-branes) in the Type 0A projection and two
unstable ones in the Type 0B projection, leaving us with a puzzle for the
matrix model dual of the theory.
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Twisted Classical Poincaré Algebras: We consider the twisting of Hopf structure for classical enveloping algebra
$U(\hat{g})$, where $\hat{g}$ is the inhomogenous rotations algebra, with
explicite formulae given for $D=4$ Poincar\'{e} algebra $(\hat{g}={\cal P}_4).$
The comultiplications of twisted $U^F({\cal P}_4)$ are obtained by conjugating
primitive classical coproducts by $F\in U(\hat{c})\otimes U(\hat{c}),$ where
$\hat{c}$ denotes any Abelian subalgebra of ${\cal P}_4$, and the universal
$R-$matrices for $U^F({\cal P}_4)$ are triangular. As an example we show that
the quantum deformation of Poincar\'{e} algebra recently proposed by Chaichian
and Demiczev is a twisted classical Poincar\'{e} algebra. The interpretation of
twisted Poincar\'{e} algebra as describing relativistic symmetries with
clustered 2-particle states is proposed.
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Towards Quantum Dielectric Branes: Curvature Corrections in Abelian Beta
Function and Nonabelian Born-Infeld Action: We initiate a programme to compute curvature corrections to the nonabelian BI
action. This is based on the calculation of derivative corrections to the
abelian BI action, describing a maximal brane, to all orders in F. An exact
calculation in F allows us to apply the SW map, reducing the maximal abelian
point of view to a minimal nonabelian point of view (replacing 1/F with [X,X]
at large F), resulting in matrix model equations of motion. We first study
derivative corrections to the abelian BI action and compute the 2-loop beta
function for an open string in a WZW (parallelizable) background. This beta
function is the first step in the process of computing string equations of
motion, which can be later obtained by computing the Weyl anomaly coefficients
or the partition function. The beta function is exact in F and computed to
orders O(H,H^2,H^3) (H=dB and curvature is R ~ H^2) and O(DF,D^2F,D^3F). In
order to carry out this calculation we develop a new regularization method for
2-loop graphs. We then relate perturbative results for abelian and nonabelian
BI actions, by showing how abelian derivative corrections yield nonabelian
commutator corrections, at large F. We begin the construction of a matrix model
describing \a' corrections to Myers' dielectric effect. This construction is
carried out by setting up a perturbative classification of the relevant
nonabelian tensor structures, which can be considerably narrowed down by the
constraint of translation invariance in the action and the possibility for
generic field redefinitions. The final matrix action is not uniquely determined
and depends upon two free parameters. These parameters could be computed via
further calculations in the abelian theory.
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On the Classification of Asymptotic Quasinormal Frequencies for
d-Dimensional Black Holes and Quantum Gravity: We provide a complete classification of asymptotic quasinormal frequencies
for static, spherically symmetric black hole spacetimes in d dimensions. This
includes all possible types of gravitational perturbations (tensor, vector and
scalar type) as described by the Ishibashi-Kodama master equations. The
frequencies for Schwarzschild are dimension independent, while for RN are
dimension dependent (the extremal RN case must be considered separately from
the non-extremal case). For Schwarzschild dS, there is a dimension independent
formula for the frequencies, except in dimension d=5 where the formula is
different. For RN dS there is a dimension dependent formula for the
frequencies, except in dimension d=5 where the formula is different.
Schwarzschild and RN AdS black hole spacetimes are simpler: the formulae for
the frequencies will depend upon a parameter related to the tortoise coordinate
at spatial infinity, and scalar type perturbations in dimension d=5 lead to a
continuous spectrum for the quasinormal frequencies. We also address non-black
hole spacetimes, such as pure dS spacetime--where there are quasinormal modes
only in odd dimensions--and pure AdS spacetime--where again scalar type
perturbations in dimension d=5 lead to a continuous spectrum for the normal
frequencies. Our results match previous numerical calculations with great
accuracy. Asymptotic quasinormal frequencies have also been applied in the
framework of quantum gravity for black holes. Our results show that it is only
in the simple Schwarzschild case which is possible to obtain sensible results
concerning area quantization or loop quantum gravity. In an effort to keep this
paper self-contained we also review earlier results in the literature.
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Solving the 2D SUSY Gross-Neveu-Yukawa Model with Conformal Truncation: We use Lightcone Conformal Truncation to analyze the RG flow of the
two-dimensional supersymmetric Gross-Neveu-Yukawa theory, i.e. the theory of a
real scalar superfield with a $\mathbb{Z}_2$-symmetric cubic superpotential.
The theory depends on a single dimensionless coupling $\bar{g}$, and is
expected to have a critical point at a tuned value $\bar{g}_*$ where it flows
in the IR to the Tricritical Ising Model (TIM); the theory spontaneously breaks
the $\mathbb{Z}_2$ symmetry on one side of this phase transition, and breaks
SUSY on the other side. We calculate the spectrum of energies as a function of
$\bar{g}$ and see the gap close as the critical point is approached, and
numerically read off the critical exponent $\nu$ in TIM. Beyond the critical
point, the gap remains nearly zero, in agreement with the expectation of a
massless Goldstino. We also study spectral functions of local operators on both
sides of the phase transition and compare to analytic predictions where
possible. In particular, we use the Zamolodchikov $C$-function to map the
entire phase diagram of the theory. Crucial to this analysis is the fact that
our truncation is able to preserve supersymmetry sufficiently to avoid any
additional fine tuning.
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Instability of charged massive scalar fields in bound states around
Kerr-Sen black holes: We show the instability of a charged massive scalar field in bound states
around Kerr-Sen black holes. By matching the near and far region solutions of
the radial part in the corresponding Klein-Gordon equation, one can show that
the frequency of bound state scalar fields contains an imaginary component
which gives rise to an amplification factor for the fields. Hence, the unstable
modes for a charged and massive scalar perturbation in Kerr-Sen background can
be shown.
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Quantum black hole entropy and Newton constant renormalization: We discuss the status of the black hole entropy formula $S_{\rm BH} = A_H
/4G$ in low energy effective field theory. The low energy expansion of the
black hole entropy is studied in a non-equilibrium situation: the semiclassical
decay of hot flat space by black hole nucleation. In this context the entropy
can be defined as an enhancement factor in the semiclassical decay rate, which
is dominated by a sphaleron-like saddle point. We find that all perturbative
divergences appearing in Euclidean calculations of the entropy can be
renormalized in low energy couplings. We also discuss some formal aspects of
the relation between the Euclidean and Hamiltonian approaches to the one loop
corrections to black hole entropy and geometric entropy, and we emphasize the
virtues of the use of covariant regularization prescriptions. In fact, the
definition of black hole entropy in terms of decay rates {\it requires} the use
of covariant measures and accordingly, covariant regularizations in path
integrals. Finally, we speculate on the possibility that low energy effective
field theory could be sufficient to understand the microscopic degrees of
freedom underlying black hole entropy. We propose a qualitative physical
picture in which black hole entropy refers to a space of quasi-coherent states
of infalling matter, together with its gravitational field. We stress that this
scenario might provide a low energy explanation of both the black hole entropy
and the information puzzle.
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Absence of Nonlocal Counter-terms in the Gauge Boson Propagator in Axial
-type Gauges: We study the two-point function for the gauge boson in the axial-type gauges.
We use the exact treatment of the axial gauges recently proposed that is
intrinsically compatible with the Lorentz type gauges in the path-integral
formulation and has been arrived at from this connection and which is a
``one-vector'' treatment. We find that in this treatment, we can evaluate the
two-point functions without imposing any additional interpretation on the axial
gauge 1/(n.q)^p-type poles. The calculations are as easy as the other
treatments based on other known prescriptions. Unlike the
``uniform-prescription'' /L-M prescription, we note, here, the absence of any
non-local divergences in the 2-point proper vertex. We correlate our
calculation with that for the Cauchy Principal Value prescription and find from
this comparison that the 2-point proper vertex differs from the CPV calculation
only by finite terms. For simplicity of treatment, the divergences have been
calculated here with n^2>0 and these have a smooth light cone limit.
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Coherent States and Squeezed States, Supercoherent States and
Supersqueezed States: This article reports on a program to obtain and understand coherent states
for general systems. Most recently this has included supersymmetric systems. A
byproduct of this work has been studies of squeezed and supersqueezed states.
To obtain a physical understanding of these systems has always been a primary
goal. In particular, in the work on supersymmetry an attempt to understand the
role of Grassmann numbers in quantum mechanics has been initiated.
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Hydrodynamics in black brane with hyperscaling violation metric
background: In this paper we consider a metric with hyperscaling violation on black brane
background. In this background we calculate the ratio of shear viscosity to
entropy density with hydrodynamics information. The calculation of this
quantity lead us to constraint $\theta$ as $3\leq\theta<4$, and $\theta\leq0$.
In that case we show that the quantity of $\frac{\eta}{s}$ not dependent to
hyperscaling violation parameter $\theta.$ Our results about ratio of shear
viscosity to entropy density in direct of $QCD$ point of view agree with other
works in literature as $1/4\pi$.
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Non-Gaussianities in generalized non-local $R^2$-like inflation: In [1], a most general higher curvature non-local gravity action was derived
that admits a particular $R^2$-like inflationary solution predicting the
spectral index of primordial scalar perturbations $n_s(N)\approx
1-\frac{2}{N}$, where $N$ is the number of e-folds before the end of inflation,
$N\gg 1$, any value of the tensor-to-scalar ratio $r(N)<0.036$ and the tensor
tilt $n_t(N)$ violating the $r= -8n_t$ condition. In this paper, we compute
scalar primordial non-Gaussianities (PNGs) in this theory and effectively
demonstrate that higher curvature non-local terms lead to reduced bispectrum
$f_{\rm NL}\left( k_1,\,k_2,\,k_3 \right)$ mimicking several classes of scalar
field models of inflation known in the literature. We obtain $\vert f_{\rm
NL}\vert \sim O(1-10)$ in the equilateral, orthogonal, and squeezed limits and
the running of these PNGs measured by the quantity $\vert\frac{d\ln f_{\rm
NL}}{d\ln k}\vert\lesssim 1$. Such PNGs are sufficiently large to be measurable
by future CMB and Large Scale Structure observations, thus providing a
possibility to probe the nature of quantum gravity. Furthermore, we demonstrate
that the $R^2$-like inflation in non-local modification of gravity brings
non-trivial predictions which go beyond the current status of effective field
theories (EFTs) of single field, quasi-single field and multiple field
inflation. A distinguishable feature of non-local $R^2$-like inflation compared
to local EFTs is that we can have running of PNGs at least an order of
magnitude higher. In summary, through our generalized non-local $R^2$-like
inflation, we obtain a robust geometric framework of inflation that can explain
any detection of observable quantities related to scalar PNGs.
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New non-local SUSY KdV conservation laws from a recursive gradient
algorithm: A complete proof of the recursive gradient approach is presented. It gives a
construction of all the hierarchy structures of N=1 Super KdV, including the
non-local one. A precise definition of the ring of superfields involved in the
non-local construction is given. In particular, new non-local conserved
quantities of N=1 Super KdV are found.
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ZZ branes from a worldsheet perspective: We show how non-compact space-time (ZZ branes) emerges as a limit of compact
space-time (FZZT branes) for specific ratios between the square of the boundary
cosmological constant and the bulk cosmological constant in the (2,2m - 1)
minimal model coupled to two-dimensional euclidean quantum gravity.
Furthermore, we show that the principal (r,s) ZZ brane can be viewed as the
basic (1,1) ZZ boundary state tensored with a (r,s) Cardy boundary state for a
general (p,q) minimal model coupled to two-dimensional quantum gravity. In this
sense there exists only one ZZ boundary state, the basic (1,1) boundary state.
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Probability of the Standard Model Appearance from a Matrix Model: The standard model of particle physics lies in an enormous number of string
vacua. In a nonperturbative formulation of string theory, various string vacua
can, in principle, be compared dynamically, and the probability distribution
over the vacuum space could be calculated. In this paper, we consider
situations where the IIB matrix model is compactified on a six-dimensional
torus with various gauge groups and various magnetic fluxes, find matrix
configurations that provide the standard model matter content, and estimate
semiclassically the probability of their appearance.
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Constructing Gravitational Dimensions: It would be extremely useful to know whether a particular low energy
effective theory might have come from a compactification of a higher
dimensional space. Here, this problem is approached from the ground up by
considering theories with multiple interacting massive gravitons. It is
actually very difficult to construct discrete gravitational dimensions which
have a local continuum limit. In fact, any model with only nearest neighbor
interactions is doomed. If we could find a non-linear extension for the
Fierz-Pauli Lagrangian for a graviton of mass mg which does not break down
until the scale Lambda_2=(mg Mpl)^(1/2), this could be used to construct a
large class of models whose continuum limit is local in the extra dimension.
