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A study of Bosonic and Fermionic Theories at Large Charge: The aim of this thesis is to systematically and consistently study strongly
coupled bosonic and fermionic conformal field theories using the large quantum
number expansion. The idea behind it is to study sectors of conformal field
theories that are characterised by large quantum numbers under global
symmetries. In this limit, the conformal field theories, even if they initially
were strongly coupled and interacting, can now be written in terms of an
effective field theory that is weakly coupled. Some common effective field
theories that appear in the literature are the bosonic conformal superfluid and
the Fermi sphere, condensed matter systems characterised by a high particle
density, making the study of such systems a cross-disciplinary matter.
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Quantum motion equation and Poincare translation invariance of
noncommutative field theory: We study the Moyal commutators and their expectation values between vacuum
states and non-vacuum states for noncommutative scalar field theory. For
noncommutative $\phi^{\star4}$ scalar field theory, we derive its
energy-momentum tensor from translation transformation and Lagrange field
equation. We generalize the Heisenberg and quantum motion equations to the form
of Moyal star-products for noncommutative $\phi^{\star4}$ scalar field theory
for the case $\theta^{0i}=0$ of spacetime noncommutativity. Then we demonstrate
the Poincar{\' e} translation invariance for noncommutative $\phi^{\star4}$
scalar field theory for the case $\theta^{0i}=0$ of spacetime noncommutativity.
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Triply Special Relativity: We describe an extension of special relativity characterized by {\it three}
invariant scales, the speed of light, $c$, a mass, $\kappa$ and a length $R$.
This is defined by a non-linear extension of the Poincare algerbra, $\cal A$,
which we describe here. For $R\to \infty$, $\cal A$ becomes the Snyder
presentation of the $\kappa$-Poincare algebra, while for $\kappa \to \infty$ it
becomes the phase space algebra of a particle in deSitter spacetime. We
conjecture that the algebra is relevant for the low energy behavior of quantum
gravity, with $\kappa$ taken to be the Planck mass, for the case of a nonzero
cosmological constant $\Lambda = R^{-2}$. We study the modifications of
particle motion which follow if the algebra is taken to define the Poisson
structure of the phase space of a relativistic particle.
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Spectra of BPS Strings in 6d Supergravity and the Swampland: We explore BPS strings in supergravity theories in six-dimensions and related
Swampland Conjectures. We first propose a general modular ansatz for
bootstrapping elliptic genera of 2d worldvolume theories on strings in the 6d
theories. By employing mirror symmetry on F-theory examples, we explicitly
compute the elliptic genera and validate our ansatz. We extend this approach to
investigate BPS strings and their spectrum in non-geometric 6d theories which
have no known F-theory constructions, and confirm the Swampland conjectures,
including the Weak Gravity Conjecture, Distance Conjecture, and Emergent String
Conjecture. We also discuss tensionless little strings that emerge near
infinite-distance limits of strong gauge coupling in the moduli space of
certain special theories.
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Gauge theory on $Z_2 \times Z_2 \ti Z_2 $ Discrete Group and a
Spontaneous $CP$ Violation Toy Model: In the spirit of Non-commutative differential calculus on discrete group, we
construct a toy model of spontaneous $CP$ violation (SCPV). Our model is
different from the well-known Weinberg-Branco model although it involves three
Higgs doublets and preserve neutral flavor current conservation (NFC) after
using the $Z_2 \ti Z_2 \ti Z_2$ discrete symmetry and imposing some constraints
on Yukawa couplings.
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Two-loop corrections to the topological mass term in thermal QED_3: We study the radiative corrections to the Chern-Simons mass term at two loops
in 2+1 dimensional quantum electrodynamics at finite temperature. We show that,
in contrast to the behavior at zero temperature, thermal effects lead to a non
vanishing contribution at this order. Using this result, as well as the large
gauge Ward identity for the leading parity violating terms in the static limit,
we determine the leading order parity violating effective action in this limit
at two loops, which generalizes the one-loop effective action proposed earlier.
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Extended Y-system for the $AdS_5/CFT_4$ correspondence: We study the analytic properties of the $AdS_5/CFT_4$ Y functions. It is
shown that the TBA equations, including the dressing factor, can be obtained
from the Y-system with some additional information on the square-root
discontinuities across semi-infinite segments in the complex plane. The
Y-system extended by the discontinuity relations constitutes a fundamental set
of local functional constraints that can be easily transformed into integral
form through Cauchy's theorem.
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N=4 Supersymmetric Quantum Mechanics with Magnetic Monopole: We propose an N=4 supersymmetric quantum mechanics of a charged particle on a
sphere in the background of Dirac magnetic monopole and study the system using
the CP(1) model approach. We explicitly calculate the symmetry algebra taking
the operator ordering ambiguity into consideration. We find that it is given by
the superalgebra SU(1|2)x SU(2). We show that the Hamiltonian can be written in
terms of the Casimir invariant of SU(2). Using this relation and the lower
bound for angular momentm we obtain the energy spectrum. We then examine the
ground energy sector to find that the N=4 supersymmetry is spontaneously broken
to N=2 for certain values of the monopole charge.
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Oscillator Level for Black Holes and Black Rings: Microscopic calculations of the Bekenstein-Hawking entropy of supersymmetric
black holes in string theory are typically based on the application to a dual
2D CFT of Cardy's formula, S=2\pi \sqrt{c q /6}, where `c' is the central
charge and `q' is the oscillator level. In the CFT, q is non-trivially related
to the total momentum. We identify a Komar integral that equals q when
evaluated at the horizon, and the total momentum when evaluated at asymptotic
infinity, thus providing a gravitational dual of the CFT result.
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Basic Twist Quantization of osp(1|2) and kappa-- Deformation of D=1
Superconformal Mechanics: The twisting function describing a nonstandard (super-Jordanian) quantum
deformation of $osp(1|2)$ is given in explicite closed form. The quantum
coproducts and universal R-matrix are presented. The non-uniqueness of the
twisting function as well as two real forms of the deformed $osp(1|2)$
superalgebras are considered. One real quantum $osp(1|2)$ superalgebra is
interpreted as describing the $\kappa$-deformation of D=1, N=1 superconformal
algebra, which can be applied as a symmetry algebra of N=1 superconformal
mechanics.
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Formal Higher-Spin Theories and Kontsevich-Shoikhet-Tsygan Formality: The formal algebraic structures that govern higher-spin theories within the
unfolded approach turn out to be related to an extension of the Kontsevich
Formality, namely, the Shoikhet-Tsygan Formality. Effectively, this allows one
to construct the Hochschild cocycles of higher-spin algebras that make the
interaction vertices. As an application of these results we construct a family
of Vasiliev-like equations that generate the Hochschild cocycles with $sp(2n)$
symmetry from the corresponding cycles. A particular case of $sp(4)$ may be
relevant for the on-shell action of the $4d$ theory. We also give the exact
equations that describe propagation of higher-spin fields on a background of
their own. The consistency of formal higher-spin theories turns out to have a
purely geometric interpretation: there exists a certain symplectic invariant
associated to cutting a polytope into simplices, namely, the Alexander-Spanier
cocycle.
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Confining potential in a color dielectric medium with parallel domain
walls: We study quark confinement in a system of two parallel domain walls
interpolating different color dielectric media. We use the phenomenological
approach in which the confinement of quarks appears considering the QCD vacuum
as a color dielectric medium. We explore this phenomenon in QCD_2, where the
confinement of the color flux between the domain walls manifests, in a scenario
where two 0-branes (representing external quark and antiquark) are connected by
a QCD string. We obtain solutions of the equations of motion via first-order
differential equations. We find a new color confining potential that increases
monotonically with the distance between the domain walls.
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Spontaneous Symmetry Breaking of Lorentz and (Galilei) Boosts in
(Relativistic) Many-Body Systems: We extend a result by Ojima on spontaneous symmetry breaking of Lorentz
boosts in thermal (KMS) states and show that it is in fact a special case in a
more general class of examples of spontaneous symmetry breaking of Lorentz
symmetry in relativistic many-body systems. Furthermore we analyse the nature
of the corresponding Goldstone phenomenon and the type of Goldstone excitations
(provided they have particle character).
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Consistency in Perturbative Calculations and Radiatively Induced Lorentz
and CPT Violations: The origin of the radiatively induced Lorentz and CPT violations, in
perturbative evaluations, of an extended version of QED, is investigated. Using
a very general calculational method, concerning the manipulations and
calculations involving divergent amplitudes, we clearly identify the possible
sources of contributions for the violating terms. We show that consistency in
the perturbative calculations, in a broader sense, leaves no room for the
existence of radiatively induced contributions which is in accordance with what
was previously conjectured and recently advocated by some authors supported on
general arguments.
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Space-like branes, accelerating cosmologies and the near `horizon' limit: It is known that there exist two different classes of time dependent
solutions in the form of space-like (or S)-branes in the low energy M/string
theory. Accelerating cosmologies are known to arise from S-branes in one class,
but not in the other where the time-like holography in the dS/CFT type
correspondence may be more transparent. We show how the accelerating
cosmologies arise from S-branes in the other class. Although we do not get the
de Sitter structure in the lowest order supergravity, the near `horizon' ($t\to
0$) limits of these S-branes are the generalized Kasner metric.
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Regular (2+1)-dimensional black holes within non-linear Electrodynamics: (2+1)-regular static black hole solutions with a nonlinear electric field are
derived. The source to the Einstein equations is an energy momentum tensor of
nonlinear electrodynamics, which satisfies the weak energy conditions and in
the weak field limit becomes the (2+1)-Maxwell field tensor. The derived class
of solutions is regular; the metric, curvature invariants and electric field
are regular everywhere. The metric becomes, for a vanishing parameter, the
(2+1)-static charged BTZ solution. A general procedure to derive solutions for
the static BTZ (2+1)-spacetime, for any nonlinear Lagrangian depending on the
electric field is formulated; for relevant electric fields one requires the
fulfillment of the weak energy conditions.
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Gauge theories on $κ$-Minkowski spaces: Twist and modular operators: We discuss the construction of $\kappa$-Poincar\'e invariant actions for
gauge theories on $\kappa$-Minkowski spaces. We consider various classes of
untwisted and (bi)twisted differential calculi. Starting from a natural class
of noncommutative differential calculi based on a particular type of twisted
derivations belonging to the algebra of deformed translations, combined with a
twisted extension of the notion of connection, we prove an algebraic relation
between the various twists and the classical dimension d of the
$\kappa$-Minkowski space(-time) ensuring the gauge invariance of the candidate
actions for gauge theories. We show that within a natural differential calculus
based on a distinguished set of twisted derivations, d=5 is the unique value
for the classical dimension at which the gauge action supports both the gauge
invariance and the $\kappa$-Poincar\'e invariance. Within standard (untwisted)
differential calculi, we show that the full gauge invariance cannot be
achieved, although an invariance under a group of transformations constrained
by the modular (Tomita) operator stemming from the $\kappa$-Poincar\'e
invariance still holds.
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Topological Strings with Scaling Violation and Toda Lattice Hierarchy: We show that there is a series of topological string theories whose
integrable structure is described by the Toda lattice hierarchy. The monodromy
group of the Frobenius manifold for the matter sector is an extension of the
affine Weyl group $\widetilde W (A_N^{(1)})$ introduced by Dubrovin. These
models are generalizations of the topological $CP^1$ string theory with scaling
violation. The logarithmic Hamiltonians generate flows for the puncture
operator and its descendants. We derive the string equation from the
constraints on the Lax and the Orlov operators. The constraints are of
different type from those for the $c=1$ string theory. Higher genus expansion
is obtained by considering the Lax operator in matrix form.
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T-duality simplifies bulk-boundary correspondence: the noncommutative
case: We state and prove a general result establishing that T-duality simplifies
the bulk-boundary correspondence, in the sense of converting it to a simple
geometric restriction map. This settles in the affirmative several earlier
conjectures of the authors, and provides a clear geometric picture of the
correspondence. In particular, our result holds in arbitrary spatial dimension,
in both the real and complex cases, and also in the presence of disorder,
magnetic fields, and H-flux. These special cases are relevant both to String
Theory and to the study of the quantum Hall effect and topological insulators
with defects in Condensed Matter Physics.
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On the Compactification of Type IIA String Theory: The ten-dimensional type IIA string effective action with cosmological
constant term is dimensionally reduced on a d-dimensional torus to derive lower
dimensional effective action. The symmetries of the reduced effective action
are examined. It is shown that the resulting six-dimensional theory does not
remain invariant under $SO(4,4)$ symmetry whereas the reduced action, in the
absence of the cosmological constant respects the symmetry as was shown by Sen
and Vafa. New class of black hole solutions are obtained in five and four
dimensions in the presence of cosmological constant. For the six-dimensional
theory, a four-brane solution is also presented.
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Effect of the quartic gradient terms on the critical exponents of the
Wilson-Fisher fixed point in $O(N)$ models: The effect of the $\ord{\partial^4}$ terms of the gradient expansion on
anomalous dimension $\eta$ and the correlation length's critical exponent $\nu$
of the Wilson-Fisher fixed point has been determined for the Euclidean $O(N)$
model for $N=1$ and the number of dimensions $2< d<4$ as well as for $N\ge 2$
and $d=3$. Wetterich's effective average action renormalization group method is
used with field-independent derivative couplings and Litim's optimized
regulator. It is shown that the critical theory for $N\ge 2$ is well
approximated by the effective average action preserving $O(N)$ symmetry with
the accuracy of $\ord{\eta}$.
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Holographic entanglement in spin network states: a focused review: In the long-standing quest to reconcile gravity with quantum mechanics,
profound connections have been unveiled between concepts traditionally
pertaining to quantum information theory, such as entanglement, and
constitutive features of gravity, like holography. Developing and promoting
these connections from the conceptual to the operational level unlocks access
to a powerful set of tools, which can be pivotal towards the formulation of a
consistent theory of quantum gravity. Here, we review recent progress on the
role and applications of quantum informational methods, in particular tensor
networks, for quantum gravity models. We focus on spin network states dual to
finite regions of space, represented as entanglement graphs in the group field
theory approach to quantum gravity, and illustrate how techniques from random
tensor networks can be exploited to investigate their holographic properties.
In particular, spin network states can be interpreted as maps from bulk to
boundary, whose holographic behaviour increases with the inhomogeneity of their
geometric data (up to becoming proper quantum channels). The entanglement
entropy of boundary states, which are obtained by feeding such maps with
suitable bulk states, is then proved to follow a bulk area law, with
corrections due to the entanglement of the bulk state. We further review how
exceeding a certain threshold of bulk entanglement leads to the emergence of a
black hole-like region, revealing intriguing perspectives for quantum
cosmology.
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A Model for Topological Fermions: We introduce a model designed to describe charged particles as stable
topological solitons of a field with values on the internal space S^3. These
solitons behave like particles with relativistic properties like Lorentz
contraction and velocity dependence of mass. This mass is defined by the energy
of the soliton. In this sense this model is a generalisation of the sine-Gordon
model from 1+1 dimensions to 3+1 dimensions, from S^1 to S^3. (We do not chase
the aim to give a four-dimensional generalisation of Coleman's isomorphism
between the Sine-Gordon model and the Thirring model which was shown in
2-dimensional space-time.) For large distances from the center of solitons this
model tends to a dual U(1)-theory with freely propagating electromagnetic
waves. Already at the classical level it describes important effects, which
usually have to be explained by quantum field theory, like
particle-antiparticle annihilation and the running of the coupling.
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A Heterotic Multimonopole Solution: An exact multimonopole solution of heterotic string theory is presented. The
solution is constructed by a modification of the 't Hooft ansatz for a
four-dimensional instanton. An analogous solution in Yang-Mills field theory
saturates a Bogomoln'yi bound and possesses the topology and far field limit of
a multimonopole configuration, but has divergent action near each source. In
the string solution, however, the divergences from the Yang-Mills sector are
precisely cancelled by those from the gravity sector. The resultant action is
finite and easily computed. The Manton metric on moduli space for the
scattering of two string monopoles is found to be flat to leading order in the
impact parameter, in agreement with the trivial scattering predicted by a test
monopole calculation.
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Constrained Dynamical Systems: Separation of Constraints into First and
Second Classes: In the Dirac approach to the generalized Hamiltonian formalism, dynamical
systems with first- and second-class constraints are investigated. The
classification and separation of constraints into the first- and second-class
ones are presented with the help of passing to an equivalent canonical set of
constraints. The general structure of second-class constraints is clarified.
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Calabi-Yau Three-folds: Poincare Polynomials and Fractals: We study the Poincare polynomials of all known Calabi-Yau three-folds as
constrained polynomials of Littlewood type, thus generalising the well-known
investigation into the distribution of the Euler characteristic and Hodge
numbers. We find interesting fractal behaviour in the roots of these
polynomials in relation to the existence of isometries, distribution versus
typicality, and mirror symmetry.
