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Squeezing in a 2-D generalized oscillator: A two-dimensional generalized oscillator with time-dependent parameters is
considered to study the two-mode squeezing phenomena. Specific choices of the
parameters are used to determine the dispersion matrix and analytic
expressions, in terms of standard hermite polynomials, of the wavefunctions and
photon distributions. (to be publish in the Third Workshop on Squeezed States
and Uncertainty Relations, Baltimore, USA, (August 1993)) | Convergence of derivative expansions in scalar field theory: The convergence of the derivative expansion of the exact renormalisation
group is investigated via the computation of the beta function of massless
scalar lambda phi^4 theory. The derivative expansion of the Polchinski flow
equation converges at one loop for certain fast falling smooth cutoffs.
Convergence of the derivative expansion of the Legendre flow equation is
trivial at one loop, but also can occur at two loops and in particular
converges for an exponential cutoff. |
Fusion of RSOS Models as a Coset Construction: Using the vertex operator approach we show that fusion of the RSOS models can
be considered as a kind of coset construction which is very similar to the
coset construction of minimal models in conformal field theory. We reproduce
the excitation spectrum and $S$-matrix of the fusion RSOS models in the regime
III and show that their correlation functions and form factors can be expressed
in terms of those of the ordinary (ABF) RSOS models. | A generating formulation for free higher spin massless fields: An action describing the dynamics of an infinite collection of massless
integer spin fields with spin s=0,1,2,3, ...$\infty$ corresponding to totally
symmetric Young tableaux representations of Poincare and anti-de Sitter groups
is constructed, in any dimension d, in terms of two functions on a
2d-dimensional manifold. The action is represented by an integral localized on
a 2d-1-dimensional hypersurface. |
Supergravity Supertubes: We find the supergravity solution sourced by a supertube: a
(1/4)-supersymmetric D0-charged IIA superstring that has been blown up to a
cylindrical D2-brane by angular momentum. The supergravity solution captures
all essential features of the supertube, including the D2-dipole moment and an
upper bound on the angular momentum: violation of this bound implies the
existence of closed timelike curves, with a consequent ghost-induced
instability of supertube probes. | Spontaneous Radiation of Black Holes: We provide an explicitly hermitian hamiltonian description for the
spontaneous radiation of black holes, which is a many-level,
multiple-degeneracy generalization of the usual Janeys-Cummings model for
two-level atoms. By standard Wigner-Wiesskopf approximation, we show that for
the first one or few particles' radiation our model yields completely the same
power spectrum as hawking radiation requires. While in the many-particle
radiation cases, numeric methods allow us to follow the evolution of
microscopic state of a black hole exactly, from which we can get the firstly
increasing then decreasing entropy variation trend for the radiation particles
just as the Page-curve exhibited. Basing on this model analysis, we claim that
two ingredients are necessary for resolutions of the information missing
puzzle, a spontaneous radiation like mechanism for the production of hawking
particles and proper account of the macroscopic superposition happening in the
full quantum description of a black hole radiation evolution and, the working
logic of replica wormholes is an effect account of this latter ingredient.
As the basis for our interpretation of black hole Hawking radiation as their
spontaneous radiation, we also provide a fully atomic like inner structure
models for their microscopic states definition and origins of their
Bekenstein-Hawking entropy, that is, exact solution families to the Einstein
equation sourced by matter constituents oscillating across the central point
and their quantization. Such a first quantization model for black holes'
microscopic state is non necessary for our spontaneous radiation description,
but has advantages comparing with other alternatives, such as string theory
fuzzball or brick wall models. |
Construction and classification of novel BPS Wilson loops in quiver
Chern-Simons-matter theories: In this paper we construct and classify novel Drukker-Trancanelli (DT) type
BPS Wilson loops along infinite straight lines and circles in $\mathcal N=2,3$
quiver superconformal Chern-Simons-matter theories,
Aharony-Bergman-Jafferis-Maldacena (ABJM) theory, and $\mathcal N=4$ orbifold
ABJM theory. Generally we have four classes of Wilson loops, and all of them
preserve the same supersymmetries as the BPS Gaiotto-Yin (GY) type Wilson
loops. There are several free complex parameters in the DT type BPS Wilson
loops, and for two classes of Wilson loops in ABJM theory and $\mathcal N=4$
orbifold ABJM theory there are supersymmetry enhancements at special values of
the parameters. We check that the differences of the DT type and GY type Wilson
loops are $Q$-exact with $Q$ being some supercharges preserved by both the DT
type and GY type Wilson loops. The results would be useful to calculate vacuum
expectation values of the DT type Wilson loops in matrix models if they are
still BPS quantum mechanically. | Supersymmetric asymptotically locally AdS$_5$ gravitational solitons: We construct supersymmetric gravitational soliton solutions of
five-dimensional gauged supergravity coupled to arbitrarily many vector
multiplets. The solutions are complete, globally stationary, $1/4$-BPS and are
asymptotically locally AdS$_5$ with conformal boundary $\mathbb{R} \times
L(p,1)$. The construction uses an $SU(2) \times U(1)-$invariant ansatz
originally used by Gutowski and Reall to construct supersymmetric
asymptotically AdS$_5$ black holes. A subset of these solutions have previously
been obtained as supersymmetric limits of a class of local solutions of
$U(1)^3$ gauged supergravity found by Chong-Cvetic-Lu-Pope, and by
Lucietti-Ovchinnikov in their classification of $SU(2)$-invariant solutions of
minimal gauged supergravity. |
Cylinder partition function of the 6-vertex model from algebraic
geometry: We compute the exact partition function of the isotropic 6-vertex model on a
cylinder geometry with free boundary conditions, for lattices of intermediate
size, using Bethe ansatz and algebraic geometry. We perform the computations in
both the open and closed channels. We also consider the partial thermodynamic
limits, whereby in the open (closed) channel, the open (closed) direction is
kept small while the other direction becomes large. We compute the zeros of the
partition function in the two partial thermodynamic limits, and compare with
the condensation curves. | Ward identities and gauge independence in general chiral gauge theories: Using the Batalin-Vilkovisky formalism, we study the Ward identities and the
equations of gauge dependence in potentially anomalous general gauge theories,
renormalizable or not. A crucial new term, absent in manifestly nonanomalous
theories, is responsible for interesting effects. We prove that gauge
invariance always implies gauge independence, which in turn ensures
perturbative unitarity. Precisely, we consider potentially anomalous theories
that are actually free of gauge anomalies thanks to the Adler-Bardeen theorem.
We show that when we make a canonical transformation on the tree-level action,
it is always possible to re-renormalize the divergences and re-fine-tune the
finite local counterterms, so that the renormalized $\Gamma $ functional of the
transformed theory is also free of gauge anomalies, and is related to the
renormalized $\Gamma $ functional of the starting theory by a canonical
transformation. An unexpected consequence of our results is that the beta
functions of the couplings may depend on the gauge-fixing parameters, although
the physical quantities remain gauge independent. We discuss nontrivial checks
of high-order calculations based on gauge independence and determine how
powerful they are. |
A Framework for the Landscape: It seems likely that string theory has a landscape of vacua that includes
very many metastable de Sitter spaces. However, as emphasized by Banks, Dine
and Gorbatov, no current framework exists for examining these metastable vacua
in string theory. In this paper we attempt to correct this situation by
introducing an eternally inflating background in which the entire collection of
accelerating cosmologies is present as intermediate states. The background is a
classical solution which consists of a bubble of zero cosmological constant
inside de Sitter space, separated by a domain wall. At early and late times the
flat space region becomes infinitely big, so an S-matrix can be defined.
Quantum mechanically, the system can tunnel to an intermediate state which is
pure de Sitter space. We present evidence that a string theory S-matrix makes
sense in this background and contains metastable de Sitter space as an
intermediate state. | Bosonization and even Grassmann variables: A new approach to bosonization in relativistic field theories and many-body
systems, based on the use of fermionic composites as integration variables in
the Berezin integral defining the partition function of the system, is tested.