But this is shown to be impossible: a theory with a single graviton must break
down by Lambda_3 = (mg^2 Mpl)^(1/3). Next, we look at how the discretization
prescribed by the truncation of the KK tower of an honest extra diemsinon
rasies the scale of strong coupling. It dictates an intricate set of
interactions among various fields which conspire to soften the strongest
scattering amplitudes and allow for a local continuum limit. A number of
canditate symmetries associated with locality in the discretized dimension are
also discussed.
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New Old Inflation: We propose a new class of inflationary solutions to the standard cosmological
problems (horizon, flatness, monopole,...), based on a modification of old
inflation. These models do not require a potential which satisfies the normal
inflationary slow-roll conditions. Our universe arises from a single tunneling
event as the inflaton leaves the false vacuum. Subsequent dynamics (arising
from either the oscillations of the inflaton field or thermal effects) keep a
second field trapped in a false minimum, resulting in an evanescent period of
inflation (with roughly 50 e-foldings) inside the bubble. This easily allows
the bubble to grow sufficiently large to contain our present horizon volume.
Reheating is accomplished when the inflaton driving the last stage of inflation
rolls down to the true vacuum, and adiabatic density perturbations arise from
moduli-dependent Yukawa couplings of the inflaton to matter fields. Our
scenario has several robust predictions, including virtual absence of gravity
waves, a possible absence of tilt in scalar perturbations, and a higher degree
of non-Gaussianity than other models. It also naturally incorporates a solution
to the cosmological moduli problem.
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KdV Charges and the Generalized Torus Partition Sum in $T{\bar T}$
deformation: We consider KdV currents in a quantum field theory obtained by deforming a
two dimensional conformal field theory on a cylinder via the irrelevant
operator $T{\bar T}$. In this paper we determine their one-point functions
modular properties. We find that the one-point functions factorize into two
components each with a definite modular weight. We also obtain a general
differential equation that the generalized torus partition sum satisfies.
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Holographic Euclidean thermal correlator: In this paper, we compute holographic Euclidean thermal correlators of the
stress tensor and $U(1)$ current from the AdS planar black hole. To this end,
we set up perturbative boundary value problems for Einstein's gravity and
Maxwell theory in the spirit of Gubser-Klebanov-Polyakov-Witten, with
appropriate gauge fixing and regularity boundary conditions at the horizon of
the black hole. The linearized Einstein equation and Maxwell equation in the
black hole background are related to the Heun equation of degenerate local
monodromy. Leveraging the connection relation of local solutions of the Heun
equation, we partly solve the boundary value problem and obtain exact two-point
thermal correlators for $U(1)$ current and stress tensor in the scalar and
shear channels.
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Wilson loops in circular quiver SCFTs at strong coupling: We study circular BPS Wilson loops in the $\mathcal{N}=2$ superconformal
$n$-node quiver theories at large $N$ and strong 't Hooft coupling by using
localization. We compute the expectation values of Wilson loops in the limit
when the 't Hooft couplings are hierarchically different and when they are
nearly equal. Based on these results, we make a conjecture for arbitrary strong
couplings.
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N=2 supergravity models with stable de Sitter vacua: In the present talk I shall review the construction of N=2 supergravity
models exhibiting stable de Sitter vacua. These solutions represent the first
instance of stable backgrounds with positive cosmological constant in the
framework of extended supergravities (N >=2). After briefly reviewing the role
of de Sitter space--times in inflationary cosmology, I shall describe the main
ingredients which were necessary for the construction of gauged N=2
supergravity models admitting stable solutions of this kind.
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Spacetime Dependent Lagrangians and the Barriola-Vilenkin Monopole Mass: This paper has been withdrawn by the authors in order to replace it with a
more correct treatment. The basic results remain the same but the treatment is
more rigorously correct.
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Application of Tomita-Takesaki theory in algebraic euclidean field
theories: The construction of the known interacting quantum field theory models is
mostly based on euclidean techniques. The expectation values of interesting
quantities are usually given in terms of euclidean correlation functions from
which one should be able to extract information about the behavior of the
correlation functions of the Minkowskian counterpart.
We think that the C*-algebraic approach to euclidean field theory gives an
appropriate setup in order to study structural aspects model independently. A
previous paper deals with a construction scheme which relates to each euclidean
field theory a Poincar\'e covariant quantum field theory model in the sense of
R. Haag and D. Kastler.
Within the framework of R. Haag and D. Kastler, the physical concept of PCT
symmetry and spin and statistics is related to the Tomita-Takesaki theory of
von Neumann algebras and this important aspects has been studied by several
authors.
We express the PCT symmetry in terms of euclidean reflexions and we
explicitly identify the corresponding modular operator and the modular
conjugation of the related Tomita-Takesaki theory. Locality, wedge duality, and
a geometric action of the modular group of the von Neumann algebra of
observables, localized within a wedge region in Minkowski space, are direct
consequences.
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The Light Front Gauge Propagator: The Status Quo: At the classical level, the inverse differential operator for the quadratic
term in the gauge field Lagrangian density fixed in the light front through the
multiplier (nA)^2 yields the standard two term propagator with single
unphysical pole of the type (kn)^-1. Upon canonical quantization on the
light-front, there emerges a third term of the form (kn^(mu)n^(nu))(kn)^-2.
This third term in the propagator has traditionally been dropped on the grounds
that is exactly cancelled by the "instantaneous" term in the interaction
Hamiltonian in the light-front. Our aim in this work is not to discuss which of
the propagators is the correct one, but rather to present at the classical
level, the gauge fixing conditions that can lead to the three-term propagator.
|
Generalized duality between local vector theories in $D=2+1$: The existence of an interpolating master action does not guarantee the same
spectrum for the interpolated dual theories. In the specific case of a
generalized self-dual (GSD) model defined as the addition of the Maxwell term
to the self-dual model in $D=2+1$, previous master actions have furnished a
dual gauge theory which is either nonlocal or contains a ghost mode. Here we
show that by reducing the Maxwell term to first order by means of an auxiliary
field we are able to define a master action which interpolates between the GSD
model and a couple of non-interacting Maxwell-Chern-Simons theories of opposite
helicities. The presence of an auxiliary field explains the doubling of fields
in the dual gauge theory. A generalized duality transformation is defined and
both models can be interpreted as self-dual models. Furthermore, it is shown
how to obtain the gauge invariant correlators of the non-interacting MCS
theories from the correlators of the self-dual field in the GSD model and
vice-versa. The derivation of the non-interacting MCS theories from the GSD
model, as presented here, works in the opposite direction of the soldering
approach.
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BPS solitons in a Dirac-Born-Infeld action: We present several classes of solitons in ($1+1$)-dimensional models where
the standard canonical kinetic term is replaced by a Dirac-Born-Infeld (DBI)
one. These are static solutions with finite energy and different properties,
namely, they can have compact support, or be kink or lump-like, according to
the type of potential chosen, which depend on the DBI parameter $\beta$.
Through a combination of numerical and analytical arguments, by which the
equation of motion is seen as that corresponding to \emph{another} canonical
model with a new $\beta$-dependent potential and a $\beta$-deformed energy
density, we construct models in which increasing smoothly the DBI parameter
both the compacton radius, the thickness of the kink and the width of the lump
get modified until each soliton reaches its standard canonical shape as $\beta
\rightarrow \infty$. In addition we present compacton solutions whose canonical
counterparts are not compact.
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Topological Matrix Model: Starting from the primal principle based on the noncommutative nature of
(9+1)-dimensional spacetime, we construct a topologically twisted version of
the supersymmetric reduced model with a certain modification. Our formulation
automatically provides extra 1+1 dimensions, thereby the dimensions of
spacetime are promoted to 10+2. With a suitable gauge choice, we can reduce the
model with (10+2)-dimensional spacetime to the one with (9+1)-dimensions and
thus we regard this gauge as the light-cone gauge. It is suggested that the
model so obtained would describe the light-cone F-theory. From this viewpoint
we argue the relation of the reduced model to the matrix model of M-theory and
the SL(2,Z) symmetry of type IIB string theory. We also discuss the general
covariance of the matrix model in a broken phase, and make some comments on the
background independence.
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Resummation at finite conformal spin: We generalize the computation of anomalous dimension and correction to OPE
coefficients at finite conformal spin considered recently in
\cite{arXiv:1806.10919, arXiv:1808.00612} to arbitrary space-time dimensions.
By using the inversion formula of Caron-Huot and the integral (Mellin)
representation of conformal blocks, we show that the contribution from
individual exchanges to anomalous dimensions and corrections to the OPE
coefficients for "double-twist" operators
$[\mathcal{O}_1\mathcal{O}_2]_{\Delta,J}$ in $s-$channel can be written at
finite conformal spin in terms of generalized Wilson polynomials. This approach
is democratic {\it wrt} space-time dimensions, thus generalizing the earlier
findings to cases where closed form expressions of the conformal blocks are not
available.
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Properties of an Alternate Lax Description of the KdV Hierarchy: We study systematically the Lax description of the KdV hierarchy in terms of
an operator which is the geometrical recursion operator. We formulate the Lax
equation for the $n$-th flow, construct the Hamiltonians which lead to
commuting flows. In this formulation, the recursion relation between the
conserved quantities follows naturally. We give a simple and compact definition
of all the Hamiltonian structures of the theory which are related through a
power law.
|
The Laplace Transform of Quantum Gravity: Following analogies with relativistic point particles, and Schild strings, we
show that the Einstein gravity and its strong coupling regime (or the Planck
mass going to 0) are related to each other through a Laplace transform. The
Feynman propagator of gravity in the strong coupling regime satisfies a
functional diffusion equation in the three-metric space with the evolution
parameter being the volume of spacetime. We conjecture that the relationship
between both regimes is consistent with the existence of an evolution operator
in which time is replaced by the volume of spacetime
|
Path Integrals on sl(2,R) Orbits: We quantise orbits of the adjoint group action on elements of the sl(2,R) Lie
algebra. The path integration along elliptic slices is akin to the coadjoint
orbit quantization of compact Lie groups, and the calculation of the characters
of elliptic group elements proceeds along the same lines as in compact groups.
The computation of the trace of hyperbolic group elements in a diagonal basis
as well as the calculation of the full group action on a hyperbolic basis
requires considerably more technique. We determine the action of hyperbolic
one-parameter subgroups of PSL(2,R) on the adjoint orbits and discuss global
subtleties in choices of adapted coordinate systems. Using the hyperbolic
slicing of orbits, we describe the quantum mechanics of an irreducible sl(2,R)
representation in a hyperbolic basis and relate the basis to the mathematics of
the Mellin integral transform. We moreover discuss the representation theory of
the double cover SL(2,R) of PSL(2,R) as well as that of its universal cover.
Traces in the representations of these groups for both elliptic and hyperbolic
elements are computed. Finally, we motivate our treatment of this elementary
quantisation problem by indicating applications.
|
The wake of a quark moving through a strongly-coupled $\mathcal N=4$
supersymmetric Yang-Mills plasma: The energy density wake produced by a heavy quark moving through a strongly
coupled N=4 supersymmetric Yang-Mills plasma is computed using gauge/string
duality.
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Correlation Functions of (2k-1, 2) Minimal Matter Coupled to 2D Quantum
Gravity: We compute N-point correlation functions of non-unitary (2k-1, 2) minimal
matter coupled to 2D quantum gravity on a sphere using the continuum Liouville
field approach. A gravitational dressing of the matter primary field with the
minimum conformal weight is used as the cosmological operator. Our results are
in agreement with the correlation functions of the one-matrix model at the k-th
critical point.
|
Four-particle solutions to Baxter equation of SL(2,C) Heisenberg spin
magnet for integer conformal Lorentz spin and their normalizability: The four reggeized gluon states for non-vanishing Lorentz conformal spin
$n_h$ are considered. To calculate their spectrum the Q-Baxter method is used.