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Attractor horizons in six-dimensional type IIB supergravity: We consider near horizon geometries of extremal black holes in
six-dimensional type IIB supergravity. In particular, we use the entropy
function formalism to compute the charges and thermodynamic entropy of these
solutions. We also comment on the role of attractor mechanism in understanding
the entropy of the Hopf T-dual solutions in type IIA supergravity.
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Correct Treatment of 1/(η\cdot k)^p Singularities in the Axial Gauge
Propagator: The propagators in axial-type, light-cone and planar gauges contain
1/(\eta\cdot k)^p-type singularities. These singularities have generally been
treated by inventing prescriptions for them. In this work, we propose an
alternative procedure for treating these singularities in the path integral
formalism using the known way of treating the singularities in Lorentz gauges.
To this end, we use a finite field-dependent BRS transformation that
interpolates between Lorentz-type and the axial-type gauges. We arrive at the
$\epsilon$-dependent tree propagator in the axial-type gauges. We examine the
singularity structure of the propagator and find that the axial gauge
propagator so constructed has {\it no} spurious poles (for real $k$). It
however has a complicated structure in a small region near $\eta\cdot k=0$. We
show how this complicated structure can effectively be replaced by a much
simpler propagator.
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Tunneling of a Massless Field through a 3D Gaussian Barrier: We propose a method for the approximate computation of the Green function of
a scalar massless field Phi subjected to potential barriers of given size and
shape in spacetime. This technique is applied to the case of a 3D gaussian
ellipsoid-like barrier, placed on the axis between two pointlike sources of the
field. Instead of the Green function we compute its temporal integral, that
gives the static potential energy of the interaction of the two sources. Such
interaction takes place in part by tunneling of the quanta of Phi across the
barrier. We evaluate numerically the correction to the potential in dependence
on the size of the barrier and on the barrier-sources distance.
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Combinatorial Dyson-Schwinger equations in noncommutative field theory: We give here the Hopf algebra structure describing the noncommutative
renormalization of a recently introduced translation-invariant model on Moyal
space. We define Hochschild one-cocyles $B_+^\gamma$ which allows us to write
down the combinatorial Dyson-Schwinger equations for noncommutative quantum
field theory. One- and two-loops examples are explicitly worked out.
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Time-Dependent Dilatonic Domain Walls: Time-dependent domain wall solutions with infinitesimal thickness are
obtained in the theory of a scalar field coupled to gravity with the dilaton,
i.e. the Jordan-Brans-Dicke gravity. The value of the dilaton is determined in
terms of the Brans-Dicke parameter $\omega$. In particular, the solutions exist
for any $\omega>0$ and as $\omega\to\infty$ we obtain new solutions in general
relativity. They have horizons whose sizes depend on $\omega$.
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Minor Identities for Quasideterminants and Quantum Determinants: We present several identities involving quasi-minors of noncommutative
generic matrices. These identities are specialized to quantum matrices,
yielding q-analogues of various classical determinantal formulas.
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Double Field Theory as the Double Copy of Yang-Mills: We show that double field theory arises from the color-kinematic double copy
of Yang-Mills theory. A precise double copy prescription for the Yang-Mills
action at quadratic and cubic order is provided that yields the double field
theory action in which the duality invariant dilaton has been integrated out.
More precisely, at quadratic order this yields the gauge invariant double field
theory, while at cubic order it yields the cubic double field theory action
subject to a gauge condition that originates from Siegel gauge in string field
theory.
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Neutron stars and phase diagram in a hard-wall AdS/QCD model: We study the phase diagram of (large-$N_c$) QCD using a simplistic
holographic hard-wall model with a dynamical scalar field and a homogeneous
Ansatz representing a smeared instanton/baryon density. The resulting phase
diagram is qualitatively consistent with expectations, including a mesonic,
baryonic, quarkyonic, and quark-gluon plasma phase. As in other holographic
models, we also find a baryonic popcorn transition, which appears at large
chemical potential as a crossover. We then evaluate the nuclear matter equation
of state, which turns out to be rather stiff with a large peaked sound velocity
above the conformal limit, construct corresponding neutron stars using the TOV
equations, and finally use a full numerical gravity/hydrodynamics computation
to extract the gravitational wave signal of neutron star mergers.
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Some considerations on the Mac Dowell-Mansouri action: A precise relation is established between the Stelle-West formulation of the
Mac Dowell-Mansouri approach to a gauge theory of gravity and the approach
based on a gauged Wess-Zumino-Witten term. In particular, it is shown that a
consistent truncation of the latter correspond to the former. A brief review of
the Lovelock-Chern-Simons motivation behind the gauged WZW ones is also done.
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AdS interpretation of two-point correlation function of QED: We have considered the two-point correlation of QED in worldline formalism.
In position space it has been written in terms of heat kernel. This leads to
introducing the $K_1$ function, which is related with the bulk-to-boundary
propagator of massless scalar field and to reveal bulk-to-boundary propagator
in the expression of photon polarization operator.
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Brane World in a Topological Black Hole Bulk: We consider a static brane in the background of a topological black hole, in
arbitrary dimensions. For hyperbolic horizons, we find a solution only when the
black hole mass assumes its minimum negative value. In this case, the tension
of the brane vanishes, and the brane position coincides with the location of
the horizon. For an elliptic horizon, we show that the massless mode of
Randall-Sundrum is recovered in the limit of large black hole mass.
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The emergence of Strange metal and Topological Liquid near Quantum
Critical Point in a solvable model: We discuss quantum phase transition by an exactly solvable model in the dual
gravity setup. By considering the effect of the scalar condensation on the
fermion spectrum near the quantum critical point(QCP), we find that there is a
topologically protected fermion zero mode associated with the metal to
insulator transition. We also show that the strange metal phase with T-linear
resistivity emerges at high enough temperature as far as the gravity has a
horizon. The phase boundaries are calculated according to the density of
states, giving insights on structures of the phase diagram near the QCP.
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The Relation Between Gauge and Non-Gauge Abelian Models: This work studies the relationship between gauge-invariant and non
gauge-invariant abelian vector models. Following a technique introduced by
Harada and Tsutsui, we show that the Proca and the Chiral Schwinger models may
both be viewed as gauge-fixed versions of genuinely gauge- invariant models.
This leads to the proposal that any consistent Abelian vector model with no
gauge symmetry can be understood as a gauge theory that had its gauge fixed,
which establishes an equivalence between gauge-invariant and non
gauge-invariant models. Finally, we show that a gauge-invariant version of the
chiral Schwinger model, after integrating out the fermionic degrees of freedom,
can be identified with the two-dimensional Stueckelberg model without the gauge
fixing term.
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Measurements without Probabilities in the Final State Proposal: The black hole final state proposal reconciles the infalling vacuum with the
unitarity of the Hawking radiation, but only for some experiments. We study
experiments that first verify the exterior, then the interior purification of
the same Hawking particle. (This is the same protocol that renders the firewall
paradox operationally meaningful in standard quantum mechanics.) We show that
the decoherence functional fails to be diagonal, even upon inclusion of
external "pointer" systems. Hence, probabilities for outcomes of these
measurements are not defined. We conclude that the final state proposal does
not offer a consistent alternative to the firewall hypothesis.
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Fermion localization on branes with generalized dynamics: In this letter we consider a specific model of braneworld with nonstandard
dynamics diffused in the literature, specifically we focus our attention on the
matter energy density, the energy of system, the Ricci scalar and the thin
brane limit. As the model is classically stable and capable of localize
gravity, as a natural extension we address the issue of fermion localization of
fermions on a thick brane constructed out from one scalar field with
nonstandard kinetic terms coupled with gravity. The contribution of the
nonstandard kinetic terms in the problem of fermion localization is analyzed.
It is found that the simplest Yukawa coupling $\eta\bar{\Psi}\phi\Psi$ support
the localization of fermions on the thick brane. It is shown that the zero mode
for left-handed can be localized on the thick brane depending on the values for
the coupling constant $\eta$.
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Noncommutative Quantum Mechanics: The Two-Dimensional Central Field: Quantum mechanics in a noncommutative plane is considered. For a general two
dimensional central field, we find that the theory can be perturbatively solved
for large values of the noncommutative parameter ($\theta$) and explicit
expressions for the eigenstates and eigenvalues are given. The Green function
is explicitly obtained and we show that it can be expressed as an infinite
series. For polynomial type potentials, we found a smooth limit for small
values of $\theta$ and for non-polynomial ones this limit is necessarily
abrupt. The Landau problem, as a limit case of a noncommutative system, is also
considered.
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Emergence of Superstring from Pure Spinor: Starting with a classical action where a pure spinor $\lambda^\alpha$ is only
a fundamental and dynamical variable, the pure spinor formalism for
superparticle and superstring is derived by following the BRST formalism. In
this formalism, not only the string variable $x^m$ but also the space-time
spinor $\theta^\alpha$ are emerged as the Faddeev-Popov (FP) ghosts of a
topological symmetry and its reducible symmetry. This study suggests that the
fundamental theory behind the pure spinor formalism of the superstring might be
a topological field theory.
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Topological Disorder Operators in Three-Dimensional Conformal Field
Theory: Many abelian gauge theories in three dimensions flow to interacting conformal
field theories in the infrared. We define a new class of local operators in
these conformal field theories which are not polynomial in the fundamental
fields and create topological disorder. They can be regarded as
higher-dimensional analogues of twist and winding-state operators in free 2d
CFTs. We call them monopole operators for reasons explained in the text. The
importance of monopole operators is that in the Higgs phase, they create
Abrikosov-Nielsen-Olesen vortices. We study properties of these operators in
three-dimensional QED using large N_f expansion. In particular, we show that
monopole operators belong to representations of the conformal group whose
primaries have dimension of order N_f. We also show that monopole operators
transform non-trivially under the flavor symmetry group, with the precise
representation depending on the value of the Chern-Simons coupling.
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Cyclic Monopoles: We study charge k SU(2) BPS monopoles which are symmetric under the cyclic
group of order k. Approximate twistor data (spectral curves and Nahm data) is
constructed using a new technique based upon a Painleve analysis of Nahm's
equation around a pole. With this data both analytical and numerical
approximate ADHMN constructions are performed to study the zeros of the Higgs
field and the monopole energy densities. The results describe, via the moduli
space approximation, a novel type of low energy k monopole scattering.
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Generalized entanglement entropy and holography: In this work, we first introduce a generalized von Neumann entropy that
depends only on the density matrix. This is based on a previous proposal by one
of us modifying the Shannon entropy by considering non-equilibrium systems on
stationary states, and an entropy functional depending only on the probability.
We propose a generalization of the replica trick and find that the resulting
modified von Neumann entropy is precisely the previous mentioned entropy that
was obtained by other assumptions. Then, we address the question whether
alternative entanglement entropies can play a role in the gauge/gravity
duality. Our focus are 2d CFT and their gravity duals. Our results show
corrections to the von Neumann entropy $S_0$ that are larger than the usual
$UV$ ones and also than the corrections to the length dependent $AdS_3$ entropy
which result comparable to the $UV$ ones. The correction terms due to the new
entropy would modify the Ryu-Takayanagi identification between the CFT and the
gravitational $AdS_3$ entropies.
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On the supersymmetric extension of asymptotic symmetries in three
spacetime dimensions: In this work we obtain known and new supersymmetric extensions of diverse
asymptotic symmetries defined in three spacetime dimensions by considering the
semigroup expansion method. The super-$BMS_3$, the superconformal algebra and
new infinite-dimensional superalgebras are obtained by expanding the
super-Virasoro algebra. The new superalgebras obtained are supersymmetric
extensions of the asymptotic algebras of the Maxwell and the
$\mathfrak{so}(2,2)\oplus\mathfrak{so}(2,1)$ gravity theories. We extend our
results to the $\mathcal{N}=2$ and $\mathcal{N}=4$ cases and find that
R-symmetry generators are required. We also show that the new
infinite-dimensional structures are related through a flat limit $\ell
\rightarrow \infty$.
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Super Lie n-algebra extensions, higher WZW models, and super p-branes
with tensor multiplet fields: We formalize higher dimensional and higher gauge WZW-type sigma-model local
prequantum field theory, and discuss its rationalized/perturbative description
in (super-)Lie n-algebra homotopy theory (the true home of the "FDA"-language
used in the supergravity literature). We show generally how the intersection
laws for such higher WZW-type sigma-model branes (open brane ending on
background brane) are encoded precisely in (super-) L-infinity-extension theory
and how the resulting "extended (super-)spacetimes" formalize spacetimes
containing sigma model brane condensates. As an application we prove in Lie
n-algebra homotopy theory that the complete super p-brane spectrum of
superstring/M-theory is realized this way, including the pure sigma-model
branes (the "old brane scan") but also the branes with tensor multiplet
worldvolume fields, notably the D-branes and the M5-brane. For instance the
degree-0 piece of the higher symmetry algebra of 11-dimensional spacetime with
an M2-brane condensate turns out to be the "M-theory super Lie algebra". We
also observe that in this formulation there is a simple formal proof of the
fact that type IIA spacetime with a D0-brane condensate is the 11-dimensional
sugra/M-theory spacetime, and of (prequantum) S-duality for type IIB string
theory. Finally we give the non-perturbative description of all this by higher
WZW-type sigma-models on higher super-orbispaces with higher WZW terms in
stacky differential cohomology.
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Some Applications of Ricci Flow in Physics: I discuss certain applications of the Ricci flow in physics. I first review
how it arises in the renormalization group (RG) flow of a nonlinear sigma
model. I then review the concept of a Ricci soliton and recall how a soliton
was used to discuss the RG flow of mass in 2-dimensions. I then present recent
results obtained with Oliynyk on the flow of mass in higher dimensions. The
final section discusses one way in which Ricci flow may arise in general
relativity, particularly for static metrics.
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Localized Tachyons and the g_cl conjecture: We consider C/Z_N and C^2/Z_N orbifolds of heterotic string theories and Z_N
orbifolds of AdS_3. We study theories with N=2 worldsheet superconformal
invariance and construct RG flows. Following Harvey, Kutasov, Martinec and
Moore, we compute g_cl and show that it decreases monotonically along RG flows-
as conjectured by them. For the heterotic string theories, the gauge degrees of
freedom do not contribute to the computation of g_cl.
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Quantum Information Bound on the Energy: According to the classical Penrose inequality, the mass at spatial infinity
is bounded from below by a function of the area of certain trapped surfaces. We
exhibit quantum field theory states that violate this relation at the
semiclassical level. We formulate a Quantum Penrose Inequality, by replacing
the area with the generalized entropy of the lightsheet of an appropriate
quantum trapped surface. We perform a number of nontrivial tests of our
proposal, and we consider and rule out alternative formulations. We also
discuss the relation to weak cosmic censorhip.
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Dynamically generated magnetic moment in the Wigner-function formalism: We study how the mass and magnetic moment of the quarks are dynamically
generated in nonequilibrium quark matter. We derive the equal-time transport
and constraint equations for the quark Wigner function in a magnetized quark
model and solve them in the semi-classical expansion. The quark mass and
magnetic moment are self-consistently coupled to the Wigner function and
controlled by the kinetic equations. While the quark mass is dynamically
generated at the classical level, the quark magnetic moment is a pure quantum
effect, induced by the quark spin interaction with the external magnetic field.
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Physical Interpretation Of Certain Strong Coupling Singularities: We interpret certain strong coupling singularities of the $E_8\times E_8$
heterotic string on K3 in terms of exotic six-dimensional theories in which
$E_8$ is a gauge symmetry. These theories are closely related to theories
obtained at small instanton singularities, which have $E_8$ as a global
symmetry.
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On (multi-)center branes and exact string vacua: Multicenter supergravity solutions corresponding to Higgs phases of
supersymmetric Yang-Mills theories are considered. For NS5 branes we identify
three cases where there is a description in terms of exact conformal field
theories. Other supergravity solutions, such as D3-branes with angular
momentum, are understood as special limits of multicenter ones. Within our
context we also consider 4-dim gravitational multi-instantons.
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Modular Invariants, Graphs and $α$-Induction for Nets of
Subfactors. III: In this paper we further develop the theory of $\alpha$-induction for nets of
subfactors, in particular in view of the system of sectors obtained by mixing
the two kinds of induction arising from the two choices of braiding. We
construct a relative braiding between the irreducible subsectors of the two
``chiral'' induced systems, providing a proper braiding on their intersection.
We also express the principal and dual principal graphs of the local subfactors
in terms of the induced sector systems. This extended theory is again applied
to conformal or orbifold embeddings of SU(n) WZW models. A simple formula for
the corresponding modular invariant matrix is established in terms of the two
inductions, and we show that it holds if and only if the sets of irreducible
subsectors of the two chiral induced systems intersect minimally on the set of
marked vertices i.e. on the ``physical spectrum'' of the embedding theory, or
if and only if the canonical endomorphism sector of the conformal or orbifold
inclusion subfactor is in the full induced system. We can prove either
condition for all simple current extensions of SU(n) and many conformal
inclusions, covering in particular all type I modular invariants of SU(2) and
SU(3), and we conjecture that it holds also for any other conformal inclusion
of SU(n) as well. As a by-product of our calculations, the dual principal graph
for the conformal inclusion $SU(3)_5 \subset SU(6)_1$ is computed for the first
time.