The method is applied to the study of a simplified version of the BCS model. |
All Loop N=2 String Amplitudes: Using the N=4 topological reformulation of N=2 strings, we compute all loop
partition function for special compactifications of N=2 strings as a function
of target moduli. We also reinterpret N=4 topological amplitudes in terms of
slightly modified N=2 topological amplitudes. We present some preliminary
evidence for the conjecture that N=2 strings is the large N limit of
Holomorphic Yang-Mills in 4 dimensions. | Gauge Symmetry Enhancement and Radiatively Induced Mass in the Large N
Nonlinear Sigma Model: We consider a hybrid of nonlinear sigma models in which two complex
projective spaces are coupled with each other under a duality. We study the
large N effective action in 1+1 dimensions. We find that some of the
dynamically generated gauge bosons acquire radiatively induced masses which,
however, vanish along the self-dual points where the two couplings
characterizing each complex projective space coincide. These points correspond
to the target space of the Grassmann manifold along which the gauge symmetry is
enhanced, and the theory favors the non-Abelian ultraviolet fixed point. |
Stability and thermodynamics of black rings: We study the phase diagram of D=5 rotating black holes and the black rings
discovered by Emparan and Reall. We address the issue of microcanonical
stability of these spacetimes and its relation to thermodynamics by using the
so-called ``Poincare method'' of stability. We are able to show that one of the
BR branches is always unstable, with a change of stability at the point where
both BR branches meet. We study the geometry of the thermodynamic state space
(``Ruppeiner geometry'') and compute the critical exponents to check the
corresponding scaling laws. We find that, at extremality, the system exhibits a
behaviour which, formally, is very similar to that of a second order phase
transition. | Seven-Sphere and the Exceptional N=7 and N=8 Superconformal Algebras: We study realizations of the exceptional non-linear (quadratically generated,
or W-type) N=8 and N=7 superconformal algebras with Spin(7) and G_2 affine
symmetry currents, respectively. Both the N=8 and N=7 algebras admit unitary
highest-weight representations in terms of a single boson and free fermions in
8 of Spin(7) and 7 of G_2, with the central charges c_8=26/5 and c_7=5,
respectively. Furthermore, we show that the general coset Ans"atze for the N=8
and N=7 algebras naturally lead to the coset spaces SO(8)xU(1)/SO(7) and
SO(7)xU(1)/G_2, respectively, as the additional consistent solutions for
certain values of the central charge. The coset space SO(8)/SO(7) is the
seven-sphere S^7, whereas the space SO(7)/G_2 represents the seven-sphere with
torsion, S^7_T. The division algebra of octonions and the associated triality
properties of SO(8) play an essential role in all these realizations. We also
comment on some possible applications of our results to string theory. |
Large Charge Four-Dimensional Extremal N=2 Black Holes with R^2-Terms: We consider N=2 supergravity in four dimensions with small R^2 curvature
corrections. We construct large charge extremal supersymmetric and
non-supersymmetric black hole solutions in all space, and analyze their
thermodynamic properties. | Bifurcations in the RG-flow of QCD: Bifurcation analysis is used to study an effective model of QCD$_4$ with
four-fermi interactions. Our analysis supports the scenario of a fixed point
merger at the lower edge of the conformal window. This indicates square root
scaling of the anomalous scaling dimensions of the fermion fields just above
the lower edge and exponential scaling just below. We also predict existence of
new fixed points in this model whose (dis)appearance may indicate transitions
of the flow within the conformal window. Furthermore, we make new predictions
for the critical value $(N_{f}/N_{c})_{\textrm{crit}}$ at the lower edge. We
also obtain exotic spiraling flows that are generated by complex scaling
dimensions of the effective four-fermi interactions. Finally, we extend the
model by adding a scalar field that couples with a Yukawa interaction term and
study the modifications it causes to RG-flows. |
N=4 SYM NMHV Loop Amplitude in Superspace: Here we construct N=4 SuperYang-Mills 6 point NMHV loop amplitude (amplitudes
with three minus helicities) as a full superspace form, using the $SU(4)_{R}$
anti-commuting spinor variables. Amplitudes with different external particle
and cyclic helicity ordering are then just a particular expansion of this
fermionic variable. We've verified this by explicit expansion obtaining
amplitudes with two gluino calculated before. We give results for all gluino
$A(\Lambda^{-}\Lambda^{-}\Lambda^{-}\Lambda^{+}\Lambda^{+}\Lambda^{+})$and all
scalar $A(\phi\phi\phi\phi\phi\phi)$scattering amplitude. A discussion of using
MHV vertex approach to obtain these amplitudes are given, which implies a
simplification for general loop amplitudes. | Neutrinos, mixed bosons, Quantum Reference Frames and entanglement: We discuss the relevance of quantum reference frames in the description of
mixed particle states. We show that the notion of rest frame for mixed
particles, which is classically ill-defined, can be introduced in the context
of quantum frames. We discuss the possible phenomenological implications,
displaying a new form of framedependent entanglement that characterizes
reactions involving mixed particles. |
BPS Sphalerons in the $F_2$ Non-Linear Sigma Model: We construct static and also time-dependent solutions in a non-linear sigma
model with target space being the flag manifold $F_2=SU(3)/U(1)^2$ on the four
dimensional Minkowski space-time by analytically solving the second order
Euler-Lagrange equation. We show the static solutions saturate an energy lower
bound and can be derived from coupled first order equations though they are
saddle point solutions. We also discuss basic properties of the time-dependent
solutions. | Construction of non-Abelian electric strings: We detail the construction of electric string solutions in $SU(2)$
Yang-Mills-Higgs theory with a scalar in the fundamental representation and
discuss the properties of the solution. We show that Schwinger gluon pair
production in the electric string background is absent. A similar construction
in other models, such as with an adjoint scalar field and the electroweak
model, does not yield solutions. |
Towards a second law for Lovelock theories: In classical general relativity described by Einstein-Hilbert gravity, black
holes behave as thermodynamic objects. In particular, the laws of black hole
mechanics can be interpreted as laws of thermodynamics. The first law of black
hole mechanics extends to higher derivative theories via the Noether charge
construction of Wald. One also expects the statement of the second law, which
in Einstein-Hilbert theory owes to Hawking's area theorem, to extend to higher
derivative theories. To argue for this however one needs a notion of entropy
for dynamical black holes, which the Noether charge construction does not
provide. We propose such an entropy function for the family of Lovelock
theories, treating the higher derivative terms as perturbations to the
Einstein-Hilbert theory. Working around a dynamical black hole solution, and
making no assumptions about the amplitude of departure from equilibrium, we
construct a candidate entropy functional valid to all orders in the low energy
effective field theory. This entropy functional satisfies a second law, modulo
a certain subtle boundary term, which deserves further investigation in
non-spherically symmetric situations. | Solving Gauge Invariant Systems without Gauge Fixing: the Physical
Projector in 0+1 Dimensional Theories: The projector onto gauge invariant physical states was recently constructed
for arbitrary constrained systems. This approach, which does not require gauge
fixing nor any additional degrees of freedom beyond the original ones---two
characteristic features of all other available methods for quantising
constrained dynamics---is put to work in the context of a general class of
quantum mechanical gauge invariant systems. The cases of SO(2) and SO(3) gauge
groups are considered specifically, and a comprehensive understanding of the
corresponding physical spectra is achieved in a straightforward manner, using
only standard methods of coherent states and group theory which are directly
amenable to generalisation to other Lie algebras. Results extend by far the few
examples available in the literature from much more subtle and delicate
analyses implying gauge fixing and the characterization of modular space. |
Evading divergences in quantum field theory: Explicit solution of a Green function in a non-renormalizable toy model
demonstrates that Green functions of the interacting theory fall off much
faster than at the tree level at large momenta. This suggests a method of
calculations in quantum field theory which is free of divergences. | Black hole entropy from Poisson brackets (demystification of some
calculations): Recently it has been suggested by S. Carlip that black hole entropy can be
derived from a central charge of the Virasoro algebra arising as a subalgebra
in the surface deformations of General Relativity in any dimension. Here it is
shown that the argumentation given in Section 2 of hep-th/9812013 and based on
the Regge-Teitelboim approach is unsatisfactory. The functionals used are
really ``non-differentiable'' under required variations and also the standard
Poisson brackets for these functionals are exactly zero so being unable to get
any Virasoro algebra with a central charge. Nevertheless Carlip's calculations
will be correct if we admit another definition for the Poisson bracket. This
new Poisson bracket differs from the standard one in surface terms only and
allows to work with ``non-differentiable'' functionals. |
A Nonstandard Supersymmetric KP Hierarchy: We show that the supersymmetric nonlinear Schr\"odinger equation can be
written as a constrained super KP flow in a nonstandard representation of the
Lax equation. We construct the conserved charges and show that this system
reduces to the super mKdV equation with appropriate identifications. We
construct various flows generated by the general nonstandard super Lax equation
and show that they contain both the KP and mKP flows in the bosonic limits.
This nonstandard supersymmetric KP hierarchy allows us to construct a new super
KP equation which is nonlocal. | Standard Models and Split Supersymmetry from Intersecting Brane
Orbifolds: We construct four dimensional three generation non-supersymmetric $SU(3)_c
\times SU(2)_L \times U(1)_Y$ intersecting D6-brane models with $\nu_R$\rq{s}.
At three stacks we find exactly the MSSM chiral fermion matter spectrum. At 4-,
5-stacks we find models with the massless fermion spectrum of the N=1 Standard
Model and massive exotic non-chiral matter; these models flow also to only the
SM. At 8-stacks we find MSSM-like models, with minimal massless exotics, made
from two different N=1 sectors. Exotic triplet masses put a lower bound on the
string scale of $2.79/2.89 \times 10^6$ GeV for a Higgs 124/126 GeV. It\rq{}s
the first appearance of N=0 stringy quivers with the MSSM and matter in
antisymmetric representations and perturbatively missing Yukawa couplings. The
present models are based on orientifolds of ${\bf T^6/(Z_3 \times Z_3)}$
compactifications of IIA theory based on the torus lattice AAA; all complex
moduli are fixed by the orbifold symmetry. We also present the spectrum rules +
GS anomaly cancellation for the ABB lattice. Moreover, we point out the
relevance of intersecting/and present D6-brane constructions on ideas related
to existence of split supersymmetry in nature. In this context we present
non-susy models with only the SM-matter and also MSSM-matter dominated models,
with massive gauginos and light higgsinos, that achieve the correct
supersymmetric GUT value for the Weinberg angle $sin^2 \theta = \frac{3}{8}$ at
a string scale $5 \cdot 10^{13} \ GeV < M_{S} < 1.4 \cdot 10^{17}$ GeV. It
appears that if only the SM survives at low energy the unification scale is
preserved at $5.03 \times 10^{13}$ GeV when n$_H$ =1, 3, 6. These models
support the existence of split supersymmetry scenario in string theory. |
The Power of Worldsheets: Applications and Prospects: We explain how perturbative string theory can be viewed as an exactly
renormalizable Weyl invariant quantum mechanics in the worldsheet
representation clarifying why string scattering amplitudes are both finite and
unambiguously normalized and explaining the origin of UV-IR relations in
spacetime. As applications we examine the worldsheet representation of
nonperturbative type IB states and of string solitons. We conclude with an
analysis of the thermodynamics of a free closed string gas establishing the
absence of the Hagedorn phase transition. We show that the 10D heterotic
strings share a stable finite temperature ground state with gauge group
SO(16)xSO(16). The free energy at the self-dual Kosterlitz-Thouless phase
transition is minimized with finite entropy and positive specific heat. The
open and closed string gas transitions to a confining long string phase at a
temperature at or below the string scale in the presence of an external
electric field. | Quenching the CME via the gravitational anomaly and holography: In the presence of a gravitational contribution to the chiral anomaly, the
chiral magnetic effect induces an energy current proportional to the square of
the temperature in equilibrium. In holography the thermal state corresponds to
a black hole. We numerically study holographic quenches in which a planar shell
of scalar matter falls into a black hole and rises its temperature. During the
process the momentum density (energy current) is conserved. The energy current
has two components, a non-dissipative one induced by the anomaly and a
dissipative flow component. The dissipative component can be measured via the
drag it asserts on an additional auxiliary color charge. Our results indicate
strong suppression very far from equilibrium. |
About the Claimed Longitudinal Nature of the Antisymmetric Tensor Field
After Quantization: It has long been claimed that antisymmetric tensor field of the second rank
is longitudinal after quantization. Such a situation is quite unacceptable from
a viewpoint of the Correspondence Principle. On the basis of the Lagrangian
formalism we calculate the Pauli-Lyuban'sky vector of relativistic spin for
this field. Even at the classical level it can be equal to zero after
application of the well-known constraints. The correct quantization procedure
permits us to propose solution of this puzzle in the modern field theory.