As a result we describe normalizable trajectory-like states, which form
continuous spectrum, as well as discrete point-like solutions, which turn out
to be non-normalizable. The point-like solutions exist due to symmetry of the
Casimir operator where conformal weights $(h,\bar h) \to (h,1-\bar h)$.
|
Higher Spin Fields and Symplectic Geometry: We argue that higher spin fields originate from Hamiltonian mechanics and
play a role of gauge fields ensuring covariance of geometric observables such
as length and volume with respect to canonical transformations in the same way
as a metric tensor in Riemannian geometry ensures covariance with respect to
diffeomorphisms. We consider a reparametrization invariant action of a point
particle in Hamiltonian form. Reparametrization invariance is achieved in the
standard way by coupling to the auxiliary world-line metric. Identifying
Hamiltonian function with a generating function for higher spin fields this
action can be viewed as an action for the point particle in a higher spin
background, while canonical transformations act as higher spin symmetries. We
define the gauge invariant length as a proper time of a particle moving along
the geodesic. Following the usual geometrical interpretation we introduce the
volume form and the scalar curvature for a combined lower spin sector. As for
the general case, we show that notions of local volume and scalar curvature are
not compatible with symplectic transformations. We propose symplectically
invariant counterparts for the total volume of the space and Einstein-Hilbert
action.
|
Radion Stabilization in Compact Hyperbolic Extra Dimensions: We consider radion stabilization in hyperbolic brane-world scenarios. We
demonstrate that in the context of Einstein gravity, matter fields which
stabilize the extra dimensions must violate the null energy condition. This
result is shown to hold even allowing for FRW-like expansion on the brane. In
particular, we explicitly demonstrate how one putative source of stabilizing
matter fails to work, and how others violate the above condition. We speculate
on a number of ways in which we may bypass this result, including the effect of
Casimir energy in these spaces. A brief discussion of supersymmetry in these
backgrounds is also given.
|
The Structure of AdS Black Holes and Chern Simons Theory in 2+1
Dimensions: We study anti-de Sitter black holes in 2+1 dimensions in terms of Chern
Simons gauge theory of anti-de Sitter group coupled to a source. Taking the
source to be an anti-de Sitter state specified by its Casimir invariants, we
show how all the relevant features of the black hole are accounted for. The
requirement that the source be a unitary representation leads to a discrete
tower of states which provide a microscopic model for the black hole.
|
Curved momentum spaces from quantum groups with cosmological constant: We bring the concept that quantum symmetries describe theories with
nontrivial momentum space properties one step further, looking at quantum
symmetries of spacetime in presence of a nonvanishing cosmological constant
$\Lambda$. In particular, the momentum space associated to the
$\kappa$-deformation of the de Sitter algebra in (1+1) and (2+1) dimensions is
explicitly constructed as a dual Poisson-Lie group manifold parametrized by
$\Lambda$. Such momentum space includes both the momenta associated to
spacetime translations and the `hyperbolic' momenta associated to boost
transformations, and has the geometry of (half of) a de Sitter manifold. Known
results for the momentum space of the $\kappa$-Poincar\'e algebra are smoothly
recovered in the limit $\Lambda\to 0$, where hyperbolic momenta decouple from
translational momenta. The approach here presented is general and can be
applied to other quantum deformations of kinematical symmetries, including
(3+1)-dimensional ones.
|
Dualization of non-Abelian BF model: We show that dualization of BF models to Stueckelberg-like massive gauge
theories allows a non-Abelian extension. We obtain local Lagrangians which are
straightforward extensions of the Abelian results.
|
Trapped surfaces and emergent curved space in the Bose-Hubbard model: A Bose-Hubbard model on a dynamical lattice was introduced in previous work
as a spin system analogue of emergent geometry and gravity. Graphs with regions
of high connectivity in the lattice were identified as candidate analogues of
spacetime geometries that contain trapped surfaces. We carry out a detailed
study of these systems and show explicitly that the highly connected subgraphs
trap matter. We do this by solving the model in the limit of no back-reaction
of the matter on the lattice, and for states with certain symmetries that are
natural for our problem. We find that in this case the problem reduces to a
one-dimensional Hubbard model on a lattice with variable vertex degree and
multiple edges between the same two vertices. In addition, we obtain a
(discrete) differential equation for the evolution of the probability density
of particles which is closed in the classical regime. This is a wave equation
in which the vertex degree is related to the local speed of propagation of
probability. This allows an interpretation of the probability density of
particles similar to that in analogue gravity systems: matter inside this
analogue system sees a curved spacetime. We verify our analytic results by
numerical simulations. Finally, we analyze the dependence of localization on a
gradual, rather than abrupt, fall-off of the vertex degree on the boundary of
the highly connected region and find that matter is localized in and around
that region.
|
On the Cosmological Relevance of the Tachyon: We analyse of the effective action of the tachyon field on a D-brane, of both
bosonic as well as superstring theory. We find that the non-standard kinetic
term of the tachyon field requires a correction to the Born-Infeld type
Lagrangian. The cosmological significance of the resulting dynamics is
explored. We also examine if the rolling tachyon can provide an effective
cosmological constant and contrast its behaviour with quintessence.
|
Dictionary on Lie Superalgebras: The main definitions and properties of Lie superalgebras are proposed a la
facon de a short dictionary, the different items following the alphabetical
order. The main topics deal with the structure of simple Lie superalgebras and
their finite dimensional representations; rather naturally, a few pages are
devoted to supersymmetry. This modest booklet has two ambitious goals: to be
elementary and easy to use. The beginner is supposed to find out here the main
concepts on superalgebras, while a more experimented theorist should recognize
the necessary tools and informations for a specific use.
|
A remark on the asymptotic form of BPS multi-dyon solutions and their
conserved charges: We evaluate the gauge invariant, dynamically conserved charges, recently
obtained from the integral form of the Yang-Mills equations, for the BPS
multi-dyon solutions of a Yang-Mills-Higgs theory associated to any compact
semi-simple gauge group G. Those charges are shown to correspond to the
eigenvalues of the next-to-leading term of the asymptotic form of the Higgs
field at spatial infinity, and so coinciding with the usual topological charges
of those solutions. Such results show that many of the topological charges
considered in the literature are in fact dynamical charges, which conservation
follows from the global properties of classical Yang-Mills theories encoded
into their integral dynamical equations. The conservation of those charges can
not be obtained from the differential form of Yang-Mills equations.
|
Non-associativity in non-geometric string and M-theory backgrounds, the
algebra of octonions, and missing momentum modes: We propose a non-associative phase space algebra for M-theory backgrounds
with locally non-geometric fluxes based on the non-associative algebra of
octonions. Our proposal is based on the observation that the non-associative
algebra of the non-geometric R-flux background in string theory can be obtained
by a proper contraction of the simple Malcev algebra generated by imaginary
octonions. Furthermore, by studying a toy model of a four-dimensional locally
non-geometric M-theory background which is dual to a twisted torus, we show
that the non-geometric background is "missing" a momentum mode. The resulting
seven-dimensional phase space can thus be naturally identified with the
imaginary octonions. This allows us to interpret the full uncontracted algebra
of imaginary octonions as the uplift of the string theory R-flux algebra to
M-theory, with the contraction parameter playing the role of the string
coupling constant $g_s$.
|
Elimination of IR/UV via Gravity in Noncommutative Field Theory: Models of particle physics with Noncommutative Geometry (NCG) generally
suffer from a manifestly non-Wilsonian coupling of infrared and ultraviolet
degrees of freedom known as the "IR/UV Problem" which would tend to compromise
their phenomenological relevance. In this Letter we explicitly show how one may
remedy this by coupling NCG to gravity. In the simplest scenario the Lagrangian
gets multiplied by a nonconstant background metric; in $\phi-4$ theory the
theorem that $\int d^4 x \phi \star \phi = \int d^4 x \phi^2$ is no longer true
and the field propagator gets modified by a factor which depends on both NCG
and the variation of the metric. A suitable limit of this factor as the
propagating momentum gets asymptotically large then eradicates the IR/UV
problem. With gravity and NCG coupled to each other, one might expect
anti-symmetric components to arise in the metric. Cosmological implications of
such are subsequently discussed.
|
Non-Gaussianities in the Cosmological Perturbation Spectrum due to
Primordial Anisotropy: We investigate possible signatures of a pre-inflationary anisotropic phase in
two-point and three-point correlation functions of the curvature perturbation
for high-momentum modes which exit the horizon after isotropization. In this
momentum regime, the early time dynamics admits a WKB description and the late
time dynamics can be described in terms of a non-Bunch Davies vacuum state
which encodes the information of initial anisotropy in the background
spacetime. We compute the bi-spectrum for curvature perturbation in a canonical
single-field action with and without higher derivative operators. We show that
the bi-spectrum at late times, in either case, is enhanced for a flattened
triangle configuration as well as a squeezed triangle configuration and compute
the corresponding $f_{NL}$ parameters. The angular dependence and the
particular momentum dependence of the $f_{NL}$ parameter appear as distinctive
features of background anisotropy at early times.
|
Distribution-theoretic methods in quantum field theory: The evolution of the distribution-theoretic methods in perturbative quantum
field theory is reviewed starting from Bogolyubov's pioneering 1952 work with
emphasis on the theory and calculations of perturbation theory integrals.
|
An exact solution of the Dirac equation with CP violation: We consider Yukawa theory in which the fermion mass is induced by a Higgs
like scalar. In our model the fermion mass exhibits a temporal dependence,
which naturally occurs in the early Universe setting. Assuming that the complex
fermion mass changes as a tanh-kink, we construct an exact, helicity
conserving, CP-violating solution for the positive and negative frequency
fermionic mode functions, which is valid both in the case of weak and strong CP
violation. Using this solution we then study the fermionic currents both in the
initial vacuum and finite density/temperature setting. Our result shows that,
due to a potentially large state squeezing, fermionic currents can exhibit a
large oscillatory magnification. Having in mind applications to electroweak
baryogenesis, we then compare our exact results with those obtained in a
gradient approximation. Even though the gradient approximation does not capture
the oscillatory effects of squeezing, it describes quite well the averaged
current, obtained by performing a mode sum. Our main conclusion is: while the
agreement with the semiclassical force is quite good in the thick wall regime,
the difference is sufficiently significant to motivate a more detailed
quantitative study of baryogenesis sources in the thin wall regime in more
realistic settings.
|
BTZ Black Hole with Gravitational Chern-Simons: Thermodynamics and
Statistical Entropy: Recently, the BTZ black hole in the presence of the gravitational
Chern-Simons (GCS) term has been studied and it has been found that the usual
thermodynamical quantities, like as the black hole mass, angular momentum, and
black hole entropy, are modified. But, for large values of the GCS coupling,
where the modification terms dominate the original terms, some exotic behaviors
occur, like as the roles of the mass and angular momentum are interchanged and
the black hole entropy depends more on the $inner$-horizon area than the outer
one. A basic physical problem of this system is that the form of entropy does
not guarantee the second law of thermodynamics, in contrast to the
Bekenstein-Hawking (BH) entropy. Moreover, this entropy does $not$ agree with
the statistical entropy, in contrast to a good agreement for small values of
the GCS coupling. Here I find that there is another entropy formula where the
usual BH form dominates the inner-horizon term again, as in the small GCS
coupling, such as the second law of thermodynamics can be guaranteed. I compare
the result of the holographic approach with the classical-
symmetry-algebra-based approach and I find exact agreements even with the
higher-derivative term of GCS. This provides a non-trivial check of the
AdS/CFT-correspondence in the presence of higher-derivative terms in the
gravity action.
|
B-type anomaly coefficients for the D3-D5 domain wall: We compute type-B Weyl anomaly coefficients for the domain wall version of N
= 4 SYM that is holographically dual to the D3-D5 probe-brane system with flux.
Our starting point is the explicit expression for the improved energy momentum
tensor of N = 4 SYM. We determine the two-point function of this operator in
the presence of the domain wall and extract the anomaly coefficients from the
result. In the same process we determine the two-point function of the
displacement operator.
|
Twisted local systems solve the (holographic) loop equation of large-N
QCD_4: We construct a holographic map from the loop equation of large-N QCD in d=2
and d=4, for planar self-avoiding loops, to the critical equation of an
equivalent effective action. The holographic map is based on two ingredients:
an already proposed holographic form of the loop equation, such that the
quantum contribution is reduced to a regularized residue; a new conformal map
from the region encircled by the based loop to a cuspidal fundamental domain in
the upper half-plane, such that the regularized residue vanishes at the cusp.