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SU(N) affine Toda solitons and breathers from transparent Dirac
potentials: Transparent scalar and pseudoscalar potentials in the one-dimensional Dirac
equation play an important role as self-consistent mean fields in 1+1
dimensional four-fermion theories (Gross-Neveu, Nambu-Jona Lasinio models) and
quasi-one dimensional superconductors (Bogoliubov-De Gennes equation). Here, we
show that they also serve as seed to generate a large class of classical
multi-soliton and multi-breather solutions of su(N) affine Toda field theories,
including the Lax representation and the corresponding vector. This generalizes
previous findings about the relationship between real kinks in the Gross-Neveu
model and classical solitons of the sinh-Gordon equation to complex twisted
kinks.
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Entropy of Quantum States: Ambiguities: The von Neumann entropy of a generic quantum state is not unique unless the
state can be uniquely decomposed as a sum of extremal or pure states. As
pointed out to us by Sorkin, this happens if the GNS representation (of the
algebra of observables in some quantum state) is reducible, and some
representations in the decomposition occur with non-trivial degeneracy. This
non-unique entropy can occur at zero temperature. We will argue elsewhere in
detail that the degeneracies in the GNS representation can be interpreted as an
emergent broken gauge symmetry, and play an important role in the analysis of
emergent entropy due to non-Abelian anomalies. Finally, we establish the
analogue of an H-theorem for this entropy by showing that its evolution is
Markovian, determined by a stochastic matrix.
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Supersymmetric Multi-trace Boundary Conditions in AdS: Boundary conditions for massive fermions are investigated in AdS_d for $d \ge
2$. For fermion masses in the range $0 \le |m| < 1/2\ell$ with $\ell$ the AdS
length, the standard notion of normalizeability allows a choice of boundary
conditions. As in the case of scalars at or slightly above the
Breitenlohner-Freedman (BF) bound, such boundary conditions correspond to
multi-trace deformations of any CFT dual. By constructing appropriate boundary
superfields, for d=3,4,5 we identify joint scalar/fermion boundary conditions
which preserve either ${\cal N}=1$ supersymmetry or ${\cal N}=1$ superconformal
symmetry on the boundary. In particular, we identify boundary conditions
corresponding via AdS/CFT (at large N) to a 595-parameter family of
double-trace marginal deformations of the low-energy theory of N M2-branes
which preserve ${\cal N} =1$ superconformal symmetry. We also establish that
(at large N and large 't Hooft coupling $\lambda$) there are no marginal or
relevant multi-trace deformations of 3+1 ${\cal N} =4$ super Yang-Mills which
preserve even ${\cal N}=1$ supersymmetry.
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The Plancherel Formula for the Universal Covering Group of SL(2,R)
Revisited: The Plancherel formula for the universal covering group of $SL(2, R)$ derived
earlier by Pukanszky on which Herb and Wolf build their Plancherel theorem for
general semisimple groups is reconsidered. It is shown that a set of unitarily
equivalent representations is treated by these authors as distinct.
Identification of this equivalence results in a Plancherel measure
($s\mathrm{Re}\tanh\pi(s+\frac{i\tau}{2}), 0\leq\tau<1)$ which is different
from the Pukanszky-Herb-Wolf measure ($s\mathrm{Re}\tanh\pi(s+i\tau),
0\leq\tau<1)$.
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A Note on Four-Point Functions in Logarithmic Conformal Field Theory: The generic structure of 4-point functions of fields residing in
indecomposable representations of arbitrary rank is given. The presented
algorithm is illustrated with some non-trivial examples and permutation
symmetries are exploited to reduce the number of free structure-functions,
which cannot be fixed by global conformal invariance alone.
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Perturbative search for dead-end CFTs: To explore the possibility of self-organized criticality, we look for CFTs
without any relevant scalar deformations (a.k.a dead-end CFTs) within
power-counting renormalizable quantum field theories with a weakly coupled
Lagrangian description. In three dimensions, the only candidates are pure
(Abelian) gauge theories, which may be further deformed by Chern-Simons terms.
In four dimensions, we show that there are infinitely many non-trivial
candidates based on chiral gauge theories. Using the three-loop beta functions,
we compute the gap of scaling dimensions above the marginal value, and it can
be as small as $\mathcal{O}(10^{-5})$ and robust against the perturbative
corrections. These classes of candidates are very weakly coupled and our
perturbative conclusion seems difficult to refute. Thus, the hypothesis that
non-trivial dead-end CFTs do not exist is likely to be false in four
dimensions.
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Trans-Planckian censorship and single-field inflaton potential: It was recently proposed that a field theory cannot be consistent with
quantum gravity if it allows a mode shorter than the Planck length to exit the
Hubble horizon. This is called the Trans-Planckian Censorship Conjecture (TCC).
We discuss the implications of the TCC on the possible shape of the inflaton
potential in single-field slow-roll inflation. We point out that (1) there is
generically an initial condition in which the total e-folding number
$N_\text{total}$ is doubled or more compared to the e-folds necessary for the
cosmic microwave background fluctuations, and (2) a sizable negative running of
spectral index is generically expected to make $N_\text{total}$ small. In
concrete setups, we find a stringent constraint on the inflationary energy
scale, $V_\text{inf}^{1/4} < \mathcal{O}(10) \, \text{TeV}$ with $r <
\mathcal{O}(10^{-50})$, and the running parameter is bounded above as
$\alpha_\text{s} \lesssim - 4 \times 10^{-3}$.
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Electron-pair condensation in parity-preserving QED3: In this paper, we present a parity-preserving QED3 with spontaneous breaking
of a local U(1)-symmetry. The breaking is accomplished by a potential of the
\vf^6-type. It is shown that a net attractive interaction appears in the
M{\o}ller scattering (s and p-wave scattering between two electrons) as
mediated by the gauge field and a Higgs scalar. This might favour a
pair-condensation mechanism.
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Bloch Electron in a Magnetic Field : Diagonalization of Tight-Binding
Models: A connection of a variety of tight-binding models of noninteracting electrons
on a rectangular lattice in a magnetic field with theta functions is
established. A new spectrum generating symmetry is discovered which essentialy
reduces the problem of diagonalization of these models. Provided that one knows
one eigenvector at one point in the parameter space of the corresponding Harper
equation one knows an eigenfunction of the corresponding model in the whole
range of momentum singlet out by the Landau gauge.
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Quantum Giant Magnons: The giant magnons are classical solitons of the O(N) sigma-model, which play
an important role in the AdS/CFT correspondence. We study quantum giant magnons
first at large N and then exactly using Bethe Ansatz, where giant magnons can
be interpreted as holes in the Fermi sea. We also identify a solvable limit of
Bethe Ansatz in which it describes a weakly-interacting Bose gas at zero
temperature. The examples include the O(N) model at large N, weakly interacting
non-linear Schrodinger model, and nearly isotropic XXZ spin chain in the
magnetic field.
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The S-matrix of the Faddeev-Reshetikhin Model, Diagonalizability and PT
Symmetry: We study the question of diagonalizability of the Hamiltonian for the
Faddeev-Reshetikhin (FR) model in the two particle sector. Although the two
particle S-matrix element for the FR model, which may be relevant for the
quantization of strings on $AdS_{5}\times S^{5}$, has been calculated recently
using field theoretic methods, we find that the Hamiltonian for the system in
this sector is not diagonalizable. We trace the difficulty to the fact that the
interaction term in the Hamiltonian violating Lorentz invariance leads to
discontinuity conditions (matching conditions) that cannot be satisfied. We
determine the most general quartic interaction Hamiltonian that can be
diagonalized. This includes the bosonic Thirring model as well as the bosonic
chiral Gross-Neveu model which we find share the same S-matrix. We explain this
by showing, through a Fierz transformation, that these two models are in fact
equivalent. In addition, we find a general quartic interaction Hamiltonian,
violating Lorentz invariance, that can be diagonalized with the same two
particle S-matrix element as calculated by Klose and Zarembo for the FR model.
This family of generalized interaction Hamiltonians is not Hermitian, but is
$PT$ symmetric. We show that the wave functions for this system are also $PT$
symmetric. Thus, the theory is in a $PT$ unbroken phase which guarantees the
reality of the energy spectrum as well as the unitarity of the S-matrix.
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Two-Dimensional Gauge Theory and Matrix Model: We study a matrix model obtained by dimensionally reducing Chern-Simon theory
on S^3. We find that the matrix integration is decomposed into sectors
classified by the representation of SU(2). We show that the N-block sectors
reproduce SU(N) Yang-Mills theory on S^2 as the matrix size goes to infinity.
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Spinor Field Realizations of the half-integer $W_{2,s}$ Strings: The grading Becchi-Rouet-Stora-Tyutin (BRST) method gives a way to construct
the integer $W_{2,s}$ strings, where the BRST charge is written as
$Q_B=Q_0+Q_1$. Using this method, we reconstruct the nilpotent BRST charges
$Q_{0}$ for the integer $W_{2,s}$ strings and the half-integer $W_{2,s}$
strings. Then we construct the exact grading BRST charge with spinor fields and
give the new realizations of the half-integer $W_{2,s}$ strings for the cases
of $s=3/2$, 5/2, and 7/2.
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Abelian duality, walls and boundary conditions in diverse dimensions: We systematically apply the formalism of duality walls to study the action of
duality transformations on boundary conditions and local and nonlocal operators
in two, three, and four-dimensional free field theories. In particular, we
construct a large class of D-branes for two-dimensional sigma-models with
toroidal targets and determine the action of the T-duality group on it. It is
manifest in this formalism that T-duality transformations on D-branes are given
by a differential-geometric version of the Fourier-Mukai transform.
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Generalised perturbation equations in bouncing cosmologies: We consider linear perturbation equations for long-wavelength scalar metric
perturbations in generalised gravity, applicable to non-singular cosmological
models including a bounce from collapse to expansion in the very early
universe. We present the general form for the perturbation equations which
follows from requiring that the inhomogeneous universe on large scales obeys
the same local equations as the homogeneous Friedmann-Robertson-Walker
background cosmology (the separate universes approach). In a
pseudo-longitudinal gauge this becomes a homogeneous second-order differential
equation for adiabatic perturbations, which reduces to the usual equation for
the longitudinal gauge metric perturbation in general relativity with vanishing
anisotropic stress. As an application we show that the scale-invariant spectrum
of perturbations in the longitudinal gauge generated during an ekpyrotic
collapse are not transferred to the growing mode of adiabatic density
perturbations in the expanding phase in a simple bounce model.
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Symplectic Three-Algebra and N=6, Sp(2N) X U(1) Superconformal
Chern-Simons-Matter Theory: We introduce an anti-symmetric metric into a 3-algebra and call it a
symplectic 3-algebra. The N=6, Sp(2N) X U(1) superconformal Chern-Simons-matter
theory with SU(4) R-symmetry in three dimensions is constructed by specifying
the 3-brackets in a symplectic 3-algebra. We also demonstrate that the N=6,
U(M) X U(N) theory can be recast into this symplectic 3-algebraic framework.
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Fractional soft limits: It is a common lore that the amplitude for a scattering process involving one
soft Nambu--Goldstone boson should scale like an integer power of the soft
momentum. We revisit this expectation by considering the $2 \to 2$ scattering
of phonons in solids. We show that, depending on the helicities of the phonons
involved in the scattering process, the scattering amplitude may in fact vanish
like a fractional power of the soft momentum. This is a peculiarity of the
4-point amplitude, which can be traced back to (1) the (spontaneous or
explicit) breaking of Lorentz invariance, and (2) the approximately collinear
kinematics arising when one of the phonons becomes soft. Our results extend to
the general class of non-relativistic shift-invariant theories of a vector
field.
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Towards the Fradkin-Vasiliev formalism in three dimensions: In this paper we show that using frame-like gauge invariant formulation for
the massive bosonic and fermionic fields in three dimensions the free
Lagrangians for these fields can be rewritten in the explicitly gauge invariant
form in terms of the appropriately chosen set of gauge invariant objects. This
in turn opens the possibility to apply the Fradkin-Vasiliev formalism to the
investigation of possible interactions of such fields.
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On the spectrum of QCD(1+1) with large numbers of flavours N_F and
colours N_C near N_F/N_C = 0: QCD(1+1) in the limit of a large number of flavours N_F and a large number of
colours N_C is examined in the small N_F/N_C regime. Using perturbation theory
in N_F/N_C, stringent results for the leading behaviour of the spectrum
departing from N_F/N_C = 0 are obtained. These results provide benchmarks in
the light of which previous truncated treatments of QCD(1+1) at large N_F and
N_C are critically reconsidered.
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Quantum and string shape fluctuations in the dual Monopole
Nambu-Jona-Lasinio model with dual Dirac strings: The magnetic monopole condensate is calculated in the dual Monopole
Nambu-Jona-Lasinio model with dual Dirac strings suggested in Refs.[1,2] as a
functional of the dual Dirac string shape. The calculation is carried out in
the tree approximation in the scalar monopole-antimonopole collective
excitation field. The integration over quantum fluctuations of the dual-vector
monopole-antimonopole collective excitation field around the Abrikosov flux
line and string shape fluctuations are performed explicitly. We claim that
there are important contributions of quantum and string shape fluctuations to
the magnetic monopole condensate.
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Coulomb branch in 3d $\mathcal{N}=2$ $SU(N)_k$ Chern-Simons gauge
theories with chiral matter content: We elaborate on quantum moduli spaces in 3d $\mathcal{N}=2$ $SU(N)_k$
Chern-Simons gauge theories with $F$ fundamental and $\bar{F}$ anti-fundamental
matter fields. The quantum flat direction on the Coulomb branch differs so much
from the classical one and from the one of the vector-like theories. In many
cases, the Coulomb branch is parametrized by the dressed monopoles. As is found
from the computation of the superconformal index, these dressed operators at
first sight appear to be dressed by massive elementary fields which don't seem
to contribute to the low-energy physics. We argue that these dressed fields can
be interpreted as a non-abelian monopole dressed (or not dressed) by massless
matter fields. Based on this analysis, we will report on the s-confinement
phases with non-trivial monopole operators, which is consistent with the
duality proposals \cite{Aharony:2014uya, Aharony:2013dha}. Along these studies,
we find that the duality reported in \cite{Aharony:2014uya} must be modified
when $k=\pm \frac{1}{2}(F-\bar{F})$ in order to have a correct duality map of
the baryonic operators.
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Path Integral Approach to Fermionic Vacuum Energy in Non-parallel
D1-Branes: The fermionic one loop vacuum energy of the superstring theory in a system of
non-parallel D1-branes is derived by applying the path integral formalism.
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Features of planar Lee-Wick electrodynamics: In this letter we study some aspects of the planar Lee-Wick electrodynamics
near a perfectly conducting line (unidimensional mirror). Specifically, the
modified Lee-wick propagator due to the presence of a conducting line is
calculated, and the interaction between the mirror and the point-like charge is
investigated. It is shown that the behavior of this interaction is very
different from the one already known for the $(3+1)$-dimensional Lee-Wick
electrodynamics, where we have a planar mirror. It is also shown that the image
method is not valid in planar Lee-Wick electrodynamics and the dimensional
reduction yields a stronger taming of divergences.
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Quantum complexity and the virial theorem: It is conjectured that in the geometric formulation of quantum computing, one
can study quantum complexity through classical entropy of statistical ensembles
established non-relativistically in the group manifold of unitary operators.
The kinetic and positional decompositions of statistical entropy are
conjectured to correspond to the Kolmogorov complexity and computational
complexity, respectively, of corresponding quantum circuits. In this paper, we
claim that by applying the virial theorem to the group manifold, one can derive
a generic relation between Kolmogorov complexity and computational complexity
in the thermal equilibrium.
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SUSY Shape-Invariant Hamiltonians for the Generalized Dirac-Coulomb
Problem: A spin $\frac 12$ relativistic particle described by a general potential in
terms of the sum of the Coulomb potential with a Lorentz scalar potential is
investigated via supersymmetry in quantum mechanics.
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Vacuum stability, string density of states and the Riemann zeta function: We study the distribution of graded degrees of freedom in classically stable
oriented closed string vacua and use the Rankin-Selberg transform to link it to
the finite one-loop vacuum energy. In particular, we find that the spectrum of
physical excitations not only must enjoy asymptotic supersymmetry but actually,
at very large mass, bosonic and fermionic states must follow a universal
oscillating pattern, whose frequencies are related to the zeros of the Riemann
zeta-function. Moreover, the convergence rate of the overall number of the
graded degrees of freedom to the value of the vacuum energy is determined by
the Riemann hypothesis. We discuss also attempts to obtain constraints in the
case of tachyon-free open-string theories.
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On the Algebraic Theory of Soliton and Antisoliton Sectors: We consider the properties of massive one particle states on a translation
covariant Haag-Kastler net in Minkowski space. In two dimensional theories,
these states can be interpreted as soliton states and we are interested in the
existence of antisolitons. It is shown that for each soliton state there are
three different possibilities for the construction of an antisoliton sector
which are equivalent if the (statistical) dimension of the corresponding
soliton sector is finite.