Obtained results develop the previous consideration of Evans [{\it Physica
A}214 (1995) 605-618]. | On the effective potential in higher-derivative superfield theories: We study the one-loop quantum corrections for higher-derivative superfield
theories, generalizing the approach for calculating the superfield effective
potential. In particular, we calculate the effective potential for two versions
of higher-derivative chiral superfield models. We point out that the
equivalence of the higher-derivative theory for the chiral superfield and the
one without higher derivatives but with an extended number of chiral
superfields occurs only when the mass term is contained in the general
Lagrangian. The presence of divergences can be taken as an indication of this
equivalence. |
String Theory, Space-Time Non-Commutativity and Structure Formation: A natural consequence of string theory is a non-commutative structure of
space-time on microscopic scales. The existence of a minimal length, and a
modification of the effective field theory are two consequences of this
space-time non-commutativity. I will first explore some consequences of the
modifications of the effective field theory for structure formation in the
context of an inflationary cosmology. Then, I will explore the possibility that
the existence of a minimal length will lead to a structure formation scenario
different from inflation. Specifically, I will discuss recent work on string
gas cosmology. | Remnants in two-dimensional quantum gravity: In this work we consider a two-dimensional quantum black hole sourced by the
trace anomaly of a conformal field theory. By using holography, we are able to
prove that the black hole size is always proportional to the number of states
inside the black hole, a result that might be interpreted as a two dimensional
version of the Bekenstein entropy law. Finally, we also show that such a black
hole has a minimal size (a remnant). Extrapolating this result for higher
dimensions, we show that this would imply that the remnant has a size way
larger than the Planck length and is, therefore, always weakly coupled. |
Computing real time correlation functions on a hybrid classical/quantum
computer: Quantum devices may overcome limitations of classical computers in studies of
nuclear structure functions and parton Wigner distributions of protons and
nuclei. In this talk, we discuss a worldline approach to compute nuclear
structure functions in the high energy Regge limit of QCD using a hybrid
quantum computer, by expressing the fermion determinant in the QCD path
integral as a quantum mechanical path integral over $0+1$-dimensional fermionic
and bosonic world-lines in background gauge fields. Our simplest example of
computing the well-known dipole model result for the structure function $F_2$
in the high energy Regge limit is feasible with NISQ era technology using few
qubits and shallow circuits. This example can be scaled up in complexity and
extended in scope to compute structure functions, scattering amplitudes and
other real-time correlation functions in QCD, relevant for example to describe
non-equilibrium transport of quarks and gluons in a Quark-Gluon-Plasma. | Magnetically-enhanced open string pair production: We consider the stringy interaction between two parallel stacks of D3 branes
placed at a separation. Each stack of D3 branes in a similar fashion carry an
electric flux and a magnetic flux with the two sharing no common field strength
index. The interaction amplitude has an imaginary part, giving rise to the
Schwinger-like pair production of open strings. We find a significantly
enhanced rate of this production when the two electric fluxes are almost
identical and the brane separation is on the order of string scale. This
enhancement will be largest if the two magnetic fluxes are opposite in
direction. This novel enhancement results from the interplay of the
non-perturbative Schwinger-type pair production due to the electric flux and
the stringy tachyon due to the magnetic flux, and may have realistic physical
applications. |
Division Algebras: 26 Dimensions; 3 Families: The link of the Division Algebras to 10-dimensional spacetime and one
leptoquark family is extended to 26-dimensional spacetime and three leptoquark
families. | Slowly rotating black hole solution in the scalar-tensor theory with
nonminimal derivative coupling and its thermodynamics: We obtain a slowly rotating black hole solution in the scalar-tensor theory
of gravity with nonminimal derivative coupling to the Einstein tensor.
Properties of the obtained solution have been examined carefully. We also
investigate the thermodynamics of the given black hole. To obtain thermodynamic
functions, namely its entropy we use the Wald procedure which is suitable for
quite general diffeomorphism-invariant theories. The applied approach allowed
us to obtain the expression for entropy and the first law of black hole
thermodynamics. Having introduced thermodynamic pressure which is related to
the cosmological constant we have examined thermodynamics of the black hole in
the so called extended phase space. The extended phase space and specifically
chosen scalar `charge' allowed us not only to obtain the generalized first law
but also derive the Smarr relation. The behaviour of black hole's temperature,
heat capacity and Gibbs free energy shows a lot of similarities with the
behaviour of the corresponding values for Schwarzschild-AdS black hole in
standard General Relativity. |
Conservative Scattering of Reissner-Nordström Black Holes at Third
Post-Minkowskian Order: Using a recently developed effective field theory formalism for extreme mass
ratios [2308.14832], we present a calculation of charged black hole scattering
at third post-Minkowskian order. The charges and masses are kept arbitrary, and
the result interpolates from the scattering of Schwarzschild to extremal
charged black holes, and beyond to charged particles in electrodynamics --
agreeing with previously reported results in all such limits. The computation
of the radial action is neatly organized in powers of the mass ratio. The probe
(0SF) contributions are readily computed by direct integration of the radial
momentum, and we use the effective field theory to compute the subleading (1SF)
contributions via background-field Feynman rules supplemented by an operator
encoding recoil of the background. Together these contributions completely
determine the conservative physics at order~$\mathcal{O}(G^{3})$. | Twisted Supersymmetric Gauge Theories and Orbifold Lattices: We examine the relation between twisted versions of the extended
supersymmetric gauge theories and supersymmetric orbifold lattices. In
particular, for the $\mathcal{N}=4$ SYM in $d=4$, we show that the continuum
limit of orbifold lattice reproduces the twist introduced by Marcus, and the
examples at lower dimensions are usually Blau-Thompson type. The orbifold
lattice point group symmetry is a subgroup of the twisted Lorentz group, and
the exact supersymmetry of the lattice is indeed the nilpotent scalar
supersymmetry of the twisted versions. We also introduce twisting in terms of
spin groups of finite point subgroups of $R$-symmetry and spacetime symmetry. |
Extended BPH Renormalization of Cutoff Scalar Field Theories: We show that general cutoff scalar field theories in four dimensions are
perturbatively renormalizable through the use of diagrammatic techniques and an
adapted BPH renormalization method. Weinberg's convergence theorem is used to
show that operators in the Lagrangian with dimension greater than four, which
are divided by powers of the cutoff, produce perturbatively only local
divergences in the two-, three-, and four-point correlation functions. We also
show that the renormalized Green's functions are the same as in ordinary
$\Phi^4$ theory up to corrections suppressed by inverse powers of the cutoff.
These conclusions are consistent with those of existing proofs based on the
renormalization group. | Classification of discrete modular symmetries in Type IIB flux vacua: We classify discrete modular symmetries in the effective action of Type IIB
string on toroidal orientifolds with three-form fluxes, emphasizing on
$T^6/\mathbb{Z}_2$ and $T^6/(\mathbb{Z}_2\times \mathbb{Z}_2^\prime)$
orientifold backgrounds. On the three-form flux background, the modular group
is spontaneously broken down to its congruence subgroup whose pattern is
severely constrained by a quantization of fluxes and tadpole cancellation
conditions. We explicitly demonstrate that the congruence subgroups appearing
in the effective action arise on magnetized D-branes wrapping certain cycles of
tori. |
Hybrid Gauge Theory: Cyclic symmetry $C_N$ is gauged in such a way that the local parametrization
is provided by a Lie group: matter fields are in irreducible representations of
$C_N$ while gauge fields are in the adjoint representation of a Lie group,
hence "hybrid". Allowed simple Lie groups are only SO(2) for $N=2$, SU(3) for
$N=3$, and SU(2) for all $N$. The implication of the local discrete symmetry
$C_N$ is evident as the ratio of the coupling constant to the usual gauge
theory one of the parametrization Lie group is given by that of the length
between any two vertices of a regular N-polygon to the radius of the
circumcircle: $2\sin(n\pi/N),\ n\in {\mathbb Z}_N$. | Remarks on the existence of Spinning Membrane Actions: It has been recently argued by some authors that is impossible to construct a
Weyl invariant spinning membrane action, where the $S$-supersymmetry associated
with the 3D superconformal algebra, is relinquished without gauge fixing.
Contrary to those assertions, we show why it is possible to construct a
Weyl-invariant spinning polynomial membrane action, without curvature
terms,where $both$ the conformal boost symmetry and $S$-supersymmetry are
explicitly broken by the action. It is shown that the gauge algebra $closes$
despite that the two latter symmetries are broken . For this to happen, a
modifed $Q$-supersymmetry transformation, a sort of new $Q+K+S$ ``sum `` rule,
is required that generates the compensating terms to cancel the spurious
contributions fromthe $S$ and conformal boost anomalous transformations. A
substantial discussion of the quantization of the spinning membrane and
anomalies is given. We review briefly the role that this spinning membrane
action may have in the theory of $D$-branes, Skyrmions and BPS monopoles in the
large $N$-limit of SU(N) Yang-Mills . |
Some Calculable Contributions to Holographic Entanglement Entropy: Using the AdS/CFT correspondence, we examine entanglement entropy for a
boundary theory deformed by a relevant operator and establish two results. The
first is that if there is a contribution which is logarithmic in the UV
cut-off, then the coefficient of this term is independent of the state of the
boundary theory. In fact, the same is true of all of the coefficients of
contributions which diverge as some power of the UV cut-off. Secondly, we show
that the relevant deformation introduces new logarithmic contributions to the
entanglement entropy. The form of some of these new contributions is similar to
that found recently in an investigation of entanglement entropy in a free
massive scalar field theory [1]. | On Gauge-Invariant Boundary Conditions for 2d Gravity with Dynamical
torsion: In the example of $R^2+T^2$ gravity on the unit two dimensional disk we
demonstrate that in the presence of an independent spin connection it is
possible to define local gauge invariant boundary conditions even on boundaries
which are not totally geodesic. One-loop partition function and the
corresponding heat kernel are calculated. |
Functional Renormalization Analytically Continued: We discuss a method to analytically continue functional renormalization group
equations from imaginary Matsubara frequencies to the real frequency axis. In
this formalism, we investigate the analytic structure of the flowing action and
the propagator for a theory of scalar fields with $O(N)$ symmetry. We go on to
show how it is possible to derive and solve flow equations for real-time
properties such as particle decay widths. Our treatment is fully
Lorentz-invariant and enables an improved, self-consistent derivative expansion
in Minkowski space. | Stability of accelerating cosmology in two scalar-tensor theory: Little
Rip versus de Sitter: We develop the general reconstruction scheme in two scalar model. The
quintom-like theory which may describe (different) non-singular Little Rip or
de Sitter cosmology is reconstructed. (In)stability of such dark energy
cosmologies as well as the flow to fixed points is studied. The stability of
Little Rip universe which leads to dissolution of bound objects sometime in
future indicates that no classical transition to de Sitter space occurs. |
A superspace formulation of the BV action: We show that the BV (Batalin Vilkovisky) action, formulated with an extended
BRST symmetry (including the shift symmetry), is also invariant under an
extended anti-BRST transformation (where the antifields are the parameters of
the transformation), when the gauge fixing Lagrangian is both BRST and
anti-BRST invariant. We show that for a general gauge fixing Lagrangian, the BV
action can be written in a manifestly extended BRST invariant manner in a
superspace with one Grassmann coordinate whereas it can be expressed in a
manifestly extended BRST and anti-BRST invariant manner in a superspace with
two Grassmann coordinates when the gauge fixing Lagrangian is invariant under
both BRST and anti-BRST transformations. | Solution of One-dimensional Dirac Equation via Poincare Map: We solve the general one-dimensional Dirac equation using a "Poincare Map"
approach which avoids any approximation to the spacial derivatives and reduces
the problem to a simple recursive relation which is very practical from the
numerical implementation point of view. To test the efficiency and rapid
convergence of this approach we apply it to a vector coupling Woods--Saxon
potential, which is exactly solvable. Comparison with available analytical
results is impressive and hence validates the accuracy and efficiency of this
method. |
On the AdS Higher Spin / O(N) Vector Model Correspondence: degeneracy of
the holographic image: We explore the conjectured duality between the critical O(N) vector model and
minimal bosonic massless higher spin (HS) theory in AdS. In the boundary free
theory, the conformal partial wave expansion (CPWE) of the four-point function
of the scalar singlet bilinear is reorganized to make it explicitly
crossing-symmetric and closed in the singlet sector, dual to the bulk HS gauge
fields. We are able to analytically establish the factorized form of the fusion
coefficients as well as the two-point function coefficient of the HS currents.