As a check, we study the first coefficient of the beta function and that part
of the second coefficient which arises from the rescaling anomaly, in passing
from the Wilsonian to the canonically normalised (holographic) effective
action.
|
Weak Scale Supersymmetry Without Weak Scale Supergravity: It is generally believed that weak scale supersymmetry implies weak scale
supergravity, in the sense that the masses of the gravitino and gravitationally
coupled moduli have masses below 100 TeV. This paper presents a realistic
framework for supersymmetry breaking in the hidden sector in which the masses
of the gravitino and gravitational moduli can be much larger. This cleanly
eliminates the cosmological problems of hidden sector models. Supersymmetry
breaking is communicated to the visible sector by anomaly-mediated
supersymmetry breaking. The framework is compatible with perturbative gauge
coupling unification, and can be realized either in models of "warped" extra
dimensions, or in strongly-coupled four-dimensional conformal field theories.
|
Non-relativistic D3-brane in the presence of higher derivative
corrections: Using alpha'^3 terms of type IIB supergravity action we study higher order
corrections to the non-relativistic non-extremal D3-brane. Utilizing the
corrected solution we evaluate corrections to temperature, entropy and shear
viscosity. We also compute the eta/s ratio which although within the range of
validity of the supergravity approximation and in the lowest order of the
correction the universal bound is respected, there is a possibility for a
violation of the bound when higher terms in the expansion are taken into
account.
|
Towards Field Theory of Turbulence: We revisit the problem of stationary distribution of vorticity in
three-dimensional turbulence. Using Clebsch variables we construct an explicit
invariant measure on stationary solutions of Euler equations with the extra
condition of fixed energy flow/dissipation. The asymptotic solution for large
circulation around large loops is studied as a WKB limit (instanton). The
Clebsch fields are discontinuous across minimal surface bounded by the loop,
with normal vorticity staying continuous. There is also a singular tangential
vorticity component proportional to $\delta(z)$ where $z$ is the normal
direction. Resulting flow has nontrivial topology. This singular tangent
vorticity component drops from the flux but dominates the energy dissipation as
well as the Biot-Savart integral for velocity field. This leads us to a
modified equation for vorticity distribution along the minimal surface compared
to that assumed in a loop equations, where the singular terms were not noticed.
In addition to describing vorticity distribution over the minimal surface, this
approach provides formula for the circulation PDF, which was elusive in the
Loop Equations.
|
On the geometry of C^3/D_27 and del Pezzo surfaces: We clarify some aspects of the geometry of a resolution of the orbifold X =
C3/D_27, the noncompact complex manifold underlying the brane quiver standard
model recently proposed by Verlinde and Wijnholt. We explicitly realize a map
between X and the total space of the canonical bundle over a degree 1 quasi del
Pezzo surface, thus defining a desingularization of X. Our analysis relys
essentially on the relationship existing between the normalizer group of D_27
and the Hessian group and on the study of the behaviour of the Hesse pencil of
plane cubic curves under the quotient.
|
Ward Identities for Hall Transport: We derive quantum field theory Ward identities based on linear area
preserving and conformal transformations in 2+1 dimensions. The identities
relate Hall viscosities, Hall conductivities and the angular momentum. They
apply both for relativistic and non relativistic systems, at zero and at finite
temperature. We consider systems with or without translation invariance, and
introduce an external magnetic field and viscous drag terms. A special case of
the identities yields the well known relation between the Hall conductivity and
half the angular momentum density.
|
Absorption of scalars by nonextremal charged black holes in string
theory: We analyze the low frequency absorption cross section of minimally coupled
massless scalar fields by different kinds of charged static black holes in
string theory, namely the D1-D5 system in d=5 and a four dimensional dyonic
four-charged black hole. In each case we show that this cross section always
has the form of some parameter of the solution divided by the black hole
Hawking temperature. We also verify in each case that, despite its explicit
temperature dependence, such quotient is finite in the extremal limit, giving a
well defined cross section. We show that this precise explicit temperature
dependence also arises in the same cross section for black holes with string
alpha' corrections: it is actually induced by them.
|
More on renormalizable exceptions to Nelson-Seiberg theorem: The Nelson-Seiberg theorem dictates conditions for the spontaneous breaking
of the supersymmetry in Wess-Zumino models with generic, possibly
non-renormalizable, superpotential; the existence of the R-symmetry is
necessary while the spontaneous breaking of the R-symmetry is sufficient. If we
restrict ourselves to generic but renormalizable theories, however, there exist
Wess-Zumino models whose vacua break the R-symmetry spontaneously while
preserving the supersymmetry. The classification and conditions of such
renormalizable exceptions are under active study. We give some new examples of
spontaneous breaking of the R-symmetry with preserved supersymmetry that are
not covered in the literature.
|
Hydrodynamic Long-Time tails From Anti de Sitter Space: For generic field theories at finite temperature, a power-law falloff of
correlation functions of conserved currents at long times is a prediction of
non-linear hydrodynamics. We demonstrate, through a one-loop computation in
Einstein gravity in Anti de Sitter space, that this effect is reproduced by the
dynamics of black hole horizons. The result is in agreement with the
gauge-gravity correspondence.
|
Dimensional regularization of nonlinear sigma models on a finite time
interval: We extend dimensional regularization to the case of compact spaces. Contrary
to previous regularization schemes employed for nonlinear sigma models on a
finite time interval (``quantum mechanical path integrals in curved space'')
dimensional regularization requires only a covariant finite two-loop
counterterm. This counterterm is nonvanishing and given by R/8.
|
Strongly Coupled Gauge Theories: High and Low Temperature Behavior of
Non-local Observables: We explore the high and low temperature behavior of non-local observables in
strongly coupled gauge theories that are dual to AdS. We develop a systematic
expansion for equal time two-point correlation, spatial Wilson loops and
entanglement entropy at finite temperature using the AdS/CFT correspondence,
leading to analytic expressions for these observables at high and low
temperature limits. This approach enables the identification of the
contributions of different regions of the bulk geometry to these gauge theory
observables.
|
Topology Change and the Emergence of Geometry in Two Dimensional Causal
Quantum Gravity: In this thesis we analyze a very simple model of two dimensional quantum
gravity based on causal dynamical triangulations (CDT). We present an exactly
solvable model which indicates that it is possible to incorporate spatial
topology changes in the nonperturbative path integral. It is shown that if the
change in spatial topology is accompanied by a coupling constant it is possible
to evaluate the path integral to all orders in the coupling and that the result
can be viewed as a hybrid between causal and Euclidian dynamical triangulation.
The second model we describe shows how a classical geometry with constant
negative curvature emerges naturally from a path integral over noncompact
manifolds. No initial singularity is present, hence the quantum geometry is
naturally compatible with the Hartle Hawking boundary condition. Furthermore,
we demonstrate that under certain conditions the quantum fluctuations are
small! To conclude, we treat the problem of spacetime topology change. Although
we are not able to completely solve the path integral over all manifolds with
arbitrary topology, we do obtain results that indicate that such a path
integral might be consistent, provided suitable causality restrictions are
imposed.
|
New N=1 Dualities: We show that the N=1 supersymmetric SU(N) gauge theory with 2N flavors
without superpotential has not only the standard Seiberg dual description but
also another dual description involving two copies of the so-called T_N theory.
This is a natural generalization to N>2 of a dual description of SU(2) gauge
theory with 4 flavors found by Csaki, Schmaltz, Skiba and Terning. We also
study dualities of other N=1 SCFTs involving copies of T_N theories. Our
duality is the basic operation from which a recently-found web of N=1 dualities
obtained by compactifying M5-branes on Riemann surfaces can be derived
field-theoretically.
|
Exact quantization conditions for cluster integrable systems: We propose exact quantization conditions for the quantum integrable systems
of Goncharov and Kenyon, based on the enumerative geometry of the corresponding
toric Calabi-Yau manifolds. Our conjecture builds upon recent results on the
quantization of mirror curves, and generalizes a previous proposal for the
quantization of the relativistic Toda lattice. We present explicit tests of our
conjecture for the integrable systems associated to the resolved C^3/Z_5 and
C^3/Z_6 orbifolds.
|
Velocity-Field Theory, Boltzmann's Transport Equation, Geometry and
Emergent Time: Boltzmann equation describes the time development of the velocity
distribution in the continuum fluid matter. We formulate the equation using the
field theory where the {\it velocity-field} plays the central role. The
properties of the fluid matter (fluid particles) appear as the density and the
viscosity. {\it Statistical fluctuation} is examined, and is clearly
discriminated from the quantum effect. The time variable is {\it emergently}
introduced through the computational process step. Besides the ordinary
potential, the general velocity potential is introduced. The collision term,
for the Higgs-type velocity potential, is explicitly obtained and the
(statistical) fluctuation is closely explained. The system is generally {\it
non-equilibrium}. The present field theory model does {\it not} conserve energy
and is an open-system model. One dimensional Navier-Stokes equation, i.e.,
Burgers equation, appears. In the latter part of the text, we present a way to
directly define the distribution function by use of the geometry, appearing in
the energy expression, and Feynman's path-integral.
|
A new look at the modified Coulomb potential in a strong magnetic field: The static Coulomb potential of Quantum Electrodynamics (QED) is calculated
in the presence of a strong magnetic field in the lowest Landau level (LLL)
approximation using two different methods. First, the vacuum expectation value
of the corresponding Wilson loop is calculated perturbatively in two different
regimes of dynamical mass $m_{dyn.}$, {\it i.e.}, $|{\mathbf{q}}_{\|}^{2}|\ll
m_{dyn.}^{2}\ll |eB|$ and $m_{dyn.}^{2}\ll |\mathbf{q}_{\|}^{2}|\ll|eB|$, where
$\mathbf{q}_{\|}$ is the longitudinal components of the momentum relative to
the external magnetic field $B$. The result is then compared with the static
potential arising from Born approximation. Both results coincide. Although the
arising potentials show different behavior in the aforementioned regimes, a
novel dependence on the angle $\theta$ between the particle-antiparticle's axis
and the direction of the magnetic field is observed. In the regime
$|{\mathbf{q}}_{\|}^{2}|\ll m_{dyn.}^{2}\ll |eB|$, for strong enough magnetic
field and depending on the angle $\theta$, a qualitative change occurs in the
Coulomb-like potential; Whereas for $\theta=0,\pi$ the potential is repulsive,
it exhibits a minimum for angles $\theta\in]0,\pi[$.
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Krylov complexity and orthogonal polynomials: Krylov complexity measures operator growth with respect to a basis, which is
adapted to the Heisenberg time evolution. The construction of that basis relies
on the Lanczos algorithm, also known as the recursion method. The mathematics
of Krylov complexity can be described in terms of orthogonal polynomials. We
provide a pedagogical introduction to the subject and work out analytically a
number of examples involving the classical orthogonal polynomials, polynomials
of the Hahn class, and the Tricomi-Carlitz polynomials.
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Lectures on Scattering Amplitudes in String Theory: In these lecture notes, we take a closer look at the calculation of
scattering amplitudes for the bosonic string. It is believed that string
theories form the UV completions of (super)gravity theories. Support for this
claim can be found in the (on-shell) scattering amplitudes of strings. On the
other hand, studying these string scattering amplitudes opens a window on the
UV behavior of the string theories themselves. In these short set of lectures,
we discuss the two-dimensional Polyakov path integral for the string, and its
gauge symmetries, the connection to Riemann surfaces and how to obtain some of
the simplest string scattering amplitudes. We end with some comments on more
advanced topics. For simplicity we limit ourselves to bosonic open string
theory in 26 dimensions.
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S-Duality of Boundary Conditions In N=4 Super Yang-Mills Theory: By analyzing brane configurations in detail, and extracting general lessons,
we develop methods for analyzing S-duality of supersymmetric boundary
conditions in N=4 super Yang-Mills theory. In the process, we find that
S-duality of boundary conditions is closely related to mirror symmetry of
three-dimensional gauge theories, and we analyze the IR behavior of large
classes of quiver gauge theories.
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A Parity Invariant Regularization in 3-D Quantum Electrodynamics: We regularize the 3-D quantum electrodynamics by a parity invariant
Pauli-Villars regularization method. We find that in the perturbation theory
the Chern-Simons term is not induced in the massless fermion case and induced
in the massive fermion case.
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Dynamics of N=2 Supersymmetric Chern-Simons Theories: We discuss several aspects of three dimensional N=2 supersymmetric gauge
theories coupled to chiral multiplets. The generation of Chern-Simons couplings
at low-energies results in novel behaviour including compact Coulomb branches,
non-abelian gauge symmetry enhancement and interesting patterns of dynamically
generated potentials. We further show how, given any pair of mirror theories
with N=4 supersymmetry, one may flow to a pair of mirror theories with N=2
supersymmetry by gauging a suitable combination of the R-symmetries. The
resulting theories again have interesting properties due to Chern-Simons
couplings.