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Description of the Heterotic String Solutions in U(N) SQCD: We continue the study of heterotic non-Abelian BPS-saturated flux tubes
(strings). Previously, such solutions were obtained [1] in a particular U(2)
gauge theory: N=2 supersymmetric QCD deformed by superpotential terms of a
special type breaking N=2 supersymmetry down to N=1. Here we generalize the
previous results to U(N) gauge theories. As was suggested by Edalati and Tong
[2], the string world sheet theory is a heterotic N=(0,2) sigma model, with the
CP(N-1) target space for bosonic fields and an extra right-handed fermion which
couples to the fermion fields of the N=(2,2) CP(N-1) model. We derive the
heterotic N=(0,2) world sheet model directly from the U(N) bulk theory.
Parameters of the bulk theory are related to those of the world sheet theory.
Qualitatively this relation turns out to be the same as in the U(2) case.
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Multigluon amplitudes, ${\cal N}=4$ constraints and the WZW model: Classical ${\cal N}=4$ Yang-Mills theory is defined by the superspace
constraints. We obtain a solution of a subset of these constraints and show
that it leads to the maximally helicity violating (MHV) amplitudes. The action
which leads to the solvable part of the constraints is a Wess-Zumino-Witten
(WZW) action on a suitably extended superspace. The non-MHV tree amplitudes can
also be expressed in terms of this action.
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Electromagnetic Strings: Complementarity between Time and Temperature: We investigate some of the intricate features in a gravity decoupling limit
of a open bosonic string theory, in a constant electromagnetic (EM-) field. We
explain the subtle nature of space-time at short distances, due to its
entanglement with the gauge field windings in the theory. Incorporating the
mass-shell condition in the theory, we show that the time coordinate is small,
of the order of EM-string scale, and the space coordinates are large. We
perform a careful analysis in the critical regime to describe the decoupling of
a series of gauge-string windings in successions, just below the Hagedorn
temperature. We argue for the condensation of gauge-string at the Hagedorn
temperature, which is followed by the decoupling of tachyonic particles. We
demonstrate the phenomena by revoking the effective noncommutative dynamics for
the D(3)-brane and obtain nonlinear corrections to U(1) gauge theory. We
discuss the spontaneous breaking of noncommutative U(1) symmetry and show that
the Hagedorn phase is described by the noninteracting gauge particles. The
notion of time reappears in the phase at the expense of temperature. It
suggests a complementarity between two distinct notions, time and temperature,
at short distances.
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Zero-Curvature Formalism of Supersymmetric Principal Chiral Model: We investigate one-parameter family of transformation on superfields of super
principal chiral model and obtain different zero-curvature representations of
the model. The parametric transformation is related to the super Riccati
equations and an infinite set of local and non-local conservation laws is
derived. A Lax representation of the model is presented which gives rise to a
superspace monodromy operator.
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Gauge Dual and Noncommutative Extension of an N=2 Supergravity Solution: We investigate some properties of a recent supergravity solution of Pilch and
Warner, which is dual to the N=4 gauge theory softly broken to N=2. We verify
that a D3-brane probe has the expected moduli space and its effective action
can be brought to N=2 form. The kinetic term for the probe vanishes on an
enhancon locus, as in earlier work on large-n N=2 theories, though for the
Pilch-Warner solution this locus is a line rather than a ring. On the gauge
theory side we find that the probe metric can be obtained from a perturbative
one-loop calculation; this principle may be useful in obtaining the
supergravity dual at more general points in the N=2 gauge theory moduli space.
We then turn on a B-field, following earlier work on the N=4 theory, to obtain
the supergravity dual to the noncommutative N=2 theory.
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Heterotic Z6-II MSSM Orbifolds in Blowup: Heterotic orbifolds provide promising constructions of MSSM-like models in
string theory. We investigate the connection of such orbifold models with
smooth Calabi-Yau compactifications by examining resolutions of the T^6/Z6-II
orbifold (which are far from unique) with Abelian gauge fluxes. These gauge
backgrounds are topologically characterized by weight vectors of twisted
states; one per fixed point or fixed line. The VEV's of these states generate
the blowup from the orbifold perspective, and they reappear as axions on the
blowup. We explain methods to solve the 24 resolution dependent Bianchi
identities and present an explicit solution. Despite that a solution may
contain the MSSM particle spectrum, the hypercharge turns out to be anomalous:
Since all heterotic MSSM orbifolds analyzed so far have fixed points where only
SM charged states appear, its gauge group can only be preserved provided that
those singularities are not blown up. Going beyond the comparison of purely
topological quantities (e.g. anomalous U(1) masses) may be hampered by the fact
that in the orbifold limit the supergravity approximation to lowest order in
alpha prime is breaking down.
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Entanglement Entropy across the Lattice-Continuum Correspondence: This paper revisits standard calculations of free field entanglement entropy
in light of the newly developed lattice-continuum correspondence. This
correspondence prescribes an explicit method to extract an approximately
continuum quantum field theory out of a fully regularized lattice theory. This
prescription will here be extended to subregion algebras, and it will be shown
how entropies of continuum boson and fermion theories can be computed by
working purely with lattice quantities. This gives a clear picture of the
origin of divergences in entanglement entropy while also presenting a concise
and detailed recipe for calculating this important quantity in continuum
theories.
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On Democratic String Field Theories: We reexamine democratic open string field theories, namely, theories in which
string fields are not constrained to a single picture number and picture
changing is obtained as a gauge transformation. We describe several
possibilities for regular free theories and attempt to construct the lowest
order interaction term and identify the lowest order gauge transformation for
some of these theories. We also discuss projections over string field spaces
that might be needed for a consistent off-shell implementation of picture
changing.
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On the sigma-model of deformed special geometry: We discuss the deformed sigma-model that arises when considering
four-dimensional N=2 abelian vector multiplets in the presence of an arbitrary
chiral background field. In addition, we allow for a class of deformations of
special geometry by non-holomorphic terms. We analyze the geometry of the
sigma-model in terms of intrinsic torsion classes. We show that, generically,
the deformed geometry is non-Kahler. We illustrate our findings with an
example. We also express the deformed sigma-model in terms of the Hesse
potential that underlies the real formulation of special geometry.
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A robust explanation of CMB anomalies with a new formulation of
inflationary quantum fluctuations: The presence of CMB Hemispherical Asymmetry (HPA) challenges the current
understanding of inflationary cosmology which does not generically predict the
parity violation in the primordial correlations. In this paper, we shall review
the recently proposed resolution to this based on a new formulation of
quantizing inflationary fluctuations by focusing on the discrete spacetime
transformations in a gravitational context. The predictive power of this
formulation is that one can generate a scale dependent HPA in the context of
single field inflation for all the primordial modes including scalar and tensor
fluctuations without introducing any additional parameters. This result can be
seen as an indication of spontaneous breaking of
$\mathcal{C}\mathcal{P}\mathcal{T}$ symmetry in an expanding Universe, if
confirmed by future observations it would be a great leap in the subject of
quantum field theory in curved spacetime.
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SUSY properties of warped AdS$_3$: We examine supersymmetric properties of null-warped AdS$_3$, or alternatively
Schrodinger geometries, dual to putative warped CFTs in two dimensions. We
classify super Schrodinger subalgebras of the superalgebra psu(1, 1$|$2)
$\oplus$ psu(1, 1$|$2), corresponding to the superconformal algebra of the
AdS$_3 \times$ S$^3$ geometry. We comment on geometric realisations and provide
a string theory description with enhanced supersymmetry in terms of
intersecting D3-branes. For type IIB supergravity solutions based on T$^{1,1}$,
we consider the relationship between five-dimensional Schrodinger solutions and
their three-dimensional null-warped counterparts, corresponding to R symmetry
twists. Finally, we study a family of null-warped AdS$_3$ solutions in a
setting where there is an ambiguity over the R symmetry and confirm that, for
examples admitting a Kaluza-Klein (KK) reduction to three dimensions, the
minimisation of a real superpotential of the three-dimensional gauged
supergravity captures the central charge and R symmetry.
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Holographic networks for (1+1)-dimensional de Sitter spacetime: Holographic tensor networks associated to tilings of (1+1)-dimensional de
Sitter spacetime are introduced. Basic features of these networks are
discussed, compared, and contrasted with conjectured properties of quantum
gravity in de Sitter spacetime. Notably, we highlight a correspondence between
the quantum information capacity of the network and the cosmological constant.
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An Infra-Red Finite Electron Propagator: We investigate the properties of a dressed electron which reduces, in a
particular class of gauges, to the usual fermion. A one loop calculation of the
propagator is presented. We show explicitly that an infra-red finite,
multiplicative, mass shell renormalisation is possible for this dressed
electron, or, equivalently, for the usual fermion in the abovementioned gauges.
The results are in complete accord with previous conjectures.
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Dissipative hydrodynamics and heavy ion collisions: Space-time evolution and subsequent particle production from minimally
viscous ($\eta/s$=0.08) QGP fluid is studied using the 2nd order
Israel-Stewart's theory of dissipative relativistic fluid. Compared to ideal
fluid, energy density or temperature evolves slowly in viscous dynamics.
Particle yield at high $p_T$ is increased. Elliptic flow on the other hand
decreases in viscous dynamics. Minimally viscous QGP fluid found to be
consistent with a large number of experimental data.
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$Q\bar Q$ potential from AdS-CFT relation at $T\geq 0$: Dependence on
orientation in internal space and higher curvature corrections: Within the classical approximation we calculate the static $Q\bar Q$
potential via the AdS/CFT relation for nonzero temperature and arbitrary
internal orientation of the quarks. We use a higher order curvature corrected
target space background. For timelike Wilson loops there arises a critical line
in the orientation-distance plane which is shifted to larger distances relative
to the calculation with uncorrected background. Beyond that line there is no
$Q\bar Q$-force. The overall vanishing of the force for antipodal orientation
known from zero tempera ture remains valid. The spacelike Wilson loops yield a
string tension for a (2+1)-dimensional gauge theory, independent of the
relative internal orientation, but sensitive to the background correction.
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The Club Sandwich: Gapless Phases and Phase Transitions with
Non-Invertible Symmetries: We provide a generalization of the Symmetry Topological Field Theory (SymTFT)
framework to characterize phase transitions and gapless phases with categorical
symmetries. The central tool is the club sandwich, which extends the SymTFT
setup to include an interface between two topological orders: there is a
symmetry boundary, which is gapped, and a physical boundary that may be
gapless, but in addition, there is also a gapped interface in the middle. The
club sandwich generalizes so-called Kennedy-Tasaki (KT) transformations.
Building on the results in [1, 2] on gapped phases with categorical symmetries,
we construct gapless theories describing phase transitions with non-invertible
symmetries by applying suitable KT transformations on known phase transitions
provided by the critical Ising model and the 3-state Potts model. We also
describe in detail the order parameters in these gapless theories
characterizing the phase transitions, which are generally mixtures of
conventional and string-type order parameters mixed together by the action of
categorical symmetries. Additionally, removing the physical boundary from the
club sandwiches results in club quiches, which characterize all possible gapped
boundary phases with (possibly non-invertible) symmetries that can arise on the
boundary of a bulk gapped phase. We also provide a mathematical
characterization of gapped boundary phases with symmetries as pivotal tensor
functors whose targets are pivotal multi-fusion categories.
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Time and M-theory: We review our recent proposal for a background independent formulation of a
holographic theory of quantum gravity. The present review incorporates the
necessary background material on geometry of canonical quantum theory,
holography and spacetime thermodynamics, Matrix theory, as well as our specific
proposal for a dynamical theory of geometric quantum mechanics, as applied to
Matrix theory. At the heart of this review is a new analysis of the conceptual
problem of time and the closely related and phenomenologically relevant problem
of vacuum energy in quantum gravity. We also present a discussion of some
observational implications of this new viewpoint on the problem of vacuum
energy.
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New 4D, N = 1 Superfield Theory: Model of Free Massive Superspin-3/2
Multiplet: We present a Lagrangian formulation for the free superspin-3/2 massive 4D,
N=1 superfield. The model is described by a dynamical real vector superfield
and an auxiliary real scalar superfield. The corresponding multiplet contains
spin-1, spin-2 and two spin-3/2 propagating component fields on-shell. The
auxillary superfield is needed to ensure that the on-shell vector superfield
carries only the irreducible representation of the Poincare supergroup with a
given mass and the fixed superspin of 3/2. The bosonic sector of the component
level of the model is also presented.
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Constant curvature holomorphic solutions of the supersymmetric
grassmannian sigma model: the case of $G(2,4)$: We explore the constant curvature holomorphic solutions of the supersymmetric
grassmannian sigma model $G(M,N)$ using in particular the gauge invariance of
the model. Supersymmetric invariant solutions are constructed via generalizing
a known result for ${C}P^{N-1}$. We show that some other such solutions also
exist. Indeed, considering the simplest case of $G(2,N)$ model, we give
necessary and sufficient conditions for getting the constant curvature
holomorphic solutions. Since, all the constant curvature holomorphic solutions
of the bosonic $G(2,4)$ $\sigma$-model are known, we treat this example in
detail.
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Gauged supergravity algebras from twisted tori compactifications with
fluxes: Using the equivalence between Scherk-Schwarz reductions and twisted tori
compactifications, we discuss the effective theories obtained by this procedure
from M-theory and N =4 type II orientifold constructions with Neveu-Schwarz and
Ramond-Ramond form fluxes turned on. We derive the gauge algebras of the
effective theories describing their general features, in particular the
symplectic embedding in the duality symmetries of the theory. The generic gauge
theory is non-abelian and its gauge group is given by the semidirect product of
subgroups of SL(7) or SL(p-3) x SL(9-p) for p=3,...,9, with generators
describing nilpotent subalgebras of e_{7(7)} or so(6,6) (in M and type II
theories respectively).
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Locality and Nonlinear Quantum Mechanics: Nonlinear modifications of quantum mechanics generically lead to nonlocal
effects which violate relativistic causality. We study these effects using the
functional Schrodinger equation for quantum fields and identify a type of
nonlocality which causes nearly instantaneous entanglement of spacelike
separated systems. We describe a simple example involving widely separated
wave-packet (coherent) states, showing that nonlinearity in the Schrodinger
evolution causes spacelike entanglement, even in free field theory.
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FZZT Brane Relations in the Presence of Boundary Magnetic Fields: We show how a boundary state different from the (1,1) Cardy state may be
realised in the (m,m+1) minimal string by the introduction of an auxiliary
matrix into the standard two hermitian matrix model. This boundary is a natural
generalisation of the free spin boundary state in the Ising model. The
resolvent for the auxiliary matrix is computed using an extension of the
saddle-point method of Zinn-Justin to the case of non-identical potentials. The
structure of the saddle-point equations result in a Seiberg-Shih like relation
between the boundary states which is valid away from the continuum limit, in
addition to an expression for the spectral curve of the free spin boundary
state. We then show how the technique may be used to analyse boundary states
corresponding to a boundary magnetic field, thereby allowing us to generalise
the work of Carroll et al. on the boundary renormalisation flow of the Ising
model, to any (m,m+1) model.
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Spin and Statistics on the Groenewold-Moyal Plane: Pauli-Forbidden
Levels and Transitions: The Groenewold-Moyal plane is the algebra A_\theta(R^(d+1)) of functions on
R^(d+1) with the star-product as the multiplication law, and the commutator
[x_\mu,x_\nu] =i \theta_{\mu \nu} between the coordinate functions. Chaichian
et al. and Aschieri et al. have proved that the Poincare group acts as
automorphisms on A_\theta(R^(d+1))$ if the coproduct is deformed. (See also the
prior work of Majid, Oeckl and Grosse et al). In fact, the diffeomorphism group
with a deformed coproduct also does so according to the results of Aschieri et
al. In this paper we show that for this new action, the Bose and Fermi
commutation relations are deformed as well. Their potential applications to the
quantum Hall effect are pointed out. Very striking consequences of these
deformations are the occurrence of Pauli-forbidden energy levels and
transitions. Such new effects are discussed in simple cases.
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The $n_{f}$ terms of the three-loop cusp anomalous dimension in QCD: In this talk we present the result for the $n_f$ dependent piece of the
three-loop cusp anomalous dimension in QCD. Remarkably, it is parametrized by
the same simple functions appearing in analogous anomalous dimensions in
${\mathcal N}=4$ SYM at one and two loops. We also compute all required master
integrals using a recently proposed refinement of the differential equation
method. The analytic results are expressed in terms of harmonic polylogarithms
of uniform weight.
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Physical realization for Riemann zeros from black hole physics: According to a conjecture attributed to Polya and Hilbert, there is a
self-adjoint operator whose eigenvalues are the the nontrivial zeros of the
Riemann zeta function. We show that the near-horizon dynamics of a massive
scalar field in the Schwarzscild black hole spacetime, under a reasonable
boundary condition, gives rise to normal mode frequencies that coincide with
the nontrivial Riemann zeros. In achieving this result, we exploit the
Bekenstein conjecture of black hole area quantization, and argue that it is
responsible for the breaking of the continuous scale symmetry of the near
horizon dynamics into a discrete one.