We insist in directly computing the free correlators from bulk graphs with the
unconventional branch. The three-point function of the scalar bilinear turns
out to be an "extremal" one at d=3. The four-leg bulk exchange graph can be
precisely related to the CPWs of the boundary dual scalar and its shadow. The
flow in the IR by Legendre transforming at leading 1/N, following the pattern
of double-trace deformations, and the assumption of degeneracy of the hologram
lead to the CPWE of the scalar four-point function at IR. Here we confirm some
previous results, obtained from more involved computations of skeleton graphs,
as well as extend some of them from d=3 to generic dimension 2<d<4. | Scattering amplitudes of massive Nambu-Goldstone bosons: Massive Nambu-Goldstone (mNG) bosons are quasiparticles whose gap is
determined exactly by symmetry. They appear whenever a symmetry is broken
spontaneously in the ground state of a quantum many-body system, and at the
same time explicitly by the system's chemical potential. In this paper, we
revisit mNG bosons and show that apart from their gap, symmetry also protects
their scattering amplitudes. Just like for ordinary gapless NG bosons, the
scattering amplitudes of mNG bosons vanish in the long-wavelength limit. Unlike
for gapless NG bosons, this statement holds for any scattering process
involving one or more external mNG states; there are no kinematic singularities
associated with the radiation of a soft mNG boson from an on-shell initial or
final state. |
Graphical Representation of SUSY and Application to QFT: We present a graphical representation of the supersymmetry and the graphical
calculation. Calculation is demonstrated for 4D Wess-Zumino model and for Super
QED. The chiral operators are graphically expressed in an illuminating way. The
tedious part of SUSY calculation, due to manipulating chiral suffixes, reduces
considerably. The application is diverse. | Wilson Renormalization Group Equations for the Critical Dynamics of
Chiral Symmetry: The critical dynamics of the chiral symmetry breaking induced by gauge
interaction is examined in the Wilson renormalization group framework in
comparison with the Schwinger-Dyson approach. We derive the beta functions for
the four-fermi couplings in the sharp cutoff renormalzation group scheme, from
which the critical couplings and the anomalous dimensions of the fermion
composite operators near criticality are immediately obtained. It is also shown
that the beta functions lead to the same critical behavior found by solving the
so-called ladder Schwinger-Dyson equation, if we restrict the radiative
corrections to a certain limited type. |
A No-go Theorem for a Gauge Vector as a Space-time Goldstone: Scalars and fermions can arise as Goldstone modes of non-linearly realised
extensions of the Poincare group (with important implications for the soft
limits of such theories): the Dirac-Born-Infeld scalar realises a
higher-dimensional Poincare symmetry, while the Volkov-Akulov fermion
corresponds to super-Poincare. In this paper we classify extensions of the
Poincare group which give rise to a vector Goldstone mode instead. Our main
result is that there are no healthy interacting $U(1)$ gauge theories that
non-linearly realise space-time symmetries beyond gauge transformations. This
implies that the special soft limits of e.g. the Born-Infeld vector cannot be
explained by space-time symmetries. | CFT duals of Kerr-Taub-NUT and beyond: The duality relating the four-dimensional Kerr-Taub-NUT black hole to a
thermal two-dimensional CFT with central charges $c_L=c_R=12 J_0$ is analyzed
in detail, generalizing an argument given recently for Kerr within the
soft-hair approach. The hidden conformal symmetry is realized in the form of
$Vir_L \times Vir_R$ diffeomorphisms which act non-trivially on the black hole
horizon. Semiclassical formulae are derived for the temperature and central
charges of the dual CFT. Assuming the applicability of the Cardy formula, these
CFT quantities precisely reproduce the macroscopic Bekenstein-Hawking area law.
Various further generalizations including the complete family of black holes in
four dimensions are discussed. |
Quintics with Finite Simple Symmetries: We construct all quintic invariants in five variables with simple Non-Abelian
finite symmetry groups. These define Calabi-Yau three-folds which are left
invariant by the action of A_5, A_6 or PSL_2(11). | Numerical Analysis of Black Hole Evaporation: Black hole formation/evaporation in two-dimensional dilaton gravity can be
described, in the limit where the number $N$ of matter fields becomes large, by
a set of second-order partial differential equations. In this paper we solve
these equations numerically. It is shown that, contrary to some previous
suggestions, black holes evaporate completely a finite time after formation. A
boundary condition is required to evolve the system beyond the naked
singularity at the evaporation endpoint. It is argued that this may be
naturally chosen so as to restore the system to the vacuum. The analysis also
applies to the low-energy scattering of $S$-wave fermions by four-dimensional
extremal, magnetic, dilatonic black holes. |
SUSY breaking mediation by throat fields: We investigate, in the general framework of KKLT, the mediation of
supersymmetry breaking by fields propagating in the strongly warped region of
the compactification manifold ('throat fields'). Such fields can couple both to
the supersymmetry breaking sector at the IR end of the throat and to the
visible sector at the UV end. We model the supersymmetry breaking sector by a
chiral superfield which develops an F-term vacuum expectation value. It turns
out that the mediation effect of vector multiplets propagating in the throat
can compete with modulus-anomaly mediation. Moreover, such vector fields are
naturally present as the gauge fields arising from isometries of the throat
(most notably the SO(4) isometry of the Klebanov-Strassler solution). Their
mediation effect is important in spite of their large 4d mass. The latter is
due to the breaking of the throat isometry by the compact manifold at the UV
end of the throat. The contribution from heavy chiral superfields is found to
be subdominant. | BPS-like potential for compactifications of heterotic M-theory?: We analyze the possibility to rewrite the action of Horava-Witten theory in a
BPS-like form, which means that it is given as a sum of squares of the
supersymmetry conditions. To this end we compactify the theory on a seven
dimensional manifold of SU(3) structure and rewrite the scalar curvature of the
compactification manifold in terms of the SU(3) structure forms. This shows
that a BPS-like form cannot be obtained in general, but only for certain types
of compactifications. |
Self-interacting scalar fields on spacetime with compact hyperbolic
spatial part: We calculate the one-loop effective potential of a self-interacting scalar
field on the spacetime of the form $\reals^2\times H^2/\Gamma$. The Selberg
trace formula associated with a co-compact discrete group $\Gamma$ in
$PSL(2,\reals )$ (hyperbolic and elliptic elements only) is used. The closed
form for the one-loop unrenormalized and renormalized effective potentials is
given. The influence of non-trivial topology on curvature induced phase
transitions is also discussed. | Effective Field Theory of non-Attractor Inflation: We present the model-independent studies of non attractor inflation in the
context of effective field theory (EFT) of inflation. Within the EFT approach
two independent branches of non-attractor inflation solutions are discovered in
which a near scale-invariant curvature perturbation power spectrum is generated
from the interplay between the variation of sound speed and the second slow
roll parameter \eta. The first branch captures and extends the previously
studied models of non-attractor inflation in which the curvature perturbation
is not frozen on super-horizon scales and the single field non-Gaussianity
consistency condition is violated. We present the general expression for the
amplitude of local-type non-Gaussianity in this branch. The second branch is
new in which the curvature perturbation is frozen on super-horizon scales and
the single field non-Gaussianity consistency condition does hold in the
squeezed limit. Depending on the model parameters, the shape of bispectrum in
this branch changes from an equilateral configuration to a folded configuration
while the amplitude of non-Gaussianity is less than unity. |
Noncommutative General Relativity: We define a theory of noncommutative general relativity for canonical
noncommutative spaces. We find a subclass of general coordinate transformations
acting on canonical noncommutative spacetimes to be volume-preserving
transformations. Local Lorentz invariance is treated as a gauge theory with the
spin connection field taken in the so(3,1) enveloping algebra. The resulting
theory appears to be a noncommutative extension of the unimodular theory of
gravitation. We compute the leading order noncommutative correction to the
action and derive the noncommutative correction to the equations of motion of
the weak gravitation field. | Extremal non-BPS black holes and entropy extremization: At the horizon, a static extremal black hole solution in N=2 supergravity in
four dimensions is determined by a set of so-called attractor equations which,
in the absence of higher-curvature interactions, can be derived as
extremization conditions for the black hole potential or, equivalently, for the
entropy function. We contrast both methods by explicitly solving the attractor
equations for a one-modulus prepotential associated with the conifold. We find
that near the conifold point, the non-supersymmetric solution has a
substantially different behavior than the supersymmetric solution. We analyze
the stability of the solutions and the extrema of the resulting entropy as a
function of the modulus. For the non-BPS solution the region of attractivity
and the maximum of the entropy do not coincide with the conifold point. |
Gravity duals of N = 2 superconformal field theories with no
electrostatic description: We construct the first eleven-dimensional supergravity solutions, which are
regular, have no smearing and possess only SO(2,4) x SO(3) x U(1)_R isometry.