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(F, D5) Bound State, SL(2, Z) Invariance and The Descendant States in
Type IIB/A String Theory: Recently the space-time configurations of a set of non-threshold bound
states, called the (F, Dp) bound states, have been constructed explicitly for
every $p$ with $2 \le p \le 7$ in both type IIA (for $p$ even) and type IIB
(for $p$ odd) string theories by the present authors. By making use of the
SL(2, Z) symmetry of type IIB theory we construct a more general SL(2, Z)
invariant bound state of the type ((F, D1), (NS5, D5)) in this theory from the
(F, D5) bound state. There are actually an infinite number of $(m,n)$ strings
forming bound states with $(m',n')$ 5-branes, where strings lie along one of
the spatial directions of the 5-branes. By applying T-duality along one of the
transverse directions we also construct the bound state ((F, D2), (KK, D6)) in
type IIA string theory. Then we give a list of possible bound states which can
be obtained from these newly constructed bound states by applying T-dualities
along the longitudinal directions as well as S-dualities to those in type IIB
theory.
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On the Electromagnetic Interactions of Anyons: Using the appropriate representation of the Poincare group and a definition
of minimal coupling, we discuss some aspects of the electromagnetic
interactions of charged anyons. In a nonrelativistic expansion, we derive a
Schrodinger-type equation for the anyon wave function which includes
spin-magnetic field and spin-orbit couplings. In particular, the gyromagnetic
ratio for charged anyons is shown to be 2; this last result is essentially a
reflection of the fact that the spin is parallel to the momentum in (2+1)
dimensions.
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Local Fields on the Brane Induced by Nonlocal Fields in the Bulk: We investigate quantum field theory in a bulk space with boundary, which
represents a 3-brane. Both flat and anti-de Sitter backgrounds are considered.
The basic idea is to keep local commutativity only on the brane, giving up this
requirement in the bulk. We explore the consequences of this proposal,
constructing a large family of nonlocal bulk fields, whose brane relatives are
local. We estimate the ultraviolet behavior of these local brane fields,
characterizing a subfamily which generates renormalizable theories on the
brane. The issue of brane conformal invariance and the relation between bulk
and brane conserved currents are also examined in this framework.
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Large N Field Theory of N=2 Strings and Self-Dual Gravity: We review some aspects of the construction of self-dual gravity and the
associated field theory of ${\cal N}=2$ strings in terms of two-dimensional
sigma models at large $N$. The theory is defined through a large $N$
Wess-Zumino-Witten model in a nontrivial background and in a particular double
scaling limit. We examine the canonical structure of the theory and describe an
infinite-dimensional Poisson algebra of currents.
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Triples, Fluxes, and Strings: We study string compactifications with sixteen supersymmetries. The moduli
space for these compactifications becomes quite intricate in lower dimensions,
partly because there are many different irreducible components. We focus
primarily, but not exclusively, on compactifications to seven or more
dimensions. These vacua can be realized in a number ways: the perturbative
constructions we study include toroidal compactifications of the heterotic/type
I strings, asymmetric orbifolds, and orientifolds. In addition, we describe
less conventional M and F theory compactifications on smooth spaces. The last
class of vacua considered are compactifications on singular spaces with
non-trivial discrete fluxes.
We find a number of new components in the string moduli space. Contained in
some of these components are M theory compactifications with novel kinds of
``frozen'' singularities. We are naturally led to conjecture the existence of
new dualities relating spaces with different singular geometries and fluxes. As
our study of these vacua unfolds, we also learn about additional topics
including: F theory on spaces without section, automorphisms of del Pezzo
surfaces, and novel physics (and puzzles) from equivariant K-theory. Lastly, we
comment on how the data we gain about the M theory three-form might be
interpreted.
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Quantum Group Gauge Theories and Covariant Quantum Algebras: The algebraic formulation of the quantum group gauge models in the framework
of the $R$-matrix approach to the theory of quantum groups is given. We
consider gauge groups taking values in the quantum groups and noncommutative
gauge fields transformed as comodules under the coaction of the gauge quantum
group $ G_{q}$. Using this approach we construct the quantum deformations of
the topological Chern-Simons models, non-abelian gauge theories and the
Einstein gravity. The noncommutative fields in these models generate $
G_{q}$-covariant quantum algebras.
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Correlators of double scaled SYK at one-loop: In this paper, we study one-loop contributions in the double-scaling limit of
the SYK model from the chord diagrams and Liouville type effective action. We
compute and clarify the meaning of each component consisting of the one-loop
corrections for the two- and time-ordered four-point functions of light
operators. We also reproduce the exact expression of the out-of-time-ordered
four-point function at arbitrary temperatures within the one-loop level, which
were previously computed from different methods.
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Topics in Black Hole Production: We revisit Voloshin's model of multiple black hole production in
trans-Planckian elementary particle collisions in D=4. Our revised computation
shows that the cross section to produce N additional black holes is suppressed
by 1/s, rather than being enhanced as was originally found. We also review the
semiclassical gravity picture of black hole production from hep-th/0409131,
making additional comments about the meaning of wavepacket subdivision.
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Nonlinear perturbations of cosmological scalar fields with non-standard
kinetic terms: We adopt a covariant formalism to derive exact evolution equations for
nonlinear perturbations, in a universe dominated by two scalar fields. These
scalar fields are characterized by non-canonical kinetic terms and an arbitrary
field space metric, a situation typically encountered in inflationary models
inspired by string theory. We decompose the nonlinear scalar perturbations into
adiabatic and entropy modes, generalizing the definition adopted in the linear
theory, and we derive the corresponding exact evolution equations. We also
obtain a nonlinear generalization of the curvature perturbation on uniform
density hypersurfaces, showing that on large scales it is sourced only by the
nonlinear version of the entropy perturbation. We then expand these equations
to second order in the perturbations, using a coordinate based formalism. Our
results are relatively compact and elegant and enable one to identify the new
effects coming from the non-canonical structure of the scalar fields
Lagrangian. We also explain how to analyze, in our formalism, the interesting
scenario of multifield Dirac-Born-Infeld inflation.
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The Attractor Flow for AdS$_5$ Black Holes in $\mathcal{N} = 2$ Gauged
Supergravity: We study the flow equations for BPS black holes in $\mathcal{N} = 2$
five-dimensional gauged supergravity coupled to any number of vector multiplets
via FI couplings. We develop the Noether-Wald procedure in this context and
exhibit the conserved charges as explicit integrals of motion, in the sense
that they can be computed at any radius on the rotating spacetime. The boundary
conditions needed to solve the first order differential equations are discussed
in great detail. We extremize the entropy function that controls the near
horizon geometry and give explicit formulae for all geometric variables at
their supersymmetric extrema. We have also considered a complexification of the
near-horizon variables that elucidates some features of the theory from the
near-horizon perspective.
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Black Hole Monodromy and Conformal Field Theory: The analytic structure of solutions to the Klein-Gordon equation in a black
hole background, as represented by monodromy data, is intimately related to
black hole thermodynamics. It encodes the "hidden conformal symmetry" of a
non-extremal black hole, and it explains why features of the inner event
horizon appear in scattering data such as greybody factors. This indicates that
hidden conformal symmetry is generic within a universality class of black
holes.
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Ostrogradsky in Theories with Multiple Fields: We review how the (absence of) Ostrogradsky instability manifests itself in
theories with multiple fields. It has recently been appreciated that when
multiple fields are present, the existence of higher derivatives may not
automatically imply the existence of ghosts. We discuss the connection with
gravitational theories like massive gravity and beyond Horndeski which manifest
higher derivatives in some formulations and yet are free of Ostrogradsky ghost.
We also examine an interesting new class of Extended Scalar-Tensor Theories of
gravity which has been recently proposed. We show that for a subclass of these
theories, the tensor modes are either not dynamical or are infinitely strongly
coupled. Among the remaining theories for which the tensor modes are
well-defined one counts one new model that is not field-redefinable to
Horndeski via a conformal and disformal transformation but that does require
the vacuum to break Lorentz invariance. We discuss the implications for the
effective field theory of dark energy and the stability of the theory.
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Palatini Higgs inflation and the refined dS conjecture: The refined de Sitter derivative conjecture provides constraints to
potentials that are low energy effective theories of quantum gravity. It can
give direct bounds on inflationary scenarios and determine whether the theory
is in the Landscape or the Swampland. Any infationary model can be checked by
these conditions and non-minimally coupled scalar field theory is not an
exception. We consider the Palatini Higgs inflation scenario taking the refined
de Sitter derivative conjecture into account. According to the latest
cosmological observations from Planck 2018, BICEP2+Keck and the bound of
non-minimal coupling parameter {\xi}, we suggest that if the refined dS
conjecture does indeed hold, then the Palatini Higgs inflation model cannot be
the low energy effective theory of a consistent quantum gravity theory since
the two parameters c1 and c2 are much smaller than order 1, which is
inconsistent with the refined dS conjecture. Therefore we suggest that it is in
the Swampland.
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An exact nilpotent non-perturbative BRST symmetry for the
Gribov-Zwanziger action in the linear covariant gauge: We point out the existence of a non-perturbative exact nilpotent BRST
symmetry for the Gribov-Zwanziger action in the Landau gauge. We then put
forward a manifestly BRST invariant resolution of the Gribov gauge fixing
ambiguity in the linear covariant gauge.
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Post-Minkowskian Scattering Angle in Einstein Gravity: Using the implicit function theorem we demonstrate that solutions to the
classical part of the relativistic Lippmann-Schwinger equation are in
one-to-one correspondence with those of the energy equation of a relativistic
two-body system. A corollary is that the scattering angle can be computed from
the amplitude itself, without having to introduce a potential. All results are
universal and provide for the case of general relativity a very simple formula
for the scattering angle in terms of the classical part of the amplitude, to
any order in the post-Minkowskian expansion.
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Hidden nonlinear su(2|2) superunitary symmetry of N=2 superextended 1D
Dirac delta potential problem: We show that the N=2 superextended 1D quantum Dirac delta potential problem
is characterized by the hidden nonlinear $su(2|2)$ superunitary symmetry. The
unexpected feature of this simple supersymmetric system is that it admits three
different $\mathbb Z_2$-gradings, which produce a separation of 16 integrals of
motion into three different sets of 8 bosonic and 8 fermionic operators. These
three different graded sets of integrals generate two different nonlinear,
deformed forms of $su(2|2)$, in which the Hamiltonian plays a role of a
multiplicative central charge. On the ground state, the nonlinear superalgebra
is reduced to the two distinct 2D Euclidean analogs of a superextended
Poincar\'e algebra used earlier in the literature for investigation of
spontaneous supersymmetry breaking. We indicate that the observed exotic
supersymmetric structure with three different $\mathbb Z_2$-gradings can be
useful for the search of hidden symmetries in some other quantum systems, in
particular, related to the Lam\'e equation.
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Investigations on Effective Electromagnetic and Gravitational Scenarios: The work aims effective and low-dimensional systems. Some different contexts
involving gravitational and electromagnetic interactions are investigated. The
electromagnetic one approaches bosonic and fermionic Effective Quantum Field
Theories non-minimally coupled in three spacetime dimensions submitted to the
expansion of Foldy-Wouthuysen Transformation, what generates (non-)relativistic
corrections. A study of the effects of an external electromagnetic field
derived from the Maxwell-Chern-Simons Electrodynamics on the obtained
interactions are executed, as well as the impact produced by the dimensional
reduction on expanded higher dimensional fermionic system in comparison to the
low-dimensional one. In the scenario of gravitational effective model, scalar
and fermionic particle scatterings reveal inter-particles interactions beyond
monopole-monopole, leading to velocity and spin contributions, and the results
are compared to a modified Electrodynamics effective model. A non-perturbative
model resourcing to Casual Dynamics Triangulation data is adopted to serve as
consistency check of the potentials resultants. Low-dimensional Maxwell-Higgs
effective models with modified kinetic terms are studied, submitting them to a
Bogomol'nyi prescription-type for calculation of inferior (non-trivial) bound
energy and the self-dual equations. Vortex solutions for gauge field
non-specified by an ansatz are achieved and their topological feature detailed.
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Noncommutative line bundle and Morita equivalence: Global properties of abelian noncommutative gauge theories based on
$\star$-products which are deformation quantizations of arbitrary Poisson
structures are studied. The consistency condition for finite noncommutative
gauge transformations and its explicit solution in the abelian case are given.
It is shown that the local existence of invertible covariantizing maps (which
are closely related to the Seiberg-Witten map) leads naturally to the notion of
a noncommutative line bundle with noncommutative transition functions. We
introduce the space of sections of such a line bundle and explicitly show that
it is a projective module. The local covariantizing maps define a new star
product $\star'$ which is shown to be Morita equivalent to $\star$.