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Magnetic Field and Curvature Effects on Pair Production I: Scalars and
Spinors: The pair production rates for spin-zero and spin-$\frac{1}{2}$ particles are
calculated on spaces of the form $M \times {\mathbb R}^{1,1}$ with $M$
corresponding to ${\mathbb R}^2$ (flat), $T^2$ (flat, compactified), $S^2$
(positive curvature) and $H^2$ (negative curvature), with and without a
background magnetic field on $M$. The motivation is to elucidate the effects of
curvature and background magnetic field. Contrasting effects for positive and
negative curvature on the two cases of spin are obtained. For positive
curvature, we find enhancement for spin-zero and suppression for
spin-$\frac{1}{2}$, with the opposite effect for negative curvature.
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Black Hole Solutions in $R^2$ Gravity: We find static spherically symmetric solutions of scale invariant $R^2$
gravity. The latter has been shown to be equivalent to General Relativity with
a positive cosmological constant and a scalar mode. Therefore, one expects that
solutions of the $R^2$ theory will be identical to that of Einstein theory.
Indeed, we find that the solutions of $R^2$ gravity are in one-to-one
correspondence with solutions of General Relativity in the case of
non-vanishing Ricci scalar. However, scalar-flat $R=0$ solutions are global
minima of the $R^2$ action and they cannot in general be mapped to solutions of
the Einstein theory. As we will discuss, the $R=0$ solutions arise in Einstein
gravity as solutions in the tensionless, strong coupling limit $M_P\rightarrow
0$. As a further result, there is no corresponding Birkhoff theorem and the
Schwarzschild black hole is by no means unique in this framework. In fact,
$R^2$ gravity has a rich structure of vacuum static spherically symmetric
solutions partially uncovered here. We also find charged static spherically
symmetric backgrounds coupled to a $U(1)$ field. Finally, we provide the
entropy and energy formulas for the $R^2$ theory and we find that entropy and
energy vanish for scalar-flat backgrounds.
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String theory and the KLT-relations between gravity and gauge theory
including external matter: We consider the Kawai-Lewellen-Tye (KLT) factorizations of gravity scalar-leg
amplitudes into products of scalar-leg Yang-Mills amplitudes. We check and
examine the factorizations at O(1) in $\alpha'$ and extend the analysis by
considering KLT-mapping in the case of generic effective Lagrangians for
Yang-Mills theory and gravity.
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The Super P-Brane Scan and S Duality: Taking into account the recent dualities we rederive the super p-brane scan.
Our main results are the importance of the metric's signature and the existence
of an S self-dual super 5-brane at D=14 with signature (7,7) or (11,3).
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The spacetime attribute of matter: We propose that spacetime is fundamentally a property of matter, inseparable
from it. This leads us to suggest that all properties of matter must be
elevated to the same status as that of spacetime in quantum field theories of
matter. We suggest a specific method for extending field theories to accomodate
this, and point out how this leads to the evolution of fields through channels
other than the spacetime channel.
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The Heavy Dirac Monopole: We present a model for the Dirac magnetic monopole, suitable for the strong
coupling regime. The magnetic monopole is static, has charge g and mass M,
occupying a volume of radius R ~ O (g^2/M). It is shown that inside each
n-monopole there exist infinite multipoles. It is given an analytical proof of
the existence of monopole-antimonopole bound state. Theses bound-states might
give additional strong light to light scattering in the proton-antiproton
collision process at FermiLab TEVATRON.
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Mandelstam cuts and light-like Wilson loops in N=4 SUSY: We perform an analytic continuation of the two-loop remainder function for
the six-point planar MHV amplitude in N=4 SUSY, found by Goncharov, Spradlin,
Vergu and Volovich from the light-like Wilson loop representation. The
remainder function is continued into a physical region, where all but two
energy invariants are negative. It turns out to be pure imaginary in the
multi-Regge kinematics, which is in an agreement with the predictions based on
the Steinmann relations for the Regge poles and Mandelstam cut contributions.
The leading term reproduces correctly the expression calculated by one of the
authors in the BFKL approach, while the subleading term presents a result, that
was not yet found with the use of the unitarity techniques. This supports the
applicability of the Wilson loop approach to the planar MHV amplitudes in N=4
SUSY.
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Gravitational Interactions of integrable models: We couple non-linear $\sigma$-models to Liouville gravity, showing that
integrability properties of symmetric space models still hold for the matter
sector. Using similar arguments for the fermionic counterpart, namely
Gross--Neveu-type models, we verify that such conclusions must also hold for
them, as recently suggested.
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$β$-deformations, potentials and KK modes: We have studied volumes of the 3-cycle and the compact 5-volumes for the
$\beta$ transformed geometry and it comes out to be decreasing except one
choice for which the torus do not stay inside the 3-cycle and ``5-cycle.''
There are 3 possible ways to construct these cycles. one is as mentioned above
and the other two are, when the torus stay inside the cycle and when both the
torus and the cycle shares a common direction. Also, we have argued that under
$\beta$ deformation there arises a non-trivial ``potential'' as the $SL(3,R)$
transformation mixes up the fields. If we start with a flat space after the
$SL(3,R)$ transformation the Ricci-scalar of the transformed geometry do not
vanishes but the transformed solution is reminiscent of NS5-brane. We have
explicitly, checked that $\beta$-transformation indeed is a marginal
deformation in the gravity side.
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Vanishing DC holographic conductivity from a magnetic monopole
condensate: We show how to obtain a vanishing DC conductivity in 3-dimensional strongly
coupled QFT's using a massive 2-form field in the bulk that satisfies a special
kind of boundary condition. The real and imaginary parts of the AC conductivity
are evaluated in this holographic setup and we show that the DC conductivity
identically vanishes even for an arbitrarily small (though nonzero) value of
the 2-form mass in the bulk. We identify the bulk action of the massive 2-form
with an effective theory describing a phase in which magnetic monopoles have
condensed in the bulk. Our results indicate that a condensate of magnetic
monopoles in a 4-dimensional bulk leads to a vanishing DC holographic
conductivity in 3-dimensional strongly coupled QFT's.
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Polarization Correlations in Pair Production from Charged and Neutral
Strings: Polarization correlations of $e^{+}e^{-}$ pair productions from charged and
neutral Nambu strings are investigated, via photon and graviton emissions,
respectively and explicit expressions for their corresponding probabilities are
derived and found to be \textit{speed} dependent. The strings are taken to be
circularly oscillating closed strings, as perhaps the simplest solution of the
Nambu action. In the extreme relativistic case, these probabilities coincide,
but, in general, are different, and such inquiries, in principle, indicate
whether the string is charged or uncharged. It is remarkable that these
dynamical relativistic quantum field theory calculations lead to a clear
violation of Local Hidden Variables theories.
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Phase transitions in Bergshoeff-Hohm-Townsend Massive Gravity: We present the Hawking-Page phase diagrams in the Bergshoeff-Hohm-Townsend
(BHT) massive gravity theory for different solutions, such as the phase
transitions between vacuum $\text{AdS}_3$ and BTZ black hole, warped
$\text{AdS}_3$ and warped BTZ black hole in grand canonical and in
non-local/quadratic ensembles, Lifshitz black hole and the new hairy black hole
solutions. We observe that except for the black holes in quadratic ensemble,
for other cases in the non-chiral theory of BHT the phase diagrams are
symmetric with respect to the direction of angular momentum, as we expected. We
conclude that for presenting the phase diagrams of warped $\text{AdS}_3$ black
holes, only the grand canonical ensemble should be used.
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Casimir Energy of a Spherical Shell: The Casimir energy for a conducting spherical shell of radius $a$ is computed
using a direct mode summation approach. An essential ingredient is the
implementation of a recently proposed method based on Cauchy's theorem for an
evaluation of the eigenfrequencies of the system. It is shown, however, that
this earlier calculation uses an improper set of modes to describe the waves
exterior to the sphere. Upon making the necessary corrections and taking care
to ensure that no mathematically ill-defined expressions occur, the technique
is shown to leave numerical results unaltered while avoiding a longstanding
criticism raised against earlier calculations of the Casimir energy.
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Scattering Amplitudes -- Wilson Loops Duality for the First Non-planar
Correction: We study the first non-planar correction to gluon scattering amplitudes in
${\cal N}=4$ SYM theory. The correction takes the form of a double trace
partial amplitude and is suppressed by one power of $1/N$ with respect to the
leading single trace contribution. We extend the duality between planar
scattering amplitudes and null polygonal Wilson loops to the double trace
amplitude. The new duality relates the amplitude to the correlation function of
two infinite null polygonal Wilson lines that are subject to a quantum
periodicity constraint. We test the duality perturbatively at one-loop order
and demonstrate it for the dual string in AdS. The duality allows us to extend
the notion of the loop integrand beyond the planar limit and to determine it
using recursion relations. It also allows one to apply the integrability-based
pentagon operator product expansion approach to the first non-planar order.
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A Remark on the Spontaneous Symmetry Breaking Mechanism in the Standard
Model: In this paper we consider the Spontaneous Symmetry Breaking Mechanism (SSBM)
in the Standard Model of particles in the unitary gauge. We show that the
computation usually presented of this mechanism can be conveniently performed
in a slightly different manner. As an outcome, the computation we present can
change the interpretation of the SSBM in the Standard Model, in that it
decouples the SU(2)-gauge symmetry in the final Lagrangian instead of breaking
it.
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On semiclassical analysis of pure spinor superstring in an AdS_5 x S^5
background: Relation between semiclassical analyses of Green-Schwarz and pure spinor
formalisms in an AdS_5 x S^5 background is clarified. It is shown that the two
formalisms have identical semiclassical partition functions for a simple family
of classical solutions. It is also shown that, when the classical string is
furthermore rigid, this in turn implies that the two formalisms predict the
same one-loop corrections to spacetime energies.
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Generalized Boltzmann Equation in a Manifestly Covariant Relativistic
Statistical Mechanics: We consider the relativistic statistical mechanics of an ensemble of $N$
events with motion in space-time parametrized by an invariant ``historical
time'' $\tau .$ We generalize the approach of Yang and Yao, based on the Wigner
distribution functions and the Bogoliubov hypotheses, to find the approximate
dynamical equation for the kinetic state of any nonequilibrium system to the
relativistic case, and obtain a manifestly covariant Boltzmann-type equation
which is a relativistic generalization of the Boltzmann-Uehling-Uhlenbeck (BUU)
equation for indistinguishable particles. This equation is then used to prove
the $H$-theorem for evolution in $\tau .$ In the equilibrium limit, the
covariant forms of the standard statistical mechanical distributions are
obtained. We introduce two-body interactions by means of the direct action
potential $V(q),$ where $q$ is an invariant distance in the Minkowski
space-time. The two-body correlations are taken to have the support in a
relative $O( 2,1)$-invariant subregion of the full spacelike region. The
expressions for the energy density and pressure are obtained and shown to have
the same forms (in terms of an invariant distance parameter) as those of the
nonrelativistic theory and to provide the correct nonrelativistic limit.
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Matroid Theory and Chern-Simons: It is shown that matroid theory may provide a natural mathematical framework
for a duality symmetries not only for quantum Yang-Mills physics, but also for
M-theory. Our discussion is focused in an action consisting purely of the
Chern-Simons term, but in principle the main ideas can be applied beyond such
an action. In our treatment the theorem due to Thistlethwaite, which gives a
relationship between the Tutte polynomial for graphs and Jones polynomial for
alternating knots and links, plays a central role. Before addressing this
question we briefly mention some important aspects of matroid theory and we
point out a connection between the Fano matroid and D=11 supergravity. Our
approach also seems to be related to loop solutions of quantum gravity based in
Ashtekar formalism.
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A C-Function For Non-Supersymmetric Attractors: We present a c-function for spherically symmetric, static and asymptotically
flat solutions in theories of four-dimensional gravity coupled to gauge fields
and moduli. The c-function is valid for both extremal and non-extremal black
holes. It monotonically decreases from infinity and in the static region
acquires its minimum value at the horizon, where it equals the entropy of the
black hole. Higher dimensional cases, involving $p$-form gauge fields, and
other generalisations are also discussed.
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Notes on the $L_\infty$-approach to local gauge field theories: It is well known that a $Q$-manifold gives rise to an $L_\infty$-algebra
structure on the tangent space at a fixed point of the homological vector
field. From the field theory perspective this implies that the expansion of a
classical Batalin-Vilkovisky (BV) formulation around a vacuum solution can be
equivalently cast into the form of an $L_\infty$-algebra. In so doing, the BV
symplectic structure determines a compatible cyclic structure on the
$L_\infty$-algebra. Moreover, $L_\infty$ quasi-isomorphisms correspond to
so-called equivalent reductions (also known as the elimination of generalized
auxiliary fields) of the respective BV systems. Although at the formal level
the relation is straightforward, its implementation in field theory requires
some care because the underlying spaces become infinite-dimensional. In the
case of local gauge theories, the relevant spaces can be approximated by nearly
finite-dimensional ones through employing the jet-bundle technique. In this
work we study the $L_\infty$-counterpart of the jet-bundle BV approach and
generalise it to a more flexible setup of so-called gauge PDEs. It turns out
that in the latter case the underlying $L_\infty$-structure is analogous to
that of Chern-Simons theory. In particular, the underlying linear space is a
module over the space-time exterior algebra and the higher $L_\infty$-maps are
multilinear. Furthermore, a counterpart of the cyclic structure turns out to be
degenerate and possibly nonlinear, and corresponds to a compatible
presymplectic structure which is known to encode the BV symplectic structure
and hence the full-scale Lagrangian BV formulation. Moreover, given a
degenerate cyclic structure one can consistently relax the $L_\infty$-axioms in
such a way that the formalism still describes non-topological models but
involves only finitely-generated modules, as we illustrate in the example of
Yang-Mills theory.
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The sinh-Gordon model beyond the self dual point and the freezing
transition in disordered systems: The S-matrix of the well-studied sinh-Gordon model possesses a remarkable
strong/weak coupling duality $b \to 1/b$. Since there is no understanding nor
evidence for such a duality based on the quantum action of the model, it should
be questioned whether the properties of the model for $b>1$ are simply obtained
by analytic continuation of the weak coupling regime $0<b<1$. In this article
we assert that the answer is no, and we develop a concrete and specific
proposal for the properties when $b>1$. Namely, we propose that in this region
one needs to introduce a background charge $Q_\infty = b + 1/b -2$ which
differs from the Liouville background charge by the shift of $-2$. We propose
that in this regime the model has non-trivial massless renormalization group
flows between two different conformal field theories. This is in contrast to
the weak coupling regime which is a theory of a single massive particle.
Evidence for our proposal comes from higher order beta functions. We show how
our proposal correctly reproduces the freezing transitions in the multi-fractal
exponents of a Dirac fermion in $2+1$ dimensions in a random magnetic field,
which provides a strong check since such transitions have several detailed
features. We also point out a connection between a semi-classical version of
this transition and the so-called Manning condensation phenomena in
polyelectrolyte physics.
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On Bethe equations of 2d conformal field theory: We study the higher spin algebras of two-dimensional conformal field theory
from the perspective of quantum integrability. Starting from Maulik-Okounkov
instanton R-matrix and applying the procedure of algebraic Bethe ansatz, we
obtain infinite commuting families of Hamiltonians of quantum ILW hierarchy
parametrized by the shape of the auxiliary torus. We calculate explicitly the
first five of these Hamiltonians. Then, we numerically verify that their joint
spectrum can be parametrized by solutions of Litvinov's Bethe ansatz equations
and we conjecture a general formula for the joint spectrum of all ILW
Hamiltonians, based on results of Feigin, Jimbo, Miwa and Mukhin.
There are two interesting degeneration limits, the infinitely thick and the
infinitely thin auxiliary torus. In one of these limits, the ILW hierarchy
degenerates to Yangian or Benjamin-Ono hierarchy and the Bethe equations can be
easily solved. The other limit is singular but we can nevertheless extract
local Hamiltonians corresponding to quantum KdV or KP hierarchy. Litvinov's
Bethe equations in this local limit provide an alternative to Bethe ansatz
equations of Bazhanov, Lukyanov and Zamolodchikov, but are more transparent,
work at any rank and are manifestly symmetric under triality symmetry of
$\mathcal{W}_{1+\infty}$. Finally, we illustrate analytic properties of the
solutions of Bethe equations in minimal models, in particular for Lee-Yang CFT.
The analytic structure of Bethe roots is very rich as it captures the
representation theory of $\mathcal{W}_N$ minimal models.
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Recent Results in String Duality: This is a talk given at YKIS '95, primarily to non-string theorists. I review
the evidence for string duality, the principle that any string theory at strong
coupling looks like another string theory at weak coupling. A postscript
summarizes developments since the conference.