They are dual to four-dimensional field theories with N = 2 superconformal
symmetry. We utilise the Toda frame of self-dual four-dimensional Euclidean
metrics with SU(2) rotational symmetry. They are obtained by transforming the
Atiyah--Hitchin instanton under SL(2,R) and are expressed in terms of theta
functions. The absence of any extra U(1) symmetry, even asymptotically, renders
inapplicable the electrostatic description of our solution. | Additional considerations in the definition and renormalization of
non-covariant gauges: In this work, we pursue further consequences of a general formalism for
non-covariant gauges developed in an earlier work (hep-th/0205042). We carry
out further analysis of the additional restrictions on renormalizations noted
in that work. We use the example of the axial gauge A_3=0. We find that if
multiplicative renormalization together with ghost-decoupling is to hold, the
``prescription-term'' (that defines a prescription) cannot be chosen
arbitrarily but has to satisfy certain non-trivial conditions (over and above
those implied by the validity of power counting) arising from the WT identities
associated with the residual gauge invariance. We also give a restricted class
of solutions to these conditions. |
Supersymmetric Spacetimes from Curved Superspace: We review the superspace technique to determine supersymmetric spacetimes in
the framework of off-shell formulations for supergravity in diverse dimensions
using the case of 3D N=2 supergravity theories as an illustrative example. This
geometric formalism has several advantages over other approaches advocated in
the last four years. Firstly, the infinitesimal isometry transformations of a
given curved superspace form, by construction, a finite-dimensional Lie
superalgebra, with its odd part corresponding to the rigid supersymmetry
transformations. Secondly, the generalised Killing spinor equation, which must
be obeyed by the supersymmetry parameters, is a consequence of the more
fundamental superfield Killing equation. Thirdly, general rigid supersymmetric
theories on a curved spacetime are readily constructed in superspace by making
use of the known off-shell supergravity-matter couplings and restricting them
to the background chosen. It is the superspace techniques which make it
possible to generate arbitrary off-shell supergravity-matter couplings.
Fourthly, all maximally supersymmetric Lorentzian spaces correspond to those
off-shell supergravity backgrounds for which the Grassmann-odd components of
the superspace torsion and curvature tensors vanish, while the Grassmann-even
components of these tensors are annihilated by the spinor derivatives. | Extremal solutions of the S3 model and nilpotent orbits of G2(2): We study extremal black hole solutions of the S3 model (obtained by setting
S=T=U in the STU model) using group theoretical methods. Upon dimensional
reduction over time, the S3 model exhibits the pseudo-Riemannian coset
structure G/K with G=G2(2) and K=SO(2,2). We study nilpotent K-orbits of G2(2)
corresponding to non-rotating single-center extremal solutions. We find six
such distinct K-orbits. Three of these orbits are supersymmetric, one is
non-supersymmetric, and two are unphysical. We write general solutions and
discuss examples in all four physical orbits. We show that all solutions in
supersymmetric orbits when uplifted to five-dimensional minimal supergravity
have single-center Gibbons-Hawking space as their four-dimensional Euclidean
hyper-K\"ahler base space. We construct hitherto unknown extremal
(supersymmetric as well as non-supersymmetric) pressureless black strings of
minimal five-dimensional supergravity and briefly discuss their relation to
black rings. |
Bhabha scattering in Very Special Relativity at finite temperature: In this paper the differential cross section for Bhabha scattering in the
Very Special Relativity (VSR) framework is calculated. The main characteristic
of the VSR is to modify the gauge invariance. This leads to different types of
interactions appearing in a non-local form. In addition, using the Thermo Field
Dynamics formalism, thermal corrections for the differential cross section of
Bhabha scattering in VSR framework are obtained. | Quantum Stability of Accelerated Black Holes: We study quantum aspects of the accelerated black holes in some detail.
Explicitly shown is the fact that a uniform acceleration stabilizes certain
charged black holes against the well-known thermal evaporation. Furthermore, a
close inspection of the geometry reveals that this is possible only for
near-extremal black holes and that most nonextremal varieties continue to
evaporate with a modified spectrum under the acceleration. We also introduce a
two-dimensional toy model where the energy-momentum flow is easily obtained for
general accelerations, and find the behavior to be in accordance with the
four-dimensional results. After a brief comparison to the classical system of a
uniformly accelerated charge, we close by pointing out the importance of this
result in the WKB expansion of the black hole pair-creation rate. |
An Addendum to the Heisenberg-Euler effective action beyond one loop: We study the effective interactions of external electromagnetic fields
induced by fluctuations of virtual particles in the vacuum of quantum
electrodynamics. Our main focus is on these interactions at two-loop order. We
discuss in detail the emergence of the renowned Heisenberg-Euler effective
action from the underlying microscopic theory of quantum electrodynamics,
emphasizing its distinction from a standard one-particle irreducible effective
action. In our explicit calculations we limit ourselves to constant and slowly
varying external fields, allowing us to adopt a locally constant field
approximation. One of our main findings is that at two-loop order there is a
finite one-particle reducible contribution to the Heisenberg-Euler effective
action in constant fields, which was previously assumed to vanish. In addition
to their conceptual significance, our results are relevant for high-precision
probes of quantum vacuum nonlinearity in strong electromagnetic fields. | Quantum $κ$-deformations of D=4 relativistic supersymmetries: We describe the quantum $\kappa$-deformation of super-Poincar\'{e} algebra,
with fundamental mass-like deformation parameter $\kappa$. We shall describe
the result in graded bicrossproduct basis, with classical Lorentz superalgebra
sector which includes half of the supercharges. |
Perturbative renormalization of lattice N=4 super Yang-Mills theory: We consider N=4 super Yang-Mills theory on a four-dimensional lattice. The
lattice formulation under consideration retains one exact supersymmetry at
non-zero lattice spacing. We show that this feature combined with gauge
invariance and the large point group symmetry of the lattice theory ensures
that the only counterterms that appear at any order in perturbation theory
correspond to renormalizations of existing terms in the bare lattice action. In
particular we find that no mass terms are generated at any finite order of
perturbation theory. We calculate these renormalizations by examining the
fermion and auxiliary boson self energies at one loop and find that they all
exhibit a common logarithmic divergence which can be absorbed by a single
wavefunction renormalization. This finding implies that at one loop only a fine
tuning of the finite parts is required to regain full supersymmetry in the
continuum limit. | Varying electric charge in multiscale spacetimes: We derive the covariant equations of motion for Maxwell field theory and
electrodynamics in multiscale spacetimes with weighted Laplacian. An effective
spacetime-dependent electric charge of geometric origin naturally emerges from
the theory, thus giving rise to a varying fine-structure constant. The theory
is compared with other varying-coupling models, such as those with a varying
electric charge or varying speed of light. The theory is also confronted with
cosmological observations, which can place constraints on the characteristic
scales in the multifractional measure. We note that the model considered here
is fundamentally different from those previously proposed in the literature,
either of the varying-e or varying-c persuasion. |
Universality between vector-like and chiral quiver gauge theories:
Anomalies and domain walls: We study low-energy dynamics of $[SU(N)]^K$ chiral quiver gauge theories in
connection with $\mathcal{N}=1$ super Yang-Mills (SYM) theory, and quantum
chromodynamics with bi-fundamental fermions (QCD(BF)). These theories can be
obtained by $\mathbb{Z}_K$ orbifold projections of $\mathcal{N}=1$ $SU(NK)$ SYM
theory, but the perturbative planar equivalence does not extend
nonperturbatively for $K\ge 3$. In order to study low-energy behaviors, we
analyze these systems using 't~Hooft anomaly matching and reliable semiclassics
on $\mathbb{R}^3\times S^1$. Thanks to 't~Hooft anomaly that involves $1$-form
center symmetry and discrete chiral symmetry, we predict that chiral symmetry
must be spontaneously broken in the confinement phase, and there exist $N$
vacua. Theories with even $K$ possess a physical $\theta$ angle despite the
presence of massless fermions, and we further predict the $N$-branch structure
associated with it; the number of vacua is enhanced to $2N$ at $\theta=\pi$ due
to spontaneous $CP$ breaking. Both of these predictions are explicitly
confirmed by reliable semiclassics on $\mathbb{R}^3\times S^1$ with the
double-trace deformation. Symmetry and anomaly of odd-$K$ theories are the same
as those of the ${\cal N}=1$ SYM, and the ones of even-$K$ theories are same as
those of QCD(BF). We unveil why there exists universality between vector-like
and chiral quiver theories, and conjecture that their ground states can be
continuously deformed without quantum phase transitions. We briefly discuss
anomaly inflow on the domain walls connecting the vacua of the theory and
possible anomaly matching scenarios. | The Off-Shell Recursion for Gravity and the Classical Double Copy for
currents: We construct the off-shell recursion for gravity and the graviton current for
the perturbative double field theory (DFT). We first formulate the perturbative
DFT, which is equivalent but simpler to perturbative general relativity, to
all-orders in fluctuations of generalised metric. The perturbative action and
equations of motion (EoM) are derived to arbitrary order for pure gravity case.