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On-Shell Diagrams for N = 8 Supergravity Amplitudes: We define recursion relations for N = 8 supergravity amplitudes using a
generalization of the on-shell diagrams developed for planar N = 4
super-Yang-Mills. Although the recursion relations generically give rise to
non-planar on-shell diagrams, we show that at tree-level the recursion can be
chosen to yield only planar diagrams, the same diagrams occurring in the planar
N = 4 theory. This implies non-trivial identities for non-planar diagrams as
well as interesting relations between the N = 4 and N = 8 theories. We show
that the on-shell diagrams of N = 8 supergravity obey equivalence relations
analogous to those of N = 4 super-Yang-Mills, and we develop a systematic
algorithm for reading off Grassmannian integral formulae directly from the
on-shell diagrams. We also show that the 1-loop 4-point amplitude of N = 8
supergravity can be obtained from on-shell diagrams.
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Effective Field Theories from Soft Limits: We derive scalar effective field theories - Lagrangians, symmetries, and all
- from on-shell scattering amplitudes constructed purely from Lorentz
invariance, factorization, a fixed power counting order in derivatives, and a
fixed order at which amplitudes vanish in the soft limit. These constraints
leave free parameters in the amplitude which are the coupling constants of
well-known theories: Nambu-Goldstone bosons, Dirac-Born-Infeld scalars, and
Galileons. Moreover, soft limits imply conditions on the Noether current which
can then be inverted to derive Lagrangians for each theory. We propose a
natural classification of all scalar effective field theories according to two
numbers which encode the derivative power counting and soft behavior of the
corresponding amplitudes. In those cases where there is no consistent
amplitude, the corresponding theory does not exist.
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The Second Sound of SU(2): Using the AdS/CFT correspondence, we calculate the transport coefficients of
a strongly interacting system with a non-abelian SU(2) global symmetry near a
second order phase transition. From the behavior of the poles in the Green's
functions near the phase transition, we determine analytically the speed of
second sound, the conductivity, and diffusion constants. We discuss
similarities and differences between this and other systems with vector order
parameters such as p-wave superconductors and liquid helium-3.
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What is the $i\varepsilon$ for the S-matrix?: Can the S-matrix be complexified in a way consistent with causality? Since
the 1960's, the affirmative answer to this question has been well-understood
for $2 \to 2$ scattering of the lightest particle in theories with a mass gap
at low momentum transfer, where the S-matrix is analytic everywhere except at
normal-threshold branch cuts. We ask whether an analogous picture extends to
realistic theories, such as the Standard Model, that include massless fields,
UV/IR divergences, and unstable particles. Especially in the presence of light
states running in the loops, the traditional $i\varepsilon$ prescription for
approaching physical regions might break down, because causality requirements
for the individual Feynman diagrams can be mutually incompatible. We
demonstrate that such analyticity problems are not in contradiction with
unitarity. Instead, they should be thought of as finite-width effects that
disappear in the idealized $2\to 2$ scattering amplitudes with no unstable
particles, but might persist at higher multiplicity. To fix these issues, we
propose an $i\varepsilon$-like prescription for deforming branch cuts in the
space of Mandelstam invariants without modifying the analytic properties. This
procedure results in a complex strip around the real part of the kinematic
space, where the S-matrix remains causal. In addition to giving a pedagogical
introduction to the analytic properties of the perturbative S-matrix from a
modern point of view, we illustrate all the points on explicit examples, both
symbolically and numerically. To help with the investigation of related
questions, we introduce a number of tools, including holomorphic cutting rules,
new approaches to dispersion relations, as well as formulae for local behavior
of Feynman integrals near branch points.
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Level-rank duality of SU(2)k Chern-Simons theory, and of hypergraph and
magic states: The level-rank duality of SU(2)k Chern-Simons theory is discussed, and
applied to graph, hypergraph, and magic states.
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Algebro-geometric Feynman rules: We give a general procedure to construct algebro-geometric Feynman rules,
that is, characters of the Connes-Kreimer Hopf algebra of Feynman graphs that
factor through a Grothendieck ring of immersed conical varieties, via the class
of the complement of the affine graph hypersurface. In particular, this maps to
the usual Grothendieck ring of varieties, defining motivic Feynman rules. We
also construct an algebro-geometric Feynman rule with values in a polynomial
ring, which does not factor through the usual Grothendieck ring, and which is
defined in terms of characteristic classes of singular varieties. This
invariant recovers, as a special value, the Euler characteristic of the
projective graph hypersurface complement. The main result underlying the
construction of this invariant is a formula for the characteristic classes of
the join of two projective varieties. We discuss the BPHZ renormalization
procedure in this algebro-geometric context and some motivic zeta functions
arising from the partition functions associated to motivic Feynman rules.
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Holomorphic potentials for graded D-branes: We discuss gauge-fixing, propagators and effective potentials for topological
A-brane composites in Calabi-Yau compactifications. This allows for the
construction of a holomorphic potential describing the low-energy dynamics of
such systems, which generalizes the superpotentials known from the ungraded
case. Upon using results of homotopy algebra, we show that the string field and
low energy descriptions of the moduli space agree, and that the deformations of
such backgrounds are described by a certain extended version of `off-shell
Massey products' associated with flat graded superbundles. As examples, we
consider a class of graded D-brane pairs of unit relative grade. Upon computing
the holomorphic potential, we study their moduli space of composites. In
particular, we give a general proof that such pairs can form acyclic
condensates, and, for a particular case, show that another branch of their
moduli space describes condensation of a two-form.
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Backreaction in Closed String Tachyon Condensation: We consider backreaction due to production of massless strings in the
background of a condensing closed string tachyon. Working in the region of weak
tachyon, we find the modified equations of motion for massless strings with
conformal perturbation theory. We solve for the positive and negative frequency
modes and estimate the backreaction on the background dilaton. In large
(supercritical) dimensions, we find that the backreaction can be significant in
a large region of spacetime. We work with the bosonic string, but we expect
these results to carry over into the heterotic case.
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A trial to find an elliptic quantum algebra for $sl_2$ using the
Heisenberg and Clifford algebra: A Heisenberg-Clifford realization of a deformed $U(sl_{2})$ by two parameters
$p$ and $q$ is discussed. The commutation relations for this deformed algebra
have interesting connection with the theta functions.
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Segmented strings, brane tilings, and the Y-system: I show that the motion of a closed string consisting of $n$ segments in
AdS$_3$ can be embedded into the mutation dynamics of the $Y^{n,0}$ brane
tiling. The determinant of the Kasteleyn matrix computes the spectral curve.
The dynamics is governed by a Y-system with additional constraints ensuring
that the string closes in target space. The constraints can be deformed by
coupling the worldsheet to a background two-form whose field strength is
proportional to the volume form.
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Tunneling between the giant gravitons in AdS5 x S5: I consider the giant gravitons in AdS5 x S5. By numerical simulation, I show
a strong indication that there is no instanton solution describing the direct
tunneling between the giant graviton in the S5 and its dual counterpart in the
AdS5. I argue that it supports the supersymmetry breaking scenario suggested in
hep-th/0008015
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Varational Equations and Symmetries in the Lagrangian Formalism: Symmetries in the Lagrangian formalism of arbitrary order are analysed with
the help of the so-called Anderson-Duchamp-Krupka equations. For the case of
second order equations and a scalar field we establish a polynomial structure
in the second order derivatives. This structure can be used to make more
precise the form of a general symmetry. As an illustration we analyse the case
of Lagrangian equations with Poincar\'e invariance or with universal
invariance.
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Generalization of the Extended Lagrangian Formalism on a Field Theory
and Applications: Formalism of extended Lagrangian represent a systematic procedure to look for
the local symmetries of a given Lagrangian action. In this work, the formalism
is discussed and applied to a field theory. We describe it in detail for a
field theory with first-class constraints present in the Hamiltonian
formulation. The method is illustrated on examples of electrodynamics,
Yang-Mills field and non-linear sigma model.
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Note on Centrally Extended su(2/2) and Serre Relations: We point out that the nontrivial central extension of the superalgebra
$su(2/2)$ is related to the some not so well-known Serre relations.
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The string tension from smeared Wilson loops at large N: We present the results of a high statistics analysis of smeared Wilson loops
in 4 dimensional SU(N) Yang-Mills theory for various values of N. The data is
used to analyze the behaviour of smeared Creutz ratios, extracting from them
the value of the string tension and other asymptotic parameters. A scaling
analysis allows us to extrapolate to the continuum limit for N=3,5,6 and 8. The
results are consistent with a $1/N^2$ approach towards the large N limit. The
same analysis is done for the TEK model (one-point lattice) for N=841 and a
non-minimal symmetric twist with flux of $k=9$. The results match perfectly
with the extrapolated large N values, confirming the validity of the reduction
idea for this range of parameters.
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Effective Gravitational Couplings of Higher-Rank Supersymmetric Gauge
Theories: When placed on four-manifolds, $ \mathcal{N} = 2 $ gauge theories couple to
topological invariants of the background via two functions $ A $ and $ B $.
General considerations allow for these functions to be fixed in terms of the
Coulomb moduli and other parameters in the theory, but only up to
multiplicative factors about which little is known. We extend earlier work on
the microscopic study of these functions in the $ \Omega $-background to $
\mathcal{N} = 2 ^{\star } $ gauge theories with higher-rank $ \mathrm{U}(N) $
gauge groups. We complement this analysis by carrying out a perturbative study
of these functions. This allows us to determine the manner in which these
multiplicative factors scale with the rank of the gauge group and the mass of
the adjoint hypermultiplet.
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Exact Computations in the Burgers Problem: We complete the program outlined in the paper of the author with A. Migdal
and sum up exactly all the fluctuations around the instanton solution of the
randomly large scale driven Burgers equation. We choose the force correlation
function $\kappa$ to be exactly quadratic function of the coordinate
difference. The resulting probability distribution satisfy the differential
equation proposed by Polyakov without an anomaly term. The result shows that
unless the anomaly term is indeed absent it must come from other possible
instanton solutions, and not from the fluctuations.
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Lorentz-Invariant Non-Commutative QED: Lorentz-invariant non-commutative QED (NCQED) is constructed such that it
should be a part of Lorentz-invariant non-commutative standard model (NCSM), a
subject to be treated in later publications. Our NCSM is based on Connes'
observation that the total fermion field in the standard model may be regarded
as a bi-module over a flavor-color algebra. In this paper, it is shown that
there exist two massless gauge fields in NCQED which are interchanged by $C'$
transformation. Since $C'$ is reduced to the conventional charge conjugation
$C$ in the commutative limit, the two gauge fields become identical to the
photon field in the same limit, which couples to only four spinors with charges
$\pm 2,\pm 1.$ Following Carlson-Carone-Zobin, our NCQED respects Lorentz
invariance employing Doplicher-Fredenhagen-Roberts' algebra instead of the
usual algebra with constant $\theta^{\mu\nu}$. In the new version
$\theta^{\mu\nu}$ becomes an integration variable. We show using a simple NC
scalar model that the $\theta$ integration gives an {\it invariant} damping
factor instead of the oscillating one to the nonplanar self-energy diagram in
the one-loop approximation. Seiberg-Witten map shows that the $\theta$
expansion of NCQED generates exotic but well-motivated derivative interactions
beyond QED with allowed charges being only $0, \pm 1, \pm 2$.
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Remarks on the geometrical properties of semiclassically quantized
strings: We discuss some geometrical aspects of the semiclassical quantization of
string solutions in Type IIB Green-Schwarz action on $\ads_5\times \sphere^5$.
We concentrate on quadratic fluctuations around classical configurations,
expressing the relevant differential operators in terms of (intrinsic and
extrinsic) invariants of the background geometry. The aim of our exercises is
to present some compact expressions encoding the spectral properties of bosonic
and fermionic fluctuations. The appearing of non-trivial structures on the
relevant bundles and their role in concrete computations are also considered.
We corroborate the presentation of general formulas by working out explicitly a
couple of relevant examples, namely the spinning string and the latitude BPS
Wilson loop.
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Closed Strings and Weak Gravity from Higher-Spin Causality: We combine old and new quantum field theoretic arguments to show that any
theory of stable or metastable higher spin particles can be coupled to gravity
only when the gravity sector has a stringy structure. Metastable higher spin
particles, free or interacting, cannot couple to gravity while preserving
causality unless there exist higher spin states in the gravitational sector
much below the Planck scale $M_{\rm pl}$. We obtain an upper bound on the mass
$\Lambda_{\rm gr}$ of the lightest higher spin particle in the gravity sector
in terms of quantities in the non-gravitational sector. We invoke the CKSZ
uniqueness theorem to argue that any weakly coupled UV completion of such a
theory must have a gravity sector containing infinite towers of asymptotically
parallel, equispaced, and linear Regge trajectories. Consequently,
gravitational four-point scattering amplitudes must coincide with the closed
string four-point amplitude for $s,t\gg1$, identifying $\Lambda_{\rm gr}$ as
the string scale. Our bound also implies that all metastable higher spin
particles in 4d with masses $m\ll \Lambda_{\rm gr}$ must satisfy a weak gravity
condition.