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Ternutator Identities: The ternary commutator or ternutator, defined as the alternating sum of the
product of three operators, has recently drawn much attention as an interesting
structure generalising the commutator. The ternutator satisfies cubic
identities analogous to the quadratic Jacobi identity for the commutator. We
present various forms of these identities and discuss the possibility of using
them to define ternary algebras.
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Two Dimensional Stringy Black Holes with One Asymptotically Flat Domain: The exact black hole solution of 2D closed string theory has, as any other
maximally extended Schwarzschild-like geometry, two asymptotically flat
spacetime domains. One can get rid of the second domain by gauging the discrete
symmetry on the SL(2,R)/U(1) coset that interchanges the two asymptotic domains
and preserves the Kruskal time orientation everywhere in the Kruskal plane.
Here it is shown that upon performing this orbifold procedure, we obtain a
theory of unoriented open and closed strings in a black hole background, with
just one asymptotically flat domain and a time-like orbifold singularity at the
origin. All of the open string states of the model are confined to the orbifold
singularity. We also discuss various physical aspects of the truncated black
hole, in particular its target duality -- the model is dual to a conventional
open string theory in the black hole geometry.
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Black Hole Formation and Space-Time Fluctuations in Two Dimensional
Dilaton Gravity and Complementarity: We study black hole formation in a model of two dimensional dilaton gravity
and 24 massless scalar fields with a boundary. We find the most general
boundary condition consistent with perfect reflection of matter and the
constraints. We show that in the semiclassical approximation and for the
generic value of the parameter which characterizes the boundary conditions, the
boundary starts receeding to infinity at the speed of light whenever the total
energy of the incoming matter flux exceeds a certain critical value. This is
also the critical energy which marks the onset of black hole formation. We then
compute the quantum fluctuations of the boundary and of the rescaled scalar
curvature and show that as soon as the incoming energy exceeds this critical
value, an asymptotic observer using normal time resolutions will always measure
large fluctuations of space-time near the horizon, even though the freely
falling observer does not. This is an aspect of black hole complementarity
relating directly the quantum gravity effects.
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On Higher Spatial Derivative Field Theories: In this work, we employ renormalization group methods to study the general
behavior of field theories possessing anisotropic scaling in the spacetime
variables. The Lorentz breaking symmetry that accompanies these models are
either soft, if no higher spatial derivative is present, or it may have a more
complex structure if higher spatial derivatives are also included. Both
situations are discussed in models with only scalar fields and also in models
with fermions as a Yukawa like model.
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Response to Tarrach's "Mode Dependent Field Renormalization and
Trivialty": We respond to Tarrach's criticisms (hep-th/9511034) of our work on lambda
Phi^4 theory. Tarrach does not discuss the same renormalization procedure that
we do. He also relies on results from perturbation theory that are not valid.
There is no "infrared divergence" or unphysical behaviour associated with the
zero-momentum limit of our effective action.
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The hidden symmetry of the heterotic string: We propose that Borcherds' Fake Monster Lie algebra is a broken symmetry of
heterotic string theory compactified on $T^7 \times T^2$. As evidence, we study
the fully flavored counting function for BPS instantons contributing to a
certain loop amplitude. The result is controlled by $\Phi_{12}$, an automorphic
form for $O(2, 26, \mathbb{Z})$. The degeneracies it encodes in its Fourier
coefficients are graded dimensions of a second-quantized Fock space for this
large symmetry algebra. This construction provides a concrete realization of
Harvey and Moore's proposed relationship between Generalized Kac-Moody
symmetries and supersymmetric string vacua.
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Large $N$ fractons: We consider theories of fractons with $N$ fields. These theories have exotic
spacetime symmetries, including a conserved dipole moment. Using collective
fields we solve these models to leading order in large $N$. The large $N$
solution reveals that these models are strongly correlated, and that
interactions generate a momentum-dependent self-energy. Dipole symmetry is
spontaneously broken throughout the phase diagram of these models, leading to a
low-energy Goldstone description of what we dub "dipole superfluids."
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Almost the supersymmetric Standard Model from intersecting D6-branes on
the Z_6' orientifold: Intersecting stacks of supersymmetric fractional branes on the Z_6'
orientifold may be used to construct the supersymmetric Standard Model. If a,b
are the stacks that generate the SU(3)_{colour} and SU(2)_L gauge particles,
then, in order to obtain {\em just} the chiral spectrum of the (supersymmetric)
Standard Model (with non-zero Yukawa couplings to the Higgs mutiplets), it is
necessary that the number of intersections a \cap b of the stacks a and b, and
the number of intersections a \cap b' of a with the orientifold image b' of b
satisfy (a \cap b,a \cap b')=(2,1) or (1,2). It is also necessary that there is
no matter in symmetric representations of the gauge group, and not too much
matter in antisymmetric representations, on either stack. Fractional branes
having all of these properties may be constructed on the Z_6' orientifold. We
construct a (four-stack) model with two further stacks, each with just a single
brane, which has precisely the matter spectrum of the supersymmetric Standard
Model, including a single pair of Higgs doublets. However, the gauge group is
SU(3)_{\rm colour} x SU(2)_L x U(1)_Y x U(1)_H. Only the Higgs doublets are
charged with respect to U(1)_H.
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Multiloop Euler-Heisenberg Lagrangians, Schwinger pair creation, and the
QED N - photon amplitudes: An update is given on our long-term effort to perform a three-loop check on
the Affleck-Alvarez-Manton/Lebedev-Ritus exponentiation conjecture for the
imaginary part of the Euler-Heisenberg Lagrangian, using 1+1 dimensional QED as
a toy model. After reviewing the history and significance of the conjecture, we
present trigonometric integral representations for the single electron loop
contributions to the three-loop Lagrangian, and develop a symmetry-based method
for the calculation of their weak-field expansion coefficients.
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D-brane Bound States from Charged Macroscopic Strings: We construct new D-brane bound states using charged macroscopic type IIB
string solutions.A generic bound state solution, when dimensionally reduced,
carries multiple gauge charges. Starting with D=9 charged macroscopic strings,
we obtain solutions in D=10, which are interpreted as carrying (F, D0, D2)
charges as well as nonzero momenta. The masses and charges are also explicitly
shown to satisfy the non-threshold bound of 1/2 BPS objects. Our solutions
reduce to the known D-brane bound state solutions with appropriate restrictions
in the parameter space. We further generalize the results to (Dp- D(p+2)) bound
state in IIA/B theories, giving an explicit example with p=1.
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Running Newton Coupling, Scale Identification and Black Hole
Thermodynamics: We discuss the quantum improvement of black hole solutions in the context of
asymptotic safety. The Newton coupling in this formulation depends on an energy
scale, which must be identified with some length scale in order to study
physical consequences to black holes. However, no physical principle has so far
been known for the identification. Here we propose that the consistency of the
first law of thermodynamics is the principle that should determine physically
sensible scale identification, at least close to the horizon. We show that this
leads to a natural solution that the Newton coupling should be a function of
the horizon area and find a universal formula for the quantum entropy, which
agrees with the standard Bekenstein-Hawking entropy for constant Newton
coupling, for Kerr black holes and other higher-dimensional black holes. This
suggests that the Newton coupling is a function of the area near the horizon,
and also away to infinity, where the quantum effects may not be so important.
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Fivebrane Instanton Corrections to the Universal Hypermultiplet: We analyze the Neveu-Schwarz fivebrane instanton in type IIA string theory
compactifications on rigid Calabi-Yau threefolds, in the low-energy
supergravity approximation. It there appears as a finite action solution to the
Euclidean equations of motion of a double-tensor multiplet (dual to the
universal hypermultiplet) coupled to N=2, D=4 supergravity. We determine the
bosonic and fermionic zero modes, and the single-centered instanton measure on
the moduli space of collective coordinates. The results are then used to
compute, in the semiclassical approximation, correlation functions that
nonperturbatively correct the universal hypermultiplet moduli space geometry of
the low-energy effective action. We find that only the Ramond-Ramond sector
receives corrections, and we discuss the breaking of isometries due to
instantons.
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On topological recursion for Wilson loops in $\mathcal N=4$ SYM at
strong coupling: We consider $U(N)$ $\mathcal N=4$ super Yang-Mills theory and discuss how to
extract the strong coupling limit of non-planar corrections to observables
involving the $\frac{1}{2}$-BPS Wilson loop. Our approach is based on a
suitable saddle point treatment of the Eynard-Orantin topological recursion in
the Gaussian matrix model. Working directly at strong coupling we avoid the
usual procedure of first computing observables at finite planar coupling
$\lambda$, order by order in $1/N$, and then taking the $\lambda\gg 1$ limit.
In the proposed approach, matrix model multi-point resolvents take a simplified
form and some structures of the genus expansion, hardly visible at low order,
may be identified and rigorously proved. As a sample application, we consider
the expectation value of multiple coincident circular supersymmetric Wilson
loops as well as their correlator with single trace chiral operators. For these
quantities we provide novel results about the structure of their genus
expansion at large tension, generalising recent results in arXiv:2011.02885.
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Light rings of five-dimensional geometries: We study massless geodesics near the photon-spheres of a large family of
solutions of Einstein-Maxwell theory in five dimensions, including BHs, naked
singularities and smooth horizon-less JMaRT geometries obtained as
six-dimensional uplifts of the five-dimensional solution. We find that a light
ring of unstable photon orbits surrounding the mass center is always present,
independently of the existence of a horizon or singularity. We compute the
Lyapunov exponent, characterizing the chaotic behaviour of geodesics near the
`photon-sphere' and the time decay of ring-down modes dominating the response
of the geometry to perturbations at late times. We show that, for geometries
free of naked singularities, the Lyapunov exponent is always bounded by its
value for a Schwarzschild BH of the same mass.
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Mass Renormalization in Lorentz-violating Scalar Field Theory: In this work we evaluate the $\gamma_{m}$ function corresponding to mass
renormalization for O($N$) scalar field theory with Lorentz violation. We
calculate this function up to two-loop order for a theory renormalized
utilizing the counterterm method in the minimal subtraction scheme with Feynman
diagrams regularized using dimensional regularization.
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Bonus Symmetry for Super Wilson Loops: The Yangian level-one hypercharge generator for the super Wilson loop in N =
4 supersymmetric Yang-Mills theory is constructed. Moreover, evidence for the
presence of a corresponding symmetry generator at all higher levels is
provided. The derivation is restricted to the strong-coupling description of
the super Wilson loop and based on the construction of novel conserved charges
for type IIB superstrings on AdS_5 x S^5.
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A Connection between Twistors and Superstring Sigma Models on Coset
Superspaces: We consider superstring sigma models that are based on coset superspaces G/H
in which H arises as the fixed point set of an order-4 automorphism of G. We
show by means of twistor theory that the corresponding first-order system,
consisting of the Maurer-Cartan equations and the equations of motion, arises
from a dimensional reduction of some generalised self-dual Yang-Mills equations
in eight dimensions. Such a relationship might help shed light on the explicit
construction of solutions to the superstring equations including their hidden
symmetry structures and thus on the properties of their gauge theory duals.
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D7-Brane Moduli vs. F-Theory Cycles in Elliptically Fibred Threefolds: We study the space of geometric and open string moduli of type IIB
compactifications from the perspective of complex structure deformations of
F-theory. In order to find a correspondence, we work in the weak coupling limit
and for simplicity focus on compactifications to 6 dimensions. Starting from
the topology of D7-branes and O7-planes, we construct the 3-cycles of the
F-theory threefold. We achieve complete agreement between the degrees of
freedom of the Weierstrass model and the complex structure deformations of the
elliptic Calabi-Yau. All relevant quantities are expressed in terms of the
topology of the base space, allowing us to formulate our results for general
base spaces.
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K(E10), Supergravity and Fermions: We study the fermionic extension of the E10/K(E10) coset model and its
relation to eleven-dimensional supergravity. Finite-dimensional spinor
representations of the compact subgroup K(E10) of E(10,R) are studied and the
supergravity equations are rewritten using the resulting algebraic variables.
The canonical bosonic and fermionic constraints are also analysed in this way,
and the compatibility of supersymmetry with local K(E10) is investigated. We
find that all structures involving A9 levels 0,1 and 2 nicely agree with
expectations, and provide many non-trivial consistency checks of the existence
of a supersymmetric extension of the E10/K(E10) coset model, as well as a new
derivation of the `bosonic dictionary' between supergravity and coset
variables. However, there are also definite discrepancies in some terms
involving level 3, which suggest the need for an extension of the model to
infinite-dimensional faithful representations of the fermionic degrees of
freedom.
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Unitarity and positivity constraints for CFT at large central charge: We consider the four-point correlator of the stress tensor multiplet in
${\cal N}=4$ SYM in the limit of large central charge $c \sim N^2$. For finite
values of $g^2N$ single-trace intermediate operators arise at order $1/c$ and
this leads to specific poles in the Mellin representation of the correlator.
The sign of the residue at these poles is fixed by unitarity. We consider
solutions consistent with crossing symmetry and this pole structure. We show
that in a certain regime all solutions result in a negative contribution to the
anomalous dimension of twist four operators. The reason behind this is a
positivity property of Mack polynomials that leads to a positivity condition
for the Mellin amplitude. This positivity condition can also be proven by
assuming the correct Regge behaviour for the Mellin amplitude. For large $g^2N$
we recover a tower of solutions in one to one correspondence with local
interactions in a effective field theory in the $AdS$ bulk, with the
appropriate suppression factors, and with definite overall signs. These signs
agree with the signs that would follow from causality constraints on the
effective field theory. The positivity constraints arising from CFT for the
Mellin amplitude take a very similar form to the causality constraint for the
forward limit of the S-matrix.
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More on La Grande Bouffe: towards higher spin symmetry breaking in AdS: We discuss higher spin gauge symmetry breaking in AdS space from a
holographic prespective. Indeed, the AdS/CFT correspondence implies that N=4
SYM theory at vanishing coupling constant is dual to a theory in AdS which
exhibits higher spin gauge symmetry enhancement. When the SYM coupling is
non-zero, the current conservation condition becomes anomalous, and
correspondingly the local higher spin symmetry in the bulk gets spontaneously
broken. In agreement with previous results and holographic expectations, we
find that the Goldstone mode responsible for the symmetry breaking in AdS has a
non-vanishing mass even in the limit in which the gauge symmetry is restored.
Moreover, we show that the mass of the Goldstone mode is exactly the one
predicted by the correspondence. Finally, we obtain the precise form of the
higher spin supercurrents in the SYM side.
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On the Liouville coupling constants: For the general operator product algebra coefficients derived by Cremmer
Roussel Schnittger and the present author with (positive integer) screening
numbers, the coupling constants determine the factors additional to the quantum
group 6j symbols.
They are given by path independent products over a two dimensional lattice in
the zero mode space. It is shown that the ansatz for the three point function
of Dorn-Otto and Zamolodchikov-Zamolodchikov precisely defines the
corresponding flat lattice connection, so that it does give a natural
generalization of these coupling constants to continuous screening numbers. The
consistency of the restriction to integer screening charges is reviewed, and
shown to be linked with the orthogonality of the (generalized) 6j symbols. Thus
extending this last relation is the key to general screening numbers.
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Inhomogeneous quantum groups IGL_{q,r}(N): Universal enveloping algebra
and differential calculus: A review of the multiparametric linear quantum group GL_qr(N), its real
forms, its dual algebra U(gl_qr(N)) and its bicovariant differential calculus
is given in the first part of the paper.
We then construct the (multiparametric) linear inhomogeneous quantum group
IGL_qr(N) as a projection from GL_qr(N+1), or equivalently, as a quotient of
GL_qr(N+1) with respect to a suitable Hopf algebra ideal.
A bicovariant differential calculus on IGL_qr(N) is explicitly obtained as a
projection from the one on GL_qr(N+1). Our procedure unifies in a single
structure the quantum plane coordinates and the q-group matrix elements T^a_b,
and allows to deduce without effort the differential calculus on the q-plane
IGL_qr(N) / GL_qr(N).
The general theory is illustrated on the example of IGL_qr(2).
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Gauge covariance and the fermion-photon vertex in three- and four-
dimensional, massless quantum electrodynamics: In the quenched approximation, the gauge covariance properties of three
vertex Ans\"{a}tze in the Schwinger-Dyson equation for the fermion self energy
are analysed in three- and four- dimensional quantum electrodynamics. Based on
the Cornwall-Jackiw-Tomboulis effective action, it is inferred that the
spectral representation used for the vertex in the gauge technique cannot
support dynamical chiral symmetry breaking. A criterion for establishing
whether a given Ansatz can confer gauge covariance upon the Schwinger-Dyson
equation is presented and the Curtis and Pennington Ansatz is shown to satisfy
this constraint. We obtain an analytic solution of the Schwinger-Dyson equation
for quenched, massless three-dimensional quantum electrodynamics for arbitrary
values of the gauge parameter in the absence of dynamical chiral symmetry
breaking.