We then derive the graviton off-shell recursion, the gravity counterpart of the
Berends-Giele recursion in Yang-Mills theory, through the so-called perturbiner
method using the EoM of the perturbative DFT. We solve the recursion
iteratively and obtain the graviton off-shell currents explicitly. We then
discuss the classical double copy for the off-shell currents. We present the
current KLT relation for gravity by extending the result proposed by Mizera and
Skrzypek for the non-gravitational effective field theories. The relation
represents graviton currents by squaring gluon currents with the KLT kernel up
to gauge transformation and regular terms that do not have any pole. Finally we
discuss the off-shell conservation of currents for nonlinear gauge choices. |
Spectral curves and $W$-representations of matrix models: We explain how the spectral curve can be extracted from the ${\cal
W}$-representation of a matrix model. It emerges from the part of the ${\cal
W}$-operator, which is linear in time-variables. A possibility of extracting
the spectral curve in this way is important because there are models where
matrix integrals are not yet available, and still they possess all their
important features. We apply this reasoning to the family of WLZZ models and
discuss additional peculiarities which appear for the non-negative value of the
family parameter $n$, when the model depends on additional couplings (dual
times). In this case, the relation between topological and $1/N$ expansions is
broken. On the other hand, all the WLZZ partition functions are
$\tau$-functions of the Toda lattice hierarchy, and these models also celebrate
the superintegrability properties. | Higher-spin charges in Hamiltonian form. II. Fermi fields: We build the asymptotic higher-spin charges associated with "improper" gauge
transformations for fermionic higher-spin gauge fields on Anti de Sitter
backgrounds of arbitrary dimension. This is achieved within the canonical
formalism. We consider massless fields of spin s+1/2, described by a symmetric
spinor-tensor of rank s in the Fang-Fronsdal approach. We begin from a detailed
analysis of the spin 5/2 example, for which we cast the Fang-Fronsdal action in
Hamiltonian form, we derive the charges and we propose boundary conditions on
the canonical variables that secure their finiteness. We then extend the
computation of charges and the characterisation of boundary conditions to
arbitrary half-integer spin. Our construction generalises to higher-spin
fermionic gauge fields the known Hamiltonian derivation of supercharges in AdS
supergravity. |
Tunneling cosmological state revisited: Origin of inflation with a
non-minimally coupled Standard Model Higgs inflaton: We suggest a path integral formulation for the tunneling cosmological state,
which admits a consistent renormalization and renormalization group (RG)
improvement in particle physics applications of quantum cosmology. We apply
this formulation to the inflationary cosmology driven by the Standard Model
(SM) Higgs boson playing the role of an inflaton with a strong non-minimal
coupling to gravity. In this way a complete cosmological scenario is obtained,
which embraces the formation of initial conditions for the inflationary
background in the form of a sharp probability peak in the distribution of the
inflaton field and the ongoing generation of the Cosmic Microwave Background
(CMB) spectrum on this background. Formation of this probability peak is based
on the same RG mechanism which underlies the generation of the CMB spectrum
which was recently shown to be compatible with the WMAP data in the Higgs mass
range $135.6 {\rm GeV} \lesssim M_H\lesssim 184.5 {\rm GeV}$. This brings to
life a convincing unification of quantum cosmology with the particle
phenomenology of the SM, inflation theory, and CMB observations. | Quantum fields, dark matter and non-standard Wigner classes: The Elko field of Ahluwalia and Grumiller is a quantum field for massive
spin-1/2 particles. It has been suggested as a candidate for dark matter. We
discuss our attempts to interpret the Elko field as a quantum field in the
sense of Weinberg. Our work suggests that one should investigate quantum fields
based on representations of the full Poincar\'e group which belong to one of
the non-standard Wigner classes. |
Higher Spins in Hyper-Superspace: We extend the results of arXiv:1401.1645 on the generalized conformal
Sp(2n)-structure of infinite multiplets of higher spin fields, formulated in
spaces with extra tensorial directions (hyperspaces), to the description of
OSp(1|2n)-invariant infinite-dimensional higher-spin supermultiplets formulated
in terms of scalar superfields on flat hyper-superspaces and on OSp(1|n)
supergroup manifolds. We find generalized superconformal transformations
relating the superfields and their equations of motion in flat hyper-superspace
with those on the OSp(1|n) supermanifold. We then use these transformations to
relate the two-, three- and four-point correlation functions of the scalar
superfields on flat hyperspace, derived by requiring the OSp(1|2n) invariance
of the correlators, to correlation functions on the OSp(1|n) group manifold. As
a byproduct, for the simplest particular case of a conventional N=1, D=3
superconformal theory of scalar superfields, we also derive correlation
functions of component fields of the scalar supermultiplet including those of
auxiliary fields. | Tidal effects for spinning particles: Expanding on the recent derivation of tidal actions for scalar particles, we
present here the action for a tidally deformed spin-$1/2$ particle. Focusing on
operators containing two powers of the Weyl tensor, we combine the Hilbert
series with an on-shell amplitude basis to construct the tidal action. With the
tidal action in hand, we compute the leading-post-Minkowskian tidal
contributions to the spin-1/2 -- spin-1/2 amplitude, arising at
$\mathcal{O}(G^{2})$. Our amplitudes provide evidence that the observed long
range spin-universality for the scattering of two point particles extends to
the scattering of tidally deformed objects. From the scattering amplitude we
find the conservative two-body Hamiltonian, linear and angular impulses,
eikonal phase, spin kick, and aligned-spin scattering angle. We present
analogous results in the electromagnetic case along the way. |
Chern-Simons Theory on Seifert Manifold and Matrix Model: Chern-Simons (CS) theories with rank $N$ and level $k$ on Seifert manifold
are discussed. The partition functions of such theories can be written as a
function of modular transformation matrices summed over different integrable
representations of affine Lie algebra $u(N)_k$ associated with boundary
Wess-Zumino-Witten (WZW) model. Using properties of modular transform matrices
we express the partition functions of these theories as a unitary matrix model.
We show that, the eigenvalues of unitary matrices are discrete and proportional
to hook lengths of the corresponding integrable Young diagram. As a result, in
the large $N$ limit, the eigenvalue density develops an upper cap. We consider
CS theory on $S^2\times S^1$ coupled with fundamental matters and express the
partition functions in terms of modular transformation matrices. Solving this
model at large $N$ we find the dominant integrable representations and show how
large $N$ representations are related to each other by transposition of Young
diagrams as a result of level rank duality. Next we consider $U(N)$ CS theory
on $S^3$ and observed that in Seifert framing the dominant representation is no
longer an integrable representation after a critical value of 't Hooft
coupling. We also show that CS on $S^3$ admits multiple (two-gap phase) large
$N$ phases with the same free energy. | Exactly solvable models and spontaneous symmetry breaking: We study a few two-dimensional models with massive and massless fermions in
the hamiltonian framework and in both conventional and light-front forms of
field theory. The new ingredient is a modification of the canonical procedure
by taking into account solutions of the operator field equations. After
summarizing the main results for the derivative-coupling and the Thirring
models, we briefly compare conventional and light-front versions of the
Federbush model including the massive current bosonization and a Bogoliubov
transformation to diagonalize the Hamiltonian. Then we sketch an extension of
our hamiltonian approach to the two-dimensional Nambu--Jona-Lasinio model and
the Thirring--Wess models. Finally, we discuss the Schwinger model in a
covariant gauge. In particular, we point out that the solution due to
Lowenstein and Swieca implies the physical vacuum in terms of a coherent state
of massive scalar field and suggest a new formulation of the model's vacuum
degeneracy. |
Relativistic wave functions and energies for nonzero angular momentum
states in light-front dynamics: Light-front dynamics (LFD) is a powerful approach to the theory of
relativistic composite systems (hadrons in the quark models and relativistic
nucleons in nuclei). Its explicitly covariant version has been recently applied
with success to describe the new CEBAF/TJNAF data on the deuteron
electromagnetic form factors. The solutions used in were however not obtained
from solving exactly the LFD equations but by means of a perturbative
calculation with respect to the non relativistic wave function. Since, a
consequent effort has been made to obtain exact solutions of LFD equations. The
first results concerning J=0 states in a scalar model have been published in
nucl-th/9912050. The construction of $J \ne 0$ states in LFD is complicated by
the two following facts. First, the generators of the spatial rotations contain
interaction and are thus difficult to handle. Second, one is always forced to
work in a truncated Fock space, and consequently, the Poincar\'e group
commutation relations between the generators -- ensuring the correct properties
of the state vector under rotation -- are in practice destroyed. In the
standard approach, with the light-front plane defined as $t+z=0$, this
violation of rotational invariance manifests by the fact that the energy
depends on the angular momentum projection on $z$-axis.
We present here a method to construct $J\ne0$ states in the explicitly
covariant formulation of LFD and show how it leads to a restoration of
rotational invariance. | Negative-Tension Branes and Tensionless 1/2 Brane in Boundary Conformal
Field Theory: In the framework of boundary conformal field theory we consider a flat
unstable D$p$-brane in the presence of a large constant electromagnetic field.
Specifically, we study the case that the electromagnetic field satisfy the
following three conditions: (i) a constant electric field is turned on along
the $x^1$ direction ($E_{1}\ne 0$); (ii) the determinant of the matrix $(\eta +
F)$ is negative so that it lies in the physical region ($-\det (\eta + F)>0$);
(iii) the 11-component of its cofactor is positive to the large electromagnetic
field. In this case, we identify exactly marginal deformations depending on the
spatial coordinate $x^1$. They correspond to tachyon profiles of hyperbolic
sine, exponential, and hyperbolic cosine types. Boundary states are constructed
for these deformations by utilizing T-duality approach and also by directly
solving the overlap conditions in BCFT. The exponential type deformation gives
a tensionless half brane connecting the perturbative string vacuum and one of
the true tachyon vacua, while the others have negative tensions. This is in
agreement with the results obtained in other approaches. |
On boundary degrees of freedom in three dimensional Anti-de Sitter
spacetime and thermofield-double: In this article, we will study the Gibbons-Hawking-York (GHY) action over a
co-dimension one hypersurface, called the ``physical boundary,'' close to the
boundary of AdS$_3$. For that, we take a coordinate system that consists of two
times, one is associated with evolution on the boundary, and the second is
associated with evolution into the bulk. The resulting action is divergent and
needs regularization. We consider two particular schemes. In the first scheme,
we will add the Einstein-Hilbert on-shell action as the counter-term, which,
while cancels the divergent part, adds the contribution of deep in the bulk,
such as an existing horizon. The resulting action includes the Liouville
action, which describes the curvature of the physical boundary. In the second
scheme, however, we prescribe a natural regularization for GHY action without
adding any counter-term. The resulting action will include two copies of
Schwarzian actions associated with the left and right-moving reparametrization
modes. At finite temperature, these modes live on two disjoint circles. We will
show that these are the thermofield-double's effective degrees of freedom.
While the first scheme is more common in practice, the second scheme may be
more convenient for Susskind-'t Hooft proposal for holography. | Twisted Poisson Structures and Non-commutative/non-associative Closed
String Geometry: In this paper we discuss non-commutative and non-associative geometries that
emerge in the context of non-geometric closed string backgrounds. T-duality and
doubled field theory plays an important role in formulating the corresponding
effective action for these kind of non-geometric string backgrounds. As we will
argue, the emerging non-commutative and non-associative algebras for the closed
string (dual) coordinates and (dual) momenta can be mathematically described by
a twisted Poisson structure, in closed analogy to the phase space of a point
particle moving in the field of a magnetic monopole. |
W-Gravity: The geometric structure of theories with gauge fields of spins two and higher
should involve a higher spin generalisation of Riemannian geometry. Such
geometries are discussed and the case of $W_\infty$-gravity is analysed in
detail. While the gauge group for gravity in $d$ dimensions is the
diffeomorphism group of the space-time, the gauge group for a certain
$W$-gravity theory (which is $W_\infty$-gravity in the case $d=2$) is the group
of symplectic diffeomorphisms of the cotangent bundle of the space-time. Gauge
transformations for $W$-gravity gauge fields are given by requiring the
invariance of a generalised line element. Densities exist and can be
constructed from the line element (generalising $\sqrt { \det g_{\mu \nu}}$)
only if $d=1$ or $d=2$, so that only for $d=1,2$ can actions be constructed.