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Supersymmetry and Positive Energy in Classical and Quantum
Two-Dimensional Dilaton Gravity: An $N = 1$ supersymmetric version of two dimensional dilaton gravity coupled
to matter is considered. It is shown that the linear dilaton vacuum
spontaneously breaks half the supersymmetries, leaving broken a linear
combination of left and right supersymmetries which squares to time
translations. Supersymmetry suggests a spinorial expression for the ADM energy
$M$, as found by Witten in four-dimensional general relativity. Using this
expression it is proven that ${M}$ is non-negative for smooth initial data
asymptotic (in both directions) to the linear dilaton vacuum, provided that the
(not necessarily supersymmetric) matter stress tensor obeys the dominant energy
condition. A {\it quantum} positive energy theorem is also proven for the
semiclassical large-$N$ equations, despite the indefiniteness of the quantum
stress tensor. For black hole spacetimes, it is shown that $M$ is bounded from
below by $e^{- 2 \phi_H}$, where $\phi_H$ is the value of the dilaton at the
apparent horizon, provided only that the stress tensor is positive outside the
apparent horizon. This is the two-dimensional analogue of an unproven
conjecture due to Penrose. Finally, supersymmetry is used to prove positive
energy theorems for a large class of generalizations of dilaton gravity which
arise in consideration of the quantum theory.
|
Quark mass and condensate in HQCD: We extend the Sakai-Sugimoto holographic model of QCD (HQCD) by including the
scalar bi-fundamental "tachyon" field in the 8-brane-anti-8-brane probe theory.
We show that this field is responsible both for the spontaneous breaking of the
chiral symmetry, and for the generation of (current algebra) quark masses, from
the point of view of the bulk theory. As a by-product we show how this leads to
the Gell-Mann- Oakes-Renner relation for the pion mass.
|
Hyperbolic Black Holes and Open String Production: In this paper we investigate open string pair production effects near
hyperbolic black holes in AdS$_5$. We study the classical dynamics of D3 probe
branes in this background and their quantum tunneling rate across the horizon
from the inside using a method similar to that of Kraus, Parikh and Wilczek.
The hyperbolic black holes can decay through these tunneling events and their
lifetime is estimated. The radiated branes move towards the boundary and do not
bounce back. Their world-lines do not intersect directly and they do not hit
the singularity either, providing a clean scenario for studying the
non-adiabatic pair production effects of open strings stretched between them
near horizon. We find that there is a well defined parameter regime where there
can be significant pair production. This requires the radiated branes to be
highly boosted. However, the radiation of such branes still has small
back-reaction on the black hole background, though the open string pair
production on them can potentially alter the background. We comment on the
possible relation of our model and the AMPS paradox. Some issues and future
directions are discussed in the end.
|
Induced CP-violation in the Euler-Heisenberg Lagrangian: In this paper, we examine the behaviour of the Euler-Heisenberg effective
action in the presence of a novel axial coupling among the gauge field and the
fermionic matter. This axial coupling is responsible to induce a CP-violating
term in the extended form of the Euler-Heisenberg effective action, which is
generated naturally through the analysis of the box diagram. However, this
anomalous model is not a viable extension of QED, and we explicitly show that
the induced CP-violating term in the Euler-Heisenberg effective Lagrangian is
obtained only by adding an axial coupling to the ordinary QED Lagrangian. In
order to perform our analysis, we use a parametrization of the vector and axial
coupling constants, $g_{v}$ and $g_{a}$, in terms of a new coupling $\beta$.
Interestingly, this parametrization allows us to explore a hidden symmetry
under the change of $g_{v}\leftrightarrow g_{a}$ in some diagrams. This
symmetry is explicitly observed in the analysis of the box diagram, where we
determine the $\lambda_i$ coefficients of $\cal{L}_{\rm ext.}^{\rm \small
EH}=\lambda_{1}\cal{F}^{2}+\lambda_{2}\cal{G}^{2}+\lambda_{3}\cal{F}\cal{G}$,
specially the coefficient $\lambda_3$ related with the CP-violating term due to
the axial coupling. As a phenomenological application of the results, we
compute the relevant cross section for the light by light scattering through
the extended Euler-Heisenberg effective action.
|
On the Decay of Massive Fields in de Sitter: Interacting massive fields with m > d H/2 in d+1 dimensional de Sitter space
are fundamentally unstable. Scalar fields in this mass range can decay to
themselves. This process (which is kinematically forbidden in Minkowski space)
can lead to an important change to the propagator and the physics of these
fields. We compute this decay rate by doing a 1-loop computation for a massive
scalar field with a cubic interaction. We resum the 1-loop result by
consistently solving the Schwinger-Dyson equations. We also perform an explicit
resummation of all chain graphs in the case of the retarded propagator. The
decay rate is exponentially suppressed for large m/H and the flat space answer
(vanishing decay rate) is reproduced in that limit.
|
Superconformal Yang-Mills quantum mechanics and Calogero model with
OSp(N|2,R) symmetry: In spacetime dimension two, pure Yang-Mills possesses no physical degrees of
freedom, and consequently it admits a supersymmetric extension to couple to an
arbitrary number, N say, of Majorana-Weyl gauginos. This results in (N,0) super
Yang-Mills. Further, its dimensional reduction to mechanics doubles the number
of supersymmetries, from N to N+N, to include conformal supercharges, and leads
to a superconformal Yang-Mills quantum mechanics with symmetry group
OSp(N|2,R). We comment on its connection to AdS_2 \times S^{N-1} and reduction
to a supersymmetric Calogero model.
|
Higher Forms and Membranes in 4D Supergravities: We review the dynamical generation of coupling constants in 4D supergravity
by means of gauge three-form fields. The latter are introduced as components of
particular chiral supermultiplets and can be coupled to membranes preserving
local supersymmetry. Such a set-up naturally arises from type-II string
compactifications on Calabi-Yau manifolds with fluxes. We present generic 4D
$\mathcal N=1$ supergravity models with three-form multiplets and study domain
wall solutions supported by membranes, which interpolate between vacua with
different values of the cosmological constant.
|
Symmetry Algebras in Chern-Simons Theories with Boundary: Canonical
Approach: I consider the classical Kac-Moody algebra and Virasoro algebra in
Chern-Simons theory with boundary within the Dirac's canonical method and
Noether procedure. It is shown that the usual (bulk) Gauss law constraint
becomes a second-class constraint because of the boundary effect. From this
fact, the Dirac bracket can be constructed explicitly without introducing
additional gauge conditions and the classical Kac-Moody and Virasoro algebras
are obtained within the usual Dirac method. The equivalence to the symplectic
reduction method is presented and the connection to the Ba\~nados's work is
clarified. It is also considered the generalization to the
Yang-Mills-Chern-Simons theory where the diffeomorphism symmetry is broken by
the (three-dimensional) Yang-Mills term. In this case, the same Kac-Moody
algebras are obtained although the two theories are sharply different in the
canonical structures. The both models realize the holography principle
explicitly and the pure CS theory reveals the correspondence of the
Chern-Simons theory with boundary/conformal field theory, which is more
fundamental and generalizes the conjectured anti-de Sitter/conformal field
theory correspondence.
|
Chiral Transition of N=4 Super Yang-Mills with Flavor on a 3-Sphere: We use the AdS/CFT correspondence to perform a numerical study of a phase
transition in strongly-coupled large-Nc N = 4 Super-Yang-Mills theory on a
3-sphere coupled to a finite number Nf of massive N = 2 hypermultiplets in the
fundamental representation of the gauge group. The gravity dual system is a
number Nf of probe D7-branes embedded in AdS_5 x S^5. We draw the phase diagram
for this theory in the plane of hypermultiplet mass versus temperature and
identify for temperatures above the Hawking-Page deconfinement temperature a
first-order phase transition line across which the chiral condensate jumps
discontinuously.
|
A Novel Multi-parameter Family of Quantum Systems with Partially Broken
N-fold Supersymmetry: We develop a systematic algorithm for constructing an N-fold supersymmetric
system from a given vector space invariant under one of the supercharges.
Applying this algorithm to spaces of monomials, we construct a new
multi-parameter family of N-fold supersymmetric models, which shall be referred
to as "type C". We investigate various aspects of these type C models in
detail. It turns out that in certain cases these systems exhibit a novel
phenomenon, namely, partial breaking of N-fold supersymmetry.
|
Localization of scalar and tensor fields in the standing wave braneworld
with increasing warp factor: We investigate scalar and tensor fields in the brane model solution for the
5D space-time with standing gravitational waves in the bulk and show that even
in the case of increasing warp factor there exist normalizable zero modes
localized on the brane.
|
TeV scale black holes thermodynamics with extra dimensions and quantum
gravity effects: TeV scale black hole thermodynamics in the presence of quantum gravity
effects encoded in the existence of a minimal length and a maximal momentum is
studied in a model universe with large extra dimensions.
|
Near-flat space limit and Einstein manifolds: We study the near-flat space limit for strings on AdS(5)xM(5), where the
internal manifold M(5) is equipped with a generic metric with U(1)xU(1)xU(1)
isometry. In the bosonic sector, the limiting sigma model is similar to the one
found for AdS(5)xS(5), as the global symmetries are reduced in the most general
case. When M(5) is a Sasaki-Einstein space like T(1,1), Y(p,q) and L(p,q,r),
whose dual CFT's have N=1 supersymmetry, the near-flat space limit gives the
same bosonic sector of the sigma model found for AdS(5)xS(5). This indicates
the generic presence of integrable subsectors in AdS/CFT.
|
Superconformal Chern-Simons Theories and the Squashed Seven Sphere: We show that there are two supersymmetric completions of the
three-dimensional Chern-Simons theory of level k with gauge group U(N)xU(N)
coupled to four sets of massless scalars and spinors in the bi-fundamental
representation, if we require Sp(2) global symmetry with the matter fields in
the fundamental representation of SU(4). One is the N=6 superconformal theory
recently studied in arXiv:0806.1218 [hep-th] and another is a new theory with
N=1 superconformal symmetry. We conjecture that the N=1 theory is dual to M
theory on AdS_4 x Squashed S^7/Z_k.
|
Two-dimensional quantum Yang-Mills theory with corners: The solution of quantum Yang-Mills theory on arbitrary compact two-manifolds
is well known. We bring this solution into a TQFT-like form and extend it to
include corners. Our formulation is based on an axiomatic system that we hope
is flexible enough to capture actual quantum field theories also in higher
dimensions. We motivate this axiomatic system from a formal
Schroedinger-Feynman quantization procedure. We also discuss the physical
meaning of unitarity, the concept of vacuum, (partial) Wilson loops and
non-orientable surfaces.
|
From Vertex Operators to Calogero-Sutherland Models: The correlation function of the product of N generalized vertex operators
satisfies an infinite set of Ward identities, related to a W_{\infty} algebra,
whose extention out of the mass shell gives rise to equations which can be
considered as a generalization of the compactified Calogero-Sutherland (CS)
hamiltonians. In particular the wave function of the ground state of the
compactified CS model is shown to be given by the value of the product of N
vertex operators between the vacuum and exitated state. The role of vertex
algebra as underlying unifying structure is pointed out.
|
TASI Lectures on Emergence of Supersymmetry, Gauge Theory and String in
Condensed Matter Systems: The lecture note consists of four parts. In the first part, we review a 2+1
dimensional lattice model which realizes emergent supersymmetry at a quantum
critical point. The second part is devoted to a phenomenon called
fractionalization where gauge boson and fractionalized particles emerge as low
energy excitations as a result of strong interactions between gauge neutral
particles. In the third part, we discuss about stability and low energy
effective theory of a critical spin liquid state where stringy excitations
emerge in a large N limit. In the last part, we discuss about an attempt to
come up with a prescription to derive holographic theory for general quantum
field theory.
|
On Exponential corrections to the 1/N expansion in two-dimensional Yang
Mills theory: We compute $e^{-AN}$ corrections to the Gross-Taylor 1/N expansion of the
paritition function of two-dimensional SU(N) and U(N) Yang Mills theory. We
find a very similar structure of mixing between holomorphic and
anti-holomorphic sectors as that described by Vafa for the 1/N expansion. Some
of the non-perturbative terms are suggestive of D-strings wrapping the $T^2$ of
the 2dYM but blowing up into a fuzzy geometry by the Myers effect in the
directions transverse to the $T^2$.
|
Chirality Change in String Theory: It is known that string theory compactifications leading to low energy
effective theories with different chiral matter content ({\it e.g.} different
numbers of standard model generations) are connected through phase transitions,
described by non-trivial quantum fixed point theories.