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Glueballs on the Baryonic Branch of Klebanov-Strassler: dimensional
deconstruction and a light scalar particle: Within gauge/gravity duality, we compute the scalar and tensor mass spectrum
in the boundary theory defined by the five-dimensional sigma-model coupled to
gravity obtained by constraining to eight scalars the truncation on T$^{1,1}$
that corresponds to the Papadopoulos-Tseytlin (PT) ansatz. We study
fluctuations around the 1-parameter family of backgrounds that lift to the
baryonic branch of the Klebanov-Strassler (KS) system, and interpolates between
the KS background and the Maldacena-Nunez one (CVMN). We adopt a gauge
invariant formalism in the treatment of the fluctuations that we interpret as
states of the dual theory. The tensor spectrum interpolates between the
discrete spectrum of the KS background and the continuum spectrum of the CVMN
background, in particular showing the emergence of a finite energy range
containing a dense set of states, as expected from dimensional deconstruction.
The scalar spectrum shows analogous features, and in addition it contains one
state that becomes parametrically light far from the origin along the baryonic
branch.
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Thermodynamic Properties of Holographic superfluids: Using the holographic model for spontaneous symmetry breaking, we study some
properties of the dual superfluid such as the thermodynamic exponents,
Joule-Thomson coefficient, compressibility etc. Our focus is on how these
properties vary with the scaling dimension and the charge of the operator that
undergoes condensation.
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6d/5d exceptional gauge theories from web diagrams: We construct novel web diagrams with a trivalent or quadrivalent gluing for
various 6d/5d theories from certain Higgsings of 6d conformal matter theories
on a circle. The theories realized on the web diagrams include 5d Kaluza-Klein
theories from circle compactifications of the 6d $G_2$ gauge theory with 4
flavors, the 6d $F_4$ gauge theory with 3 flavors, the 6d $E_6$ gauge theory
with 4 flavors and the 6d $E_7$ gauge theory with 3 flavors. The Higgsings also
give rise to 5d Kaluza-Klein theories from twisted compactifications of 6d
theories including the 5d pure SU(3) gauge theory with the Chern-Simons level 9
and the 5d pure SU(4) gauge theory with the Chern-Simons level 8. We also
compute the Nekrasov partition functions of the theories by applying the
topological vertex formalism to the newly obtained web diagrams.
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Generic anisotropic Lifshitz scalar field theory: masslesslike massive
minimal subtraction: We formulate the simplest minimal subtraction version for massive $\lambda
\phi^4$ scalar fields with $O(N)$ symmetry for generic anisotropic Lifshitz
space-times. An appropriate partial$-p$ operation is applied in the bare
two-point vertex function diagrams, which separates the original diagram into a
sum of two different integrals which are the coefficients of the corresponding
polynomials in the mass and external momentum. Within the proposed method, the
coefficient of the mass terms can be discarded and we obtain a minimal
subtraction method almost identical to the same scheme in the massless theory
in {\it every external momentum/mass subspace}. We restrict our demonstration
of the method up to three-loop order in the two-point vertex part. We verify
the consistency of our method by a diagrammatic computation of static critical
exponents, which validates the universality hypothesis.
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Three-dimensional N=2 supergravity theories: From superspace to
components: For general off-shell N=2 supergravity-matter systems in three spacetime
dimensions, a formalism is developed to reduce the corresponding actions from
superspace to components. The component actions are explicitly computed in the
cases of Type I and Type II minimal supergravity formulations. We describe the
models for topologically massive supergravity which correspond to all the known
off-shell formulations for three-dimensional N=2 supergravity. We also present
a universal setting to construct supersymmetric backgrounds associated with
these off-shell supergravities.
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The tunneling radiation of Kehagias-Sfetsos black hole under generalized
uncertainty principle: We further the investigation on the Parikh-Kraus-Wilczeck tunneling radiation
of Kehagias-Sfetsos black hole under the generalized uncertainty principle. We
obtain the entropy difference involving the influence from the inequality. The
two terms as generalizations of the Heisenberg's uncertainty promote or retard
the emission of this kind of black holes respectively.
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Post-radiation evolution of black holes: The expectation-value equations for the collapse of a macroscopic,
spherically symmetric, and uncharged body are integrated up to the limit of
validity of semiclassical theory. The collapse finishes with a true stable
black hole of the mass microscopically exceeding the vacuum-induced charge. The
apparent horizon is almost closed. The most important feature of the solution
is the presence of an irremovable Cauchy horizon.
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Fractional Strings in (p,q) 5-brane and Quiver Matrix String Theory: We study the (p,q)5-brane dynamics from the viewpoint of Matrix string theory
in the T-dualized ALE background. The most remarkable feature in the
(p,q)5-brane is the existence of ``fractional string'', which appears as the
instanton of 5-brane gauge theory. We approach to the physical aspects of
fractional string by means of the two types of Matrix string probes: One of
which is that given in hep-th/9710065. As the second probe we present the
Matrix string theory describing the fractional string itself. We calculate the
moduli space metrics in the respective cases and argue on the specific
behaviors of fractional string. Especially, we show that the ``joining''
process of fractional strings can be realized as the transition from the
Coulomb branch to the Higgs branch of the fractional string probe. In this
argument, we emphasize the importance of some monodromies related with the
theta-angle of the 5-brane gauge theory.
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F-theory compactifications on manifolds with SU(3) structure: In this paper we derive part of the low energy action corresponding to
F-theory compactifications on specific eight manifolds with SU(3) structure.
The setup we use can actually be reduced to compactification of six-dimensional
supergravity coupled to tensor multiplets on a T^2 with duality twists. The
resulting theory is a N=2 gauged supergravity coupled to vector-tensor
multiplets.
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New Vortex-String Worldsheet Theories from Supersymmetric Localization: We use supersymmetric localization techniques to study the low-energy
dynamics of BPS vortex-strings in four-dimensional N=2 theories. We focus on
theories with SU(Nc)xU(1) gauge group and Nf hypermultiplets, all in the
fundamental representation of SU(Nc) but with general U(1) charges. Recently,
we proposed a condition that determines whether the low-energy string dynamics
is captured by a two-dimensional worldsheet theory that decouples from the
bulk. For strings for which this decoupling applies, we propose a prescription
for extracting the two-sphere partition function of the string worldsheet
theory from the four-ellipsoid partition function of the parent theory. We
obtain a general formula for the worldsheet two-sphere partition function in
terms of the parameters of the four-dimensional theory and identify N=(2,2)
GLSMs that possess these partition functions in a large class of examples. In
these examples, the weak coupling regime of the four-dimensional theory is
mapped to the weak coupling regime of the worldsheet theory. In addition, we
study the classical string zero-modes in flat space and obtain predictions for
the worldsheet spectra, which agree with the low-energy spectra of the GLSMs
obtained in the localization analysis. For Nf=2Nc=4, we discuss the map between
string worldsheet theories under four-dimensional S-duality and use our
prescription to study examples in which the weak coupling regime of the
four-dimensional theory is mapped to the strong coupling regime of the
worldsheet theory.
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Singular Monopoles and Gravitational Instantons: We model A_k and D_k asymptotically locally flat gravitational instantons on
the moduli spaces of solutions of U(2) Bogomolny equations with prescribed
singularities. We study these moduli spaces using Ward correspondence and find
their twistor description. This enables us to write down the K\"ahler potential
for A_k and D_k gravitational instantons in a relatively explicit form.
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Resummation of local and non-local scalar self energies via the
Schwinger-Dyson equation in de Sitter spacetime: We consider a massless and minimally coupled self interacting quantum scalar
field in the inflationary de Sitter spacetime. The scalar potential is taken to
be a hybrid of cubic and quartic self interactions, $V(\phi)= \lambda
\phi^4/4!+\beta \phi^3/3!$ ($\lambda >0$). Compared to the earlier well studied
$\beta=0$ case, the present potential has a rolling down effect due to the
$\phi^3$ term, along with the usual bounding effect due to the $\phi^4$ term.
$V(\phi)$ has shapewise qualitative similarity with the standard slow roll
single field inflationary potentials. We begin by constructing the
Schwinger-Dyson equation for the scalar Feynman propagator up to two loop, at
${\cal O}(\lambda)$, ${\cal O}(\beta^2)$, ${\cal O}(\lambda^2)$ and ${\cal
O}(\lambda \beta^2)$. Using this equation, we consider first the local part of
the scalar self energy and compute the mass of the scalar field, dynamically
generated via the late time non-perturbative secular logarithms, by resumming
the daisy-like graphs. We also argue that unlike the quartic case, considering
merely the one loop results for the purpose of resummation does not give us any
sensible result here. We next construct the non-perturbative two particle
irreducible effective action up to three loop and derive from it the
Schwinger-Dyson equation once again. This equation is satisfied by the
non-perturbative Feynman propagator. By series expanding this propagator, the
resummed local part of the self energy is shown to yield the same dynamical
mass as that of the above. We next use this equation to resum the effect of the
non-local part of the scalar self energy in the Feynman propagator, and show
that even though the perturbatively corrected propagator shows secular growth
at late times, there exists a resummed solution which is vanishing for large
spacelike separations.
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Casimir operators of the exceptional group $F_4$: the chain $B_4\subset
F_4\subset D_{13}$: Expressions are given for the Casimir operators of the exceptional group
$F_4$ in a concise form similar to that used for the classical groups. The
chain $B_4\subset F_4\subset D_{13}$ is used to label the generators of $F_4$
in terms of the adjoint and spinor representations of $B_4$ and to express the
26-dimensional representation of $F_4$ in terms of the defining representation
of $D_{13}$. Casimir operators of any degree are obtained and it is shown that
a basis consists of the operators of degree 2, 6, 8 and 12.
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Gravitational Dielectric Effect and Myers Effect: In this paper we study the gravitational dielectric phenomena of a D2-brane
in the background of Kaluza-Klein monopoles and D6-branes. In both cases the
spherical D2-brane with nonzero radius becomes classical solution of the
D2-brane action. We also investigate the gravitational Myers effect in the
background of D6-branes. This phenomenon occurs since the tension of the
D2-brane balances with the repulsive force between D0-branes and D6-branes.
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Influence of an Electric Field on the Propagation of a Photon in a
Magnetic field: In this work, a constant and uniform magnetic field is less than the
Schwinger critical value. In turn, an additional constant and uniform electric
field is taken much smaller than the magnetic field value. The propagation of a
photon in this electromagnetic field is investigating. In particular, in the
presence of a weak electric field, the root divergence is absent in the photon
effective mass near the thresholds of pair creation. The effective mass of a
real photon with a preset polarization is considered in the quantum energy
region as well as in the quasiclassical one.
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Quasinormal frequencies using the hidden conformal symmetry of the
Schwarzschild black hole: We show that the hidden conformal symmetry of the Schwarzschild black hole is
realized from the AdS$_2$ sector of the AdS$_2\times S^2$, but not from the
Rindler spacetime which is the genuine near-horizon geometry of the
Schwarzschild black hole. This implies that purely imaginary quasinormal
frequencies obtained using the hidden conformal symmetry is not suitable for
describing the largely damped modes around the Schwarzschild black hole.
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Coherent states over Grassmann manifolds and the WKB-exactness in path
integral: \(\Un{N}\) coherent states over Grassmann manifold,
\(\grsmn{N}{n}\simeq\Un{N}/ (\Un{n}\times \Un{N-n})\), are formulated to be
able to argue the WKB-exactness, so called the localization of
Duistermaat-Heckman, in the path integral representation of a character
formula. The exponent in the path integral formula is proportional to an
integer \(k\) that labels the \(\Un{N}\) representation. Thus when \(k
\rightarrow\infty\) a usual semiclassical approximation, by regarding \(k \sim
1 / \hbar\), can be performed yielding to a desired conclusion. The mechanism
of the localization is uncovered by means of a view from an extended space
realized by the Schwinger boson technique.
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Gravitational field of relativistic gyratons: The metric ansatz is used to describe the gravitational field of a beam-pulse
of spinning radiation (gyraton) in an arbitrary number of spacetime dimensions
D. First we demonstrate that this metric belongs to the class of metrics for
which all scalar invariants constructed from the curvature and its covariant
derivatives vanish. Next, it is shown that the vacuum Einstein equations reduce
to two linear problems in (D-2)-dimensional Euclidean space. The first is to
find the static magnetic potential created by a point-like source. The second
requires finding the electric potential created by a point-like source
surrounded by given distribution of the electric charge. To obtain a generic
gyraton-type solution of the vacuum Einstein equations it is sufficient to
allow the coefficients in the corresponding harmonic decompositions of
solutions of the linear problems to depend arbitrarily on retarded time and
substitute the obtained expressions in the metric ansatz. We discuss properties
of the solutions for relativistic gyratons and consider special examples.
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Gauged N=2 Supergravity in Nine-Dimensions and Domain Wall Solutions: We present massive N=2 supergravity with SO(2)-gauging in nine-dimensions by
direct construction. A full lagrangian and transformation rules are fixed,
respectively up to quartic and quadratic fermion terms. Corresponding to the
generalized Scherk-Schwarz dimensional reduction utilizing SL(2,R) symmetry,
this theory allows three arbitrary mass parameters m_0, m_1and m_2 in addition
to the minimal gauge coupling g, so that our system has the most general form
compared with other results in the past. Unlike ordinary gauged maximal
supergravity theories in other dimensions, the scalar potential is positive
definite for arbitrary values of the mass parameters. As an application, we
also analyze the stability and supersymmetry for 7-brane domain wall solutions
for this gauged maximal supergravity, keeping the three mass parameters.
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Inflationary Infrared Divergences: Geometry of the Reheating Surface vs.
delta N Formalism: We describe a simple way of incorporating fluctuations of the Hubble scale
during the horizon exit of scalar perturbations into the delta N formalism. The
dominant effect comes from the dependence of the Hubble scale on low-frequency
modes of the inflaton. This modifies the coefficient of the log-enhanced term
appearing in the curvature spectrum at second order in field fluctuations. With
this modification, the relevant coefficient turns out to be proportional to the
second derivative of the tree-level spectrum with respect to the inflaton phi
at horizon exit. A logarithm with precisely the same coefficient appears in a
calculation of the log-enhancement of the curvature spectrum based purely on
the geometry of the reheating surface. We take this agreement as strong support
for the proposed implementation of the delta N formalism. Moreover, our
analysis makes it apparent that the log-enhancement of the inflationary
power-spectrum is indeed physical if this quantity is defined using a global
coordinate system on the reheating surface (or any other post-inflationary
surface of constant energy density). However, it can be avoided by defining the
spectrum using invariant distances on this surface.
|
Invariant Correlations in Simplicial Gravity: Some first results are presented regarding the behavior of invariant
correlations in simplicial gravity, with an action containing both a bare
cosmological term and a lattice higher derivative term. The determination of
invariant correlations as a function of geodesic distance by numerical methods
is a difficult task, since the geodesic distance between any two points is a
function of the fluctuating background geometry, and correlation effects become
rather small for large distances. Still, a strikingly different behavior is
found for the volume and curvature correlation functions. While the first one
is found to be negative definite at large geodesic distances, the second one is
always positive for large distances. For both correlations the results are
consistent in the smooth phase with an exponential decay, turning into a power
law close to the critical point at $G_c$. Such a behavior is not completely
unexpected, if the model is to reproduce the classical Einstein theory at
distances much larger than the ultraviolet cutoff scale.
|
Extended corner symmetry, charge bracket and Einstein's equations: We develop the covariant phase space formalism allowing for non-vanishing
flux, anomalies and field dependence in the vector field generators. We
construct a charge bracket that generalizes the one introduced by Barnich and
Troessaert and includes contributions from the Lagrangian and its anomaly. This
bracket is uniquely determined by the choice of Lagrangian representative of
the theory. We then extend the notion of corner symmetry algebra to include the
surface translation symmetries and prove that the charge bracket provides a
canonical representation of the extended corner symmetry algebra. This
representation property is shown to be equivalent to the projection of the
gravitational equations of motion on the corner, providing us with an encoding
of the bulk dynamics in a locally holographic manner.
|
4D, N=1 Supergravity Genomics: The off-shell representation theory of 4D, $\mathcal{N}=1$ supermultiplets
can be categorized in terms of distinct irreducible graphical representations
called adinkras as part of a larger effort we call supersymmetry `genomics.'