These two cases and the corresponding $W$-gravity actions are considered in
detail. In $d=2$, the gauge group is effectively only a subgroup of the
symplectic diffeomorphism group. Some of the constraints that arise for $d=2$
are similar to equations arising in the study of self-dual four-dimensional
geometries and can be analysed using twistor methods, allowing contact to be
made with other formulations of $W$-gravity. While the twistor transform for
self-dual spaces with one Killing vector reduces to a Legendre transform, that
for two Killing vectors gives a generalisation of the Legendre transform. | Matrix model and dimensions at hypercube vertices: In hypercube approach to correlation functions in Chern-Simons theory (knot
polynomials) the central role is played by the numbers of cycles, in which the
link diagram is decomposed under different resolutions. Certain functions of
these numbers are further interpreted as dimensions of graded spaces,
associated with hypercube vertices. Finding these functions is, however, a
somewhat non-trivial problem. In arXiv:1506.07516 it was suggested to solve it
with the help of the matrix model technique, in the spirit of AMM/EO
topological recursion. In this paper we further elaborate on this idea and
provide a vast collection of non-trivial examples, related both to ordinary and
virtual links and knots. Remarkably, most powerful versions of the formalism
freely convert ordinary knots/links to virtual and back -- moreover, go beyond
the knot-related set of the (2,2)-valent graphs. |
The Planckian Conspiracy: String Theory and the Black Hole Information
Paradox: It has been argued that the consistency of quantum theory with black hole
physics requires nonlocality not present in ordinary effective field theory. We
examine the extent to which such nonlocal effects show up in the perturbative
S-matrix of string theory. | Quantum Field Theory, Causal Structures and Weyl Transformations: We suggest that in the proper definition, Quantum Field Theories are quantum
mechanical system which 'live' on the space of causal structures ${\cal C}$ of
spacetime. That is, for any QFT a Hilbert space ${\cal H}$ on which local
operators live is assigned not for each Lorentzian metric $g$, but for each
causal structure ${\cal C}$. In practice one uses 'conformal frames' which all
provide equivalent descriptions of the same QFT. To put it differently, Quantum
Field Theories only know about causal structure of spacetime, and not its full
Lorentzian metric. The Weyl group and the local RG flow naturally arise when
one compares equivalent descriptions in different conformal frames. This is
reduced to the usual RG flow of coupling constants when one only compares
descriptions in conformal frames related by spacetime-independent Weyl
rescalings. We point out that in this picture minimal coupling of a QFT to the
metric is inconsistent and comment on the necessary violation of the
equivalence principle in the presence of scalars. |
String/M-theories About Our World Are Testable in the traditional
Physics Way: Some physicists hope to use string/M-theory to construct a comprehensive
underlying theory of our physical world a "final theory". Can such a theory be
tested? A quantum theory of gravity must be formulated in 10 dimensions, so
obviously testing it experimentally requires projecting it onto our 4D world
(called "compactification"). Most string theorists study theories, including
aspects such as AdS/CFT, not phenomena, and are not much interested in testing
theories beyond the Standard Model about our world. Compactified theories
generically have many realistic features whose necessary presence provides some
tests, such as gravity, Yang-Mills forces like the Standard Model ones, chiral
fermions that lead to parity violation, softly broken supersymmetry, Higgs
physics, families, hierarchical fermion masses and more. All tests of theories
in physics have always depended on assumptions and approximate calculations,
and tests of compactified string/M-theories do too. String phenomenologists
have also formulated some explicit tests for compactified theories. In
particular, I give examples of tests from compactified M-theory (involving
Higgs physics, predictions for superpartners at LHC, electric dipole moments,
and more). It is clear that compactified theories exist that can describe
worlds like ours, and it is clear that even if a multiverse were real it does
not prevent us from finding comprehensive compactified theories like one that
might describe our world. I also discuss what we might mean by a final theory,
what we might want it to explain, and comment briefly on multiverse issues from
the point of view of finding a theory that describes our world. | Non-Hermitian Quantum Quenches in Holography: The notion of non-Hermitian PT symmetric quantum theory has recently been
generalized to the gauge/gravity duality. We study the evolution of such
non-Hermitian holographic field theories when the couplings are varied with
time with particular emphasis on the question non-unitary time vs. unitary time
evolution. We show that a non-unitary time evolution in the dual quantum theory
corresponds to a violation of the Null Energy Condition (NEC) in the bulk of
the asymptotically AdS spacetime. We find that upon varying the non-Hermitian
coupling the horizon of a bulk AdS black hole shrinks. On the other hand
varying the Hermitian coupling in the presence of a constant non-Hermitian
coupling still violates the NEC but results in a growing horizon. We also show
that by introducing a non-Hermitian gauge field the time evolution can be made
unitary, e.g. the NEC in the bulk is obeyed, and an exactly equivalent purely
Hermitian description can be given. |
Cluster Expansion Approach to the Effective Potential in
$Φ^4_{2+1}$-Theory: We apply a truncated set of dynamical equations of motion for connected
equal-time Green functions up to the 4-point level to the investigation of
spontaneous ground state symmetry breaking in $\Phi^4_{2+1}$ quantum field
theory. Within our momentum space discretization we obtain a second order phase
transition as soon as the connected 3-point function is included. However, an
additional inclusion of the connected 4-point function still shows a
significant influence on the shape of the effective potential and the critical
coupling. | Swampland Conditions for Higher Derivative Couplings from CFT: There are effective field theories that cannot be embedded in any UV complete
theory. We consider scalar effective field theories, with and without dynamical
gravity, in $D$-dimensional anti-de Sitter (AdS) spacetime with large radius
and derive precise bounds (analytically) on the coupling constants of higher
derivative interactions $\phi^2\Box^k\phi^2$ by only requiring that the dual
CFT obeys the standard conformal bootstrap axioms. In particular, we show that
all such coupling constants, for even $k\ge 2$, must satisfy positivity,
monotonicity, and log-convexity conditions in the absence of dynamical gravity.
Inclusion of gravity only affects constraints involving the
$\phi^2\Box^2\phi^2$ interaction which now can have a negative coupling
constant. Our CFT setup is a Lorentzian four-point correlator in the Regge
limit. We also utilize this setup to derive constraints on effective field
theories of multiple scalars. We argue that similar analysis should impose
nontrivial constraints on the graviton four-point scattering amplitude in AdS. |
Holographic dual of collimated radiation: We propose a new and simple method of estimating the radiation due to an
accelerated quark in a strongly coupled medium, within the framework of the
AdS/CFT correspondence. In particular, we offer a heuristic explanation of the
collimated nature of synchrotron radiation produced by a circling quark, which
was recently studied in Phys.Rev.D81 (2010) 126001. The gravitational dual of
such quark is a coiling string in AdS, whose backreaction on the spacetime
geometry remains tightly confined, as if 'beamed' towards the boundary. While
this appears to contradict conventional expectations from the scale/radius
duality, we resolve the issue by observing that the backreaction of a
relativistic string is reproduced by a superposition of gravitational shock
waves. We further demonstrate that this proposal allows us to reduce the
problem of computing the boundary stress tensor to merely calculating geodesics
in AdS, as opposed to solving linearized Einstein's equations. | A Mathematica code for calculating massless spectrum of (0,2)
Landau-Ginzburg orbifold: In this short paper, we try to explain how to use our program which has been
written in Wolfram Mathematica to get the massless spectrum of any
Landau-Ginzburg orbifold. The technique has been developed by Witten-Kachru
theoretically, but calculating it for an explicit Landau-Ginzburg model is
exhausting and in general, beyond human ability to calculate using pen and
paper. |
Holographic antiferromganetic quantum criticality and AdS$_2$ scaling
limit: A holographic description on antiferromagnetic quantum phase transition (QPT)
induced by magnetic field and the criticality in the vicinity of quantum
critical point (QCP) have been investigated numerically recently. In this
paper, we show that the properties of QPT in this holographic model are
governed by a CFT dual to the emergent AdS$_2$ in the IR region, which confirms
that the dual boundary theory is a strong coupling theory with dynamic exponent
$z=2$ and logarithmic corrections appear. We also compare them with the results
from Hertz model by solving RG equation at its upper critical dimension and
with some experimental data from pyrochlores Er$_{2-2x}$Y$_{2x}$Ti$_2$O$_7$ and
BiCoPO$_5$. | Two-dimensional Black Hole With Torsion: The 2D model of gravity with zweibeins $e^{a}$ and the Lorentz connection
one-form $\omega^{a}_{\ b}$ as independent gravitational variables is
considered and it is shown that the classical equations of motion are exactly
integrated in coordinate system determined by components of 2D torsion. For
some choice of integrating constant the solution is of the charged black hole
type. The conserved charge and ADM mass of the black hole are calculated. |
Nonabelian Generalization of Electric-Magnetic Duality - a Brief Review: A loop space formulation of Yang-Mills theory high-lighting the significance
of monopoles for the existence of gauge potentials is used to derive a
generalization of electric-magnetic duality to the nonabelian theory. The
result implies that the gauge symmetry is doubled from SU(N) to $SU(N) \times
\widetilde{SU}(N)$, while the physical degrees of freedom remain the same, so
that the theory can be described in terms of either the usual Yang-Mills
potential $A_\mu(x)$ or its dual $\tilde{A}_\mu(x)$. Nonabelian `electric'
charges appear as sources of $A_\mu$ but as monopoles of $\tilde{A}_\mu$, while
their `magnetic' counterparts appear as monopoles of $A_\mu$ but sources of
$\tilde{A}_\mu$. Although these results have been derived only for classical
fields, it is shown for the quantum theory that the Dirac phase factors (or
Wilson loops) constructed out of $A_\mu$ and $\tilde{A}_\mu$ satisfy the 't
Hooft commutation relations, so that his results on confinement apply. Hence
one concludes, in particular, that since colour SU(3) is confined then dual
colour $\widetilde{SU}(3)$ is broken. Such predictions can lead to many very
interesting physical consequences which are explored in a companion paper. | Effective Action of Spontaneously Broken Gauge Theories: The effective action of a Higgs theory should be gauge-invariant. However,
the quantum and/or thermal contributions to the effective potential seem to be
gauge-dependent, posing a problem for its physical interpretation. In this
paper, we identify the source of the problem and argue that in a Higgs theory,
perturbative contributions should be evaluated with the Higgs fields in the
polar basis, not in the Cartesian basis. Formally, this observation can be made
from the derivation of the Higgs theorem, which we provide. We show explicitly
that, properly defined, the effective action for the Abelian Higgs theory is
gauge invariant to all orders in perturbation expansion when evaluated in the
covariant gauge in the polar basis. In particular, the effective potential is
gauge invariant. We also show the equivalence between the calculations in the
covariant gauge in the polar basis and the unitary gauge. These points are
illustrated explicitly with the one-loop calculations of the effective action.
With a field redefinition, we obtain the physical effective potential. The
SU(2) non-Abelian case is also discussed. |
Open-closed duality and Double Scaling: Nonperturbative terms in the free energy of Chern-Simons gauge theory play a
key role in its duality to the closed topological string. We show that these
terms are reproduced by performing a double scaling limit near the point where
the perturbation expansion diverges. This leads to a derivation of closed
string theory from this large-N gauge theory along the lines of noncritical
string theories. We comment on the possible relevance of this observation to
the derivation of superpotentials of asymptotically free gauge theories and its
relation to infrared renormalons. | An Introduction into the Feynman Path Integral: In this lecture a short introduction is given into the theory of the Feynman
path integral in quantum mechanics. The general formulation in Riemann spaces
will be given based on the Weyl- ordering prescription, respectively product
ordering prescription, in the quantum Hamiltonian. Also, the theory of
space-time transformations and separation of variables will be outlined. As
elementary examples I discuss the usual harmonic oscillator, the radial
harmonic oscillator, and the Coulomb potential. Lecture given at the graduate
college ''Quantenfeldtheorie und deren Anwendung in der Elementarteilchen- und
Festk\"orperphysik'', Universit\"at Leipzig, 16-26 November 1992. |
Exact solution of the supersymmetric sinh-Gordon model with boundary: The boundary supersymmetric sinh-Gordon model is an integrable quantum field
theory in 1+1 dimensions with bulk N=1 supersymmetry, whose bulk and boundary S
matrices are not diagonal. We present an exact solution of this model. In
particular, we derive an exact inversion identity and the corresponding
thermodynamic Bethe Ansatz equations. We also compute the boundary entropy, and
find a rich pattern of boundary roaming trajectories corresponding to c < 3/2
superconformal models. | The conformal squid: We introduce a discrete, graph theoretic approach to conformal field theory
correlators. In a certain basis, called the squid basis, the correlator of N
scalar operators can be expressed as the determinant of a natural, conformally
covariant metric on a weighted graph, called the squid graph. We present the
construction of this metric and discuss its possible role in constraining
conformal data. |
The multitrace matrix model: An alternative to Connes NCG and IKKT model: We present a new multitrace matrix model, which is a generalization of the
real quartic one matrix model, exhibiting dynamical emergence of a fuzzy
two-sphere and its non-commutative gauge theory. This provides a novel and a
much simpler alternative to Connes non-commutative geometry and to the IKKT
matrix model for emergent geometry in two dimensions. | Asymptotic Dynamics in Quantum Field Theory - When does the coupling
switch off?: We discuss the approach to asymptotic dynamics due to Kulish and Faddeev. We
show that there are problems in applying this method to theories with four
point interactions. The source of the difficulties is identified and a more
general method is constructed. This is then applied to various theories
including some where the coupling does switch off at large times and some where
it does not. |
Chaotic string motion in a near pp-wave limit: We revisit classical string motion in a near pp-wave limit of
AdS$_5\times$S$^5$. It is known that the Toda lattice models are integrable.
But if the exponential potential is truncated at finite order, then the system
may become non-integrable. In particular, when the exponential potential in a
three-particle periodic Toda chain is truncated at the third order of the
dynamical variables, the resulting system becomes a well-known non-integrable
system, Henon-Heiles model. The same thing may happen in a near pp-wave limit
of AdS$_5\times$S$^5$, on which the classical string motion becomes chaotic. | A new integral representation for the scalar products of Bethe states
for the XXX spin chain: Based on the method of separation of variables due to Sklyanin, we construct
a new integral representation for the scalar products of the Bethe states for
the SU(2) XXX spin 1/2 chain obeying the periodic boundary condition. Due to
the compactness of the symmetry group, a twist matrix must be introduced at the
boundary in order to extract the separated variables properly. Then by deriving
the integration measure and the spectrum of the separated variables, we express
the inner product of an on-shell and an off-shell Bethe states in terms of a
multiple contour integral involving a product of Baxter wave functions. Its
form is reminiscent of the integral over the eigenvalues of a matrix model and
is expected to be useful in studying the semi-classical limit of the product. |
Scattering of Giant Magnons in CP^3: We study classical scattering phase of CP^2 dyonic giant magnons in R_t x
CP^3. We construct two-soliton solutions explicitly by the dressing method.
Using these solutions, we compute the classical time delays for the scattering
of giant magnons, and compare them to boundstate S-matrix elements derived from
the conjectured AdS_4/CFT_3 S-matrix by Ahn and Nepomechie in the strong
coupling limit. Our result is consistent with the conjectured S-matrix. The
dyonic solutions play an essential role in revealing the polarization
dependence of scattering phase. | New nonlocal effective action: We suggest a new method for the calculation of the nonlocal part of the
effective action. It is based on resummation of perturbation series for the
heat kernel and its functional trace at large values of the proper time
parameter. We derive a new, essentially nonperturbative, nonlocal contribution
to the effective action in spacetimes with dimensions $d>2$. |
Five-dimensional super Yang-Mills theory from ABJM theory: We derive five-dimensional super Yang-Mills theory from mass-deformed ABJM
theory by expanding about $S^2$ for large Chern-Simons level $K$. We obtain the
Yang-Mills coupling constant $g_{YM}^2 = 4\pi^2 R/K$. If we consider
$S^3/{\mb{Z}_K}$ as a fiber bundle over $S^2$ then $R/K$ is the circumference
of the fiber. The value on the coupling constant agrees with what one gets by
compactifying M five-brane on that fiber. For this computation we take $R,K\to
\infty$ while keeping $R/K$ at a fixed finite value. We also study mass
deformed star-three-product BLG theory at K=1 and $R\to \infty$. In that limit
we obtain Lorentz covariant supersymmetry variations and gauge variations of a
non-Abelian tensor multiplet. | Quantum Mirror Map for Del Pezzo Geometries: Mirror maps play an important role in studying supersymmetric gauge theories.
In these theories the dynamics is often encoded in an algebraic curve where two
sets of periods enjoy the symplectic structure. The A-periods contribute to
redefinitions of chemical potentials known as mirror maps. Using the
quantization of the $D_5$ del Pezzo geometry, which enjoys the symmetry of the
$D_5$ Weyl group, we are able to identify clearly the group-theoretical
structure and the multi-covering structure for the mirror map. With the
structures, we can apply the mirror map to superconformal Chern-Simons theories
describing the worldvolume of multiple M2-branes on various backgrounds, where
we find that the redefinition of the chemical potential is obtained directly
from the mirror map. Besides, we have interesting observations for the mirror
map: The representations appearing in the quantum mirror map are the same as
those appearing in the BPS indices except for the trivial case of degree 1 and
the coefficients are all integers. |
Quantum complex sine-Gordon dressed boundaries: In this paper we investigate the quantum reflection factor for the CSG
dressed boundary, previously constructed by dressing the Dirichlet boundary
with the integrable CSG defect. We analyse classical bound states and use
semi-classical methods to investigate the quantum boundary spectrum. We
conjecture a fully quantum reflection matrix for a particle reflecting from an
unexcited boundary. By using the reflection and boundary bootstrap equations,
the reflection matrix for a charge Q=+n soliton reflecting from the mth excited
boundary is constructed. Evidence supporting our conjecture is given by
checking that the bootstrap closes and that the reflection matrices agrees with
known results in the classical limit. A partial analysis of the poles in the
reflection matrices which arise from Coleman-Thun diagrams is given. | A geometric basis for the standard-model gauge group: A geometric approach to the standard model in terms of the Clifford algebra
Cl_7 is advanced. A key feature of the model is its use of an algebraic spinor
for one generation of leptons and quarks. Spinor transformations separate into
left-sided ("exterior") and right-sided ("interior") types. By definition,
Poincare transformations are exterior ones. We consider all rotations in the
seven-dimensional space that (1) conserve the spacetime components of the
particle and antiparticle currents and (2) do not couple the right-chiral
neutrino. These rotations comprise additional exterior transformations that
commute with the Poincare group and form the group SU(2)_L, interior ones that
constitute SU(3)_C, and a unique group of coupled double-sided rotations with
U(1)_Y symmetry. The spinor mediates a physical coupling of Poincare and
isotopic symmetries within the restrictions of the Coleman--Mandula theorem.
The four extra spacelike dimensions in the model form a basis for the Higgs
isodoublet field, whose symmetry requires the chirality of SU(2). The charge
assignments of both the fundamental fermions and the Higgs boson are produced
exactly. |
Quantum flux operators for Carrollian diffeomorphism in general
dimensions: We construct Carrollian scalar field theories in general dimensions, mainly
focusing on the boundaries of Minkowski and Rindler spacetime, whose quantum
flux operators form a faithful representation of Carrollian diffeomorphism up
to a central charge, respectively. At future/past null infinity, the fluxes are
physically observable and encode rich information of the radiation. The central
charge may be regularized to be finite by the spectral zeta function or heat
kernel method on the unit sphere. For the theory at the Rindler horizon, the
effective central charge is proportional to the area of the bifurcation surface
after regularization. Moreover, the zero mode of supertranslation is identified
as the modular Hamiltonian, linking Carrollian diffeomorphism to quantum
information theory. Our results may hold for general null hypersurfaces and
provide new insight in the study of the Carrollian field theory, asymptotic
symmetry group and entanglement entropy. | Correct path-integral formulation of the quantum thermal field theory in
the coherent state representation: This paper has been superseded by hep-th/0510131. |
Short distance non-perturbative effects of large distance modified
gravity: In a model of large distance modified gravity we compare the nonperturbative
Schwarzschild solution of hep-th/0407049 to approximate solutions obtained
previously. In the regions where there is a good qualitative agreement between
the two, the nonperturbative solution yields effects that could have
observational significance. These effects reduce, by a factor of a few, the
predictions for the additional precession of the orbits in the Solar system,
still rendering them in an observationally interesting range. The very same
effects lead to a mild anomalous scaling of the additional scale-invariant
precession rate found by Lue and Starkman. | Strong Coupling Limit of ${\cal N}=2$ SCFT Free Energy and Higher
Derivative AdS/CFT Correspondence: We study the role of higher derivative terms (Riemann curvature squared ones)
in thermodynamics of SCFTs via AdS/CFT correspondence. Using IIB string
effective action (d5 AdS gravity) with such HD terms deduced from heterotic
string via duality we calculate strong coupling limit of ${\cal N}=2$ SCFT free
energy with the account of next to leading term in large $N$ expansion. It is
compared with perturbative result following from boundary QFT. Considering
modification of such action where HD terms form Weyl squared tensor we found
(strong coupling limit) free energy in such theory. It is interesting that
leading and next to leading term of large $N$ expanded free energy may