We point out that such compactifications are also connected on a purely
classical level, through transitions that can be described using standard
effective field theory. We illustrate this with examples, including some in
which the transition proceeds entirely through supersymmetric configurations.
|
Thermodynamic Volume and the Extended Smarr Relation: We continue to explore the scaling transformation in the reduced action
formalism of gravity models. As an extension of our construction, we consider
the extended forms of the Smarr relation for various black holes, adopting the
cosmological constant as the bulk pressure as in some literatures on black
holes. Firstly, by using the quasi-local formalism for charges, we show that,
in a general theory of gravity, the volume in the black hole thermodynamics
could be defined as the thermodynamic conjugate variable to the bulk pressure
in such a way that the first law can be extended consistently. This, so called,
thermodynamic volume can be expressed explicitly in terms of the metric and
field variables. Then, by using the scaling transformation allowed in the
reduced action formulation, we obtain the extended Smarr relation involving the
bulk pressure and the thermodynamic volume. In our approach, we do not resort
to Euler's homogeneous scaling of charges while incorporating the would-be
hairy contribution without any difficulty.
|
Behaviour of Charged Spinning Massless Particles: We revisit the classical theory of a relativistic massless charged point
particle with spin and interacting with an external electromagnetic field. In
particular, we give a proper definition of its kinetic energy and its total
energy, the latter being conserved when the external field is stationary. We
also write the conservation laws for the linear and angular momenta. Finally,
we find that the particle's velocity may differ from $c$ as a result of the
spin---electromagnetic field interaction, without jeopardizing Lorentz
invariance.
|
A Mellin space approach to the conformal bootstrap: We describe in more detail our approach to the conformal bootstrap which uses
the Mellin representation of $CFT_d$ four point functions and expands them in
terms of crossing symmetric combinations of $AdS_{d+1}$ Witten exchange
functions. We consider arbitrary external scalar operators and set up the
conditions for consistency with the operator product expansion. Namely, we
demand cancellation of spurious powers (of the cross ratios, in position space)
which translate into spurious poles in Mellin space. We discuss two contexts in
which we can immediately apply this method by imposing the simplest set of
constraint equations. The first is the epsilon expansion. We mostly focus on
the Wilson-Fisher fixed point as studied in an epsilon expansion about $d=4$.
We reproduce Feynman diagram results for operator dimensions to $O(\epsilon^3)$
rather straightforwardly. This approach also yields new analytic predictions
for OPE coefficients to the same order which fit nicely with recent numerical
estimates for the Ising model (at $\epsilon =1$). We will also mention some
leading order results for scalar theories near three and six dimensions. The
second context is a large spin expansion, in any dimension, where we are able
to reproduce and go a bit beyond some of the results recently obtained using
the (double) light cone expansion. We also have a preliminary discussion about
numerical implementation of the above bootstrap scheme in the absence of a
small parameter.
|
Duality Group for Calabi-Yau 2-Moduli Space: We present an efficient method for computing the duality group $\Gamma$ of
the moduli space \cM for strings compactified on a Calabi-Yau manifold
described by a two-moduli deformation of the quintic polynomial immersed in
$\CP(4)$, $\cW={1\over5}(\iy_1^5+\cdots+\iy_5^5)-a\,\iy_4^3 \iy_5^2 -b\,
\iy_4^2 \iy_5^3$. We show that $\Gamma$ is given by a $3$--dimensional
representation of a central extension of $B_5$, the braid group on five
strands.
|
Asymptotic behavior in a model with Yukawa interaction from
Schwinger-Dyson equations: A system of Schwinger-Dyson equations for pseudoscalar four-dimensional
Yukawa model in the two-particle approximation is investigated. The simplest
iterative solution of the system corresponds to the mean-field approximation
(or, equivalently, to the leading order of 1/N-expansion) and includes a
non-physical Landau pole in deep-Euclidean region for the pseudoscalar
propagator $\Delta$. It is argued, however, that a full solution may be free
from non-physical singularities and has the self-consistent asymptotic behavior
$p^2_e\Delta\simeq C\,\log^{-4/5}\frac{p^2_e}{M^2}$. An approximate solution
confirms the positivity of $C$ and the absence of Landau pole.
|
Hairy black holes in scalar extended massive gravity: We construct static, spherically symmetric black hole solutions in scalar
extended ghost-free massive gravity and show the existence of hairy black holes
in this class of extension. While the existence seems to be a generic feature,
we focus on the simplest models of this extension and find that asymptotically
flat hairy black holes can exist without fine-tuning the theory parameters,
unlike the bi-gravity extension, where asymptotical flatness requires
fine-tuning in the parameter space. Like the bi-gravity extension, we are
unable to obtain asymptotically dS regular black holes in the simplest models
considered, but it is possible to obtain asymptotically AdS black holes.
|
Scalar field theory in Snyder space-time: alternatives: We construct two types of scalar field theory on Snyder space-time. The first
one is based on the natural momenta addition inherent to the coset momentum
space. This construction uncovers a non-associative deformation of the
Poincar\'e symmetries. The second one considers Snyder space-time as a subspace
of a larger non-commutative space. We discuss different possibilities to
restrict the extra-dimensional scalar field theory to a theory living only on
Sndyer space-time and present the consequences of these restrictions on the
Poincar\'e symmetries. We show moreover how the non-associative approach and
the Doplicher-Fredenhagen-Roberts space can be seen as specific approximations
of the extra-dimensional theory. These results are obtained for the 3d
Euclidian Snyder space-time constructed from $\SO(3,1)/\SO(3)$, but our results
extend to any dimension and signature.
|
Topological Anti-Topological Fusion in Four-Dimensional Superconformal
Field Theories: We present some new exact results for general four-dimensional superconformal
field theories. We derive differential equations governing the coupling
constant dependence of chiral primary correlators. For N=2 theories we show
that the Zamolodchikov metric on the moduli space and the operator mixing of
chiral primaries are quasi-topological quantities and constrained by
holomorphy. The equations that we find are the four-dimensional analogue of the
tt* equations in two-dimensions, discovered by the method of "topological
anti-topological fusion" by Cecotti and Vafa. Our analysis relies on conformal
perturbation theory and the superconformal Ward identities and does not use a
topological twist.
|
On the enumeration of irreducible k-fold Euler sums and their roles in
knot theory and field theory: A generating function is given for the number, $E(l,k)$, of irreducible
$k$-fold Euler sums, with all possible alternations of sign, and exponents
summing to $l$. Its form is remarkably simple: $\sum_n E(k+2n,k) x^n =
\sum_{d|k}\mu(d) (1-x^d)^{-k/d}/k$, where $\mu$ is the M\"obius function.
Equivalently, the size of the search space in which $k$-fold Euler sums of
level $l$ are reducible to rational linear combinations of irreducible basis
terms is $S(l,k) = \sum_{n<k}{\lfloor(l+n-1)/2\rfloor\choose n}$. Analytical
methods, using Tony Hearn's REDUCE, achieve this reduction for the 3698
convergent double Euler sums with $l\leq44$; numerical methods, using David
Bailey's MPPSLQ, achieve it for the 1457 convergent $k$-fold sums with
$l\leq7$; combined methods yield bases for all remaining search spaces with
$S(l,k)\leq34$. These findings confirm expectations based on Dirk Kreimer's
connection of knot theory with quantum field theory. The occurrence in
perturbative quantum electrodynamics of all 12 irreducible Euler sums with
$l\leq 7$ is demonstrated. It is suggested that no further transcendental
occurs in the four-loop contributions to the electron's magnetic moment.
Irreducible Euler sums are found to occur in explicit analytical results, for
counterterms with up to 13 loops, yielding transcendental knot-numbers, up to
23 crossings.
|
Aspects of holography for theories with hyperscaling violation: We analyze various aspects of the recently proposed holographic theories with
general dynamical critical exponent z and hyperscaling violation exponent
$\theta$. We first find the basic constraints on $z, \theta$ from the gravity
side, and compute the stress-energy tensor expectation values and scalar
two-point functions. Massive correlators exhibit a nontrivial exponential
behavior at long distances, controlled by $\theta$. At short distance, the
two-point functions become power-law, with a universal form for $\theta > 0$.
Next, the calculation of the holographic entanglement entropy reveals the
existence of novel phases which violate the area law. The entropy in these
phases has a behavior that interpolates between that of a Fermi surface and
that exhibited by systems with extensive entanglement entropy. Finally, we
describe microscopic embeddings of some $\theta \neq 0$ metrics into full
string theory models -- these metrics characterize large regions of the
parameter space of Dp-brane metrics for $p\neq 3$. For instance, the theory of
N D2-branes in IIA supergravity has z=1 and $\theta = -1/3$ over a wide range
of scales, at large $g_s N$.
|
Inflation from Minkowski Space: We propose a class of scalar models that, once coupled to gravity, lead to
cosmologies that smoothly and stably connect an inflationary quasi-de Sitter
universe to a low, or even zero-curvature, maximally symmetric spacetime in the
asymptotic past, strongly violating the null energy condition ($\dot H\gg H^2$)
at intermediate times. The models are deformations of the conformal galileon
lagrangian and are therefore based on symmetries, both exact and approximate,
that ensure the quantum robustness of the whole picture. The resulting
cosmological backgrounds can be viewed as regularized extensions of the
galilean genesis scenario, or, equivalently, as `early-time-complete'
realizations of inflation. The late-time inflationary dynamics possesses
phenomenologically interesting properties: it can produce a large
tensor-to-scalar ratio within the regime of validity of the effective field
theory and can lead to sizeable equilateral nongaussianities.
|
Unification in Intersecting Brane Models: We propose a unification scenario for supersymmetric intersecting brane
models. The quarks and leptons are embedded into adjoint representations of
SO(32), which are obtained and break by type I string compactified on
orbifolds. Its single unified gauge coupling can give rise to different gauge
couplings below the unification scale, due to effects of magnetic fluxes. The
crucial mechanism is brane recombination preserving supersymmetry.
|
Supersymmetric Bethe Ansatz and Baxter Equations from Discrete Hirota
Dynamics: We show that eigenvalues of the family of Baxter Q-operators for
supersymmetric integrable spin chains constructed with the gl(K|M)-invariant
$R$-matrix obey the Hirota bilinear difference equation. The nested Bethe
ansatz for super spin chains, with any choice of simple root system, is then
treated as a discrete dynamical system for zeros of polynomial solutions to the
Hirota equation. Our basic tool is a chain of Backlund transformations for the
Hirota equation connecting quantum transfer matrices. This approach also
provides a systematic way to derive the complete set of generalized Baxter
equations for super spin chains.
|
Towards NMHV amplitudes at strong coupling: Pentagon Operator Product Expansion provides a non-perturbative framework for
analysis of scattering amplitudes in planar maximally supersymmetric gauge
theory building up on their duality to null polygonal super Wilson loop and
integrability. In this paper, we construct a systematic expansion for the main
ingredients of the formalism, i.e., pentagons, at large 't Hooft coupling as a
power series in its inverse value. The calculations are tested against
relations provided by the so-called Descent Equation which mixes transitions at
different perturbative orders. We use leading order results to have a first
glimpse into the structure of scattering amplitude at NMHV level at strong
coupling.
|
Inhomogeneity of a rotating quark-gluon plasma from holography: Rotation affects the transition temperature between confined (hadronic) and
deconfined (quark-gluon plasma) phases of the strongly interacting matter
produced in non-central heavy ion collisions. A holographic description of this
effect was presented recently, considering an AdS black hole with cylindrical
symmetry in rotation. Here we extend this approach in order to analyse the more
realistic case of strongly interacting matter that, rather than living in a
cylindrical shell, spreads over a region around the rotational axis. In this
case, the confined and deconfined phases may coexist. The holographic
description of the plasma behaviour under rotation is shown to be consistent
with the concept of local temperature for rotating frames developed by Tolman
and Ehrenfest.
|
White Holes, Black Holes and Cpt in Two Dimensions: It is argued that a unitarity-violating but weakly CPT invariant
superscattering matrix exists for leading-order large-$N$ dilaton gravity, if
and only if one includes in the Hilbert space planckian ``thunderpop"
excitations which create white holes. CPT apparently cannot be realized in a
low-energy effective theory in which such states have been integrated out.
Rules for computing the leading-large-$N$ superscattering are described in
terms of quantum field theory on a single multiply-connected spacetime obtained
by sewing the future (past) horizons of the original spacetime with the past
(future) horizons of its CPT conjugate. Some difficulties which may arise in
going beyond leading order in $1/N$ are briefly discussed.
|
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