Recent evidence has emerged pointing to the existence of three such fundamental
adinkras associated with distinct equivalence classes of a Coxeter group. A
partial description of these adinkras is given in terms of two types, termed
cis-and trans-adinkras (the latter being a degenerate doublet) in analogy to
cis/trans isomers in chemistry. Through a new and simple procedure that uses
adinkras, we find the irreducible off-shell adinkra representations of 4D,
$\mathcal{N}=1$ supergravity, in the old-minimal, non-minimal, and conformal
formulations. This procedure uncovers what appears to be a selection rule
useful to reverse engineer adinkras to higher dimensions. We categorize the
supergravity representations in terms of the number of cis-($n_c$) and
trans-($n_t$) adinkras in the representation and synthesize our new results
with our previous supersymmetry genomics results into a group theoretic
framework.
|
Conformal field theories on deformed spheres, anomalies, and
supersymmetry: We study the free energy of four-dimensional CFTs on deformed spheres. For
generic nonsupersymmetric CFTs only the coefficient of the logarithmic
divergence in the free energy is physical, which is an extremum for the round
sphere. We then specialize to $\mathcal{N}=2$ SCFTs where one can preserve some
supersymmetry on a compact manifold by turning on appropriate background
fields. For deformations of the round sphere the $c$ anomaly receives
corrections proportional to the supersymmetric completion of the (Weyl)$^2$
term, which we determine up to one constant by analyzing the scale dependence
of various correlators in the stress-tensor multiplet. We further show that the
double derivative of the free energy with respect to the marginal couplings is
proportional to the two-point function of the bottom components of the marginal
chiral multiplet placed at the two poles of the deformed sphere. We then use
anomaly considerations and counter-terms to parametrize the finite part of the
free energy which makes manifest its dependence on the K\"ahler potential. We
demonstrate these results for a theory with a vector multiplet and a massless
adjoint hypermultiplet using results from localization. Finally, by choosing a
special value of the hypermultiplet mass where the free energy is independent
of the deformation, we derive an infinite number of constraints between various
integrated correlators in $\mathcal{N}=4$ super Yang-Mills with any gauge group
and at all values of the coupling, extending previous results.
|
Phase Diagram of Gross-Neveu Model at Finite Temperature, Density and
Constant Curvature: We discuss a phase structure of chiral symmetry breaking in the Gross-Neveu
model at finite temperature, density and constant curvature. The effective
potential is evaluated in the leading order of the $1/N$-expansion and in a
weak curvature approximation. The third order critical line is found on the
critical surface in the parameter space of temperature, chemical potential and
constant curvature.
|
The Four-Loop $\mathcal{N}=4$ SYM Sudakov Form Factor: We present the Sudakov form factor in full color $\mathcal{N}=4$
supersymmetric Yang-Mills theory to four loop order and provide uniformly
transcendental results for the relevant master integrals through to weight
eight.
|
Mirror Symmetry and a $G_2$ Flop: By applying mirror symmetry to D-branes in a Calabi-Yau geometry we shed
light on a $G_2$ flop in M-theory relevant for large $N$ dualities in ${\cal
N}=1$ supersymmetric gauge theories. Furthermore, we derive superpotential for
M-theory on corresponding $G_2$ manifolds for all A-D-E cases. This provides an
effective method for geometric engineering of ${\cal N}=1$ gauge theories for
which mirror symmetry gives exact information about vacuum geometry. We also
find a number of interesting dual descriptions.
|
Deformed $σ$-models, Ricci flow and Toda field theories: It is shown that the Pohlmeyer map of a $\sigma$-model with a toric
two-dimensional target space naturally leads to the `sausage' metric. We then
elaborate the trigonometric deformation of the $\mathrm{CP}^{n-1}$-model,
proving that its $T$-dual metric is K\"ahler and solves the Ricci flow
equation. Finally, we discuss a relation between flag manifold $\sigma$-models
and Toda field theories.
|
Boundary form factors in the Smirnov--Fateev model with a diagonal
boundary $S$ matrix: The boundary conditions with diagonal boundary $S$ matrix and the boundary
form factors for the Smirnov--Fateev model on a half line has been considered
in the framework of the free field representation. In contrast to the case of
the sine-Gordon model, in this case the free field representation is shown to
impose severe restrictions on the boundary $S$ matrix, so that a finite number
of solutions is only consistent with the free field realization.
|
Quantum effects of a massive 3-form coupled to a Dirac field: We consider the coupling of A_{\mu\nu\rho} to the generic current of matter
field, later identified with the spin density current of a Dirac field. In
fact, one of the objectives of this paper is to investigate the impact of the
quantum fluctuations of A_{\mu\nu\rho} on the effective dynamics of the spinor
field. The consistency of the field equations, even at the classical level,
requires the introduction of a mass term for A_{\mu\nu\rho}. In this case, the
Casimir vacuum pressure includes a contribution that is explicitly dependent on
the mass of A_{\mu\nu\rho} and leads us to conclude that the mass term plays
the same role as the infrared cutoff needed to regularize the finite volume
partition functional previously calculated in the massless case. Remarkably,
even in the presence of a mass term, A_{\mu\nu\rho} contains a mixture of
massless and massive spin-0 fields so that the resulting equation is still
gauge invariant. This is yet another peculiar, but physically relevant property
of A_{\mu\nu\rho} since it is reflected in the effective dynamics of the spinor
fields and confirms the confining property of A_{\mu\nu\rho} already expected
from the earlier calculation of the Wilson loop.
|
RSOS Quantum Chains Associated with Off-Critical Minimal Models and
$\mathbb{Z}_n$ Parafermions: We consider the $\varphi_{1,3}$ off-critical perturbation ${\cal M}(m,m';t)$
of the general non-unitary minimal models where $2\le m\le m'$ and $m, m'$ are
coprime and $t$ measures the departure from criticality corresponding to the
$\varphi_{1,3}$ integrable perturbation. We view these models as the continuum
scaling limit in the ferromagnetic Regime III of the Forrester-Baxter
Restricted Solid-On-Solid (RSOS) models on the square lattice. We also consider
the RSOS models in the antiferromagnetic Regime II related in the continuum
scaling limit to $\mathbb{Z}_n$ parfermions with $n=m'-2$. Using an elliptic
Yang-Baxter algebra of planar tiles encoding the allowed face configurations,
we obtain the Hamiltonians of the associated quantum chains defined as the
logarithmic derivative of the transfer matrices with periodic boundary
conditions. The transfer matrices and Hamiltonians act on a vector space of
paths on the $A_{m'-1}$ Dynkin diagram whose dimension is counted by
generalized Fibonacci numbers.
|
Logarithmic corrections to black hole entropy and holography: We compute logarithmic corrections to the black hole entropy $S_{\rm bh}$ in
a holographic set up where the cosmological constant $\Lambda$ and Newton's
constant $G_D$ are taken to be thermodynamic parameters, related to variations
in bulk pressure \(P\) and central charge \(c\). In the bulk, the logarithmic
corrections are of the form: $\mathcal{S} = S_{\rm bh} - k \ln S_{\rm bh} +
\cdots$ arising due to fluctuations in thermodynamic volume, induced by a
variable $\Lambda$, in addition to energy fluctuations. We explicitly compute
this coefficient $k$ for the BTZ black hole and show that the result matches
with the one coming from the logarithmic corrections to the Cardy's formula. We
propose an entropy function in the CFT, which exactly reproduces the
logarithmic corrections to black hole entropy in arbitrary dimensions.
|
Four Dimensional Black Holes and Duality in Superstring Theory: Some recent results on the applications of duality (and related)
transformations to general four-dimensional, spherically symmetric,
asymptotically flat and time-independent string configurations are summarized.
Two classes of results have been obtained. First, these transformations are
used to generate the general such solution to the lowest-order field equations
in the alpha' expansion. Second, the action and implications of duality (based
on time-translation) on the general configuration is determined. It is found to
interchange two pairs of the six parameters which label these configurations,
namely: (1) the mass with the dilaton charge, and (2) the axion charge with the
Taub-NUT parameter. For the special case of the Schwarzshild black hole this
implies the relation M -> - k/M, where k is a known, positive, quantity. It is
argued that, in some circumstances, dual theories need not be equivalent in the
simplest sense.
|
The transformations of non-abelian gauge fields under translations: I consider infinitesimal translations $x'^{\alpha}=x^{\alpha}+\delta
x^{\alpha}$ and demand that Noether's approach gives a symmetric
energy-momentum tensor as it is required for gravitational sources. This
argument determines the transformations of non-abelian gauge fields under
infinitesimal translations to differ from the usually assumed invariance by the
gauge transformation, $A'^a_{\gamma} (x') - A^a_{\gamma}(x) = \partial_{\gamma}
[ \delta x_{\beta} A^{a \beta}(x)] + C^a_{bc} \delta x_{\beta} A^{c \beta}(x)
A^{b}_{\gamma}(x)$ where the $C^a_{bc}$ are the structure constants of the
gauge group.
|
Majorana Fermions in a Box: Majorana fermion dynamics may arise at the edge of Kitaev wires or
superconductors. Alternatively, it can be engineered by using trapped ions or
ultracold atoms in an optical lattice as quantum simulators. This motivates the
theoretical study of Majorana fermions confined to a finite volume, whose
boundary conditions are characterized by self-adjoint extension parameters.
While the boundary conditions for Dirac fermions in $(1+1)$-d are characterized
by a 1-parameter family, $\lambda = - \lambda^*$, of self-adjoint extensions,
for Majorana fermions $\lambda$ is restricted to $\pm i$. Based on this result,
we compute the frequency spectrum of Majorana fermions confined to a 1-d
interval. The boundary conditions for Dirac fermions confined to a 3-d region
of space are characterized by a 4-parameter family of self-adjoint extensions,
which is reduced to two distinct 1-parameter families for Majorana fermions. We
also consider the problems related to the quantum mechanical interpretation of
the Majorana equation as a single-particle equation. Furthermore, the equation
is related to a relativistic Schr\"odinger equation that does not suffer from
these problems.
|
Dual Pairs of Gauged Linear Sigma Models and Derived Equivalences of
Calabi-Yau threefolds: In this work we study the phase structure of skew symplectic sigma models,
which are a certain class of two-dimensional N = (2,2) non-Abelian gauged
linear sigma models. At low energies some of them flow to non-linear sigma
models with Calabi-Yau target spaces, which emerge from non-Abelian strong
coupling dynamics. The observed phase structure results in a non-trivial
duality proposal among skew symplectic sigma models and connects non-complete
intersection Calabi-Yau threefolds, that are non-birational among another, in a
common quantum Kahler moduli space. As a consequence we find non-trivial
identifications of spectra of topological B-branes, which from a modern
algebraic geometry perspective imply derived equivalences among Calabi-Yau
varieties. To further support our proposals, we calculate the two sphere
partition function of skew symplectic sigma models to determine geometric
invariants, which confirm the anticipated Calabi-Yau threefold phases. We show
that the two sphere partition functions of a pair of dual skew symplectic sigma
models agree in a non-trivial fashion. To carry out these calculations, we
develop a systematic approach to study higher-dimensional Mellin-Barnes type
integrals. In particular, these techniques admit the evaluation of two sphere
partition functions for gauged linear sigma models with higher rank gauge
groups, but are applicable in other contexts as well.
|
Batalin-Tyutin Quantization of the (2+1) dimensional nonabelian
Chern-Simons field theory: The (2+1) dimensional nonabelian Chern-Simons theory coupled to complex
scalar fields is quantized by using the Batalin-Tyutin canonical Hamiltonian
method which systematically embeds second-class constraint system into
first-class one. We obtain the gauge-invariant nonabelian Wess-Zumino type
action in the extended phase space.
|
AdS_4/CFT_3 Construction from Collective Fields: We pursue the construction of higher-spin theory in AdS_4 from CFT_3 of the
O(N) vector model in terms of canonical collective fields. In null plane
quantization an exact map is established between the two spaces. The
coordinates of the AdS_4 space-time are generated from the collective
coordinates of the bi-local field. This, in the light cone gauge, provides an
exact one to one reconstruction of bulk AdS_4 space-time and higher-spin
fields.
|
The Infrared Physics of Bad Theories: We study the complete moduli space of vacua of 3d $\mathcal{N}=4$ $U(N)$ SQCD
theories with $N_f$ fundamentals, building on the algebraic description of the
Coulomb branch, and deduce the low energy physics in any vacuum from the local
geometry of the moduli space. We confirm previous claims for good and ugly SQCD
theories, and show that bad theories flow to the same interacting fixed points
as good theories with additional free twisted hypermultiplets. A Seiberg-like
duality proposed for bad theories with $N \le N_f \le 2N-2$ is ruled out: the
spaces of vacua of the putative dual theories are different. However such bad
theories have a distinguished vacuum, which preserves all the global
symmetries, whose infrared physics is that of the proposed dual. We finally
explain previous results on sphere partition functions and elucidate the
relation between the UV and IR $R$-symmetry in this symmetric vacuum.
|
The static potential in QED$_3$ with non-minimal coupling: Here we study the effect of the non-minimal coupling $j^{\mu}\eps
\partial^{\nu} A^{\alpha} $ on the static potential in multiflavor QED$_3$.
Both cases of four and two components fermions are studied separately at
leading order in the $1/N $ expansion. Although a non-local Chern-Simons term
appears, in the four components case the photon is still massless leading to a
confining logarithmic potential similar to the classical one. In the two
components case, as expected, the parity breaking fermion mass term generates a
traditional Chern-Simons term which makes the photon massive and we have a
screening potential which vanishes at large inter-charge distance. The extra
non-minimal couplings have no important influence on the static potential at
large inter-charge distances. However, interesting effects show up at finite
distances. In particular, for strong enough non-minimal coupling we may have a
new massive pole in the photon propagator while in the opposite limit there may
be no poles at all in the irreducible case. We also found that, in general, the
non-minimal couplings lead to a finite range {\bf repulsive} force between
charges of opposite signs.
|
D0-D8-F1 in Massive IIA SUGRA: We present some new supersymmetric solutions of massive IIA supergravity
involving D0-branes, a D8-brane and a string. For the bosonic fields we use a
general ansatz with SO(8) symmetry.
|
Non-Equilibrium Thermo Field Dynamics for Relativistic Complex Scalar
and Dirac Fields: Relativistic quantum field theories for complex scalar and Dirac fields are
investigated in non-equilibrium thermo field dynamics. The thermal vacuum is
defined by the Bogoliubov transformed creation and annihilation operators. Two
independent Bogoliubov parameters are introduced for a charged field. Its
difference naturally induces the chemical potential. Time-dependent thermal
Bogoliubov transformation generates the thermal counter terms. We fix the terms
by the self-consistency renormalization condition. Evaluating the thermal
self-energy under the self-consistency renormalization condition, we derive the
quantum Boltzmann equations for the relativistic fields.
|
Bethe Ansatze for 19-vertex Models: The nineteen-vertex models of Zamolodchikov-Fateev, Izergin-Korepin and the
supersymmetric osp(1|2) with periodic boundary conditions are studied. We find
the spectrum of these quantum spin chains using the Coordinate Bethe Ansatz.
The approche is a suitable parametrization of their wavefunctions. We also
applied the Algebraic Bethe Ansatz in order to obtain the eigenvalues and
eigenvectors of the corresponding transfer matrices.
|
Special flow equation and GKP-Witten relation: We develop a framework for the reconstruction of the bulk theory dual to
conformal field theory (CFT) without any assumption by means of a flow
equation. To this end we investigate a minimal extension of the free flow
equation and find that at a special parametrization the conformal
transformation for a normalized smeared operator exactly becomes the isometry
of anti-de Sitter space (AdS). By employing this special flow equation to
O$(N)$ vector models, we explicitly show that the AdS geometry as well as the
scalar field satisfying the GKP-Witten relation concurrently emerge in this
framework.
|
Surface term, corner term, and action growth in F(Riemann) gravity
theory: After reformulating $F($Riemann$)$ gravity theory as a second derivative
theory by introducing two auxiliary fields to the bulk action, we derive the
surface term as well as the corner term supplemented to the bulk action for a
generic non-smooth boundary such that the variational principle is well posed.
We also introduce the counter term to make the boundary term invariant under
the reparametrization for the null segment. Then as a demonstration of the
power of our formalism, not only do we apply our expression for the full action
to evaluate the corresponding action growth rate of the Wheeler-DeWitt patch in
the Schwarzchild anti-de Sitter black hole for the $F(R)$ gravity and critical
gravity, where the corresponding late time behavior recovers the previous one
derived by other approaches, but also in the asymptotically Anti-de Sitter
black hole for the critical Einsteinian cubic gravity, where the late time
growth rate vanishes but still saturates the Lloyd bound.
|
Comparison between holographic deformed AdS and soft wall models for
fermions: We compare the holographic dressed soft wall and the exponentially deformed
AdS models for spin 1/2 fermions. We present the dressed soft wall model and
its analytical solutions for the left and right modes, and the corresponding
spectra, also including modifications considering hyperfine spin-spin and meson
cloud interactions, as well as anomalous dimensions. Then, we discuss the
deformed AdS model for spin 1/2 fermions and present their effective
Schr\"odinger equations for the left and right modes, for which only numerical
solutions are available. Then, we consider a polynomial expansion of the
effective potential of the deformed AdS model and show that in the quadratic
approximation it leads to exact analytical solutions comparable with the
dressed soft wall model and obtain the corresponding spectra for left and right
modes. We show a numerical comparison of the mass spectra of spin 1/2 baryons
for the dressed soft wall and the deformed AdS models. We present a detailed
relation between the quadratic approximation of the deformed AdS and the
dressed soft wall models for their spectra, wave functions and comments on the
deep inelastic scattering on both models. We find that these two models are
{\sl not} equivalent even in the quadratic approximation, but it is possible to
relate their left and right modes for particular choices of their parameters.
|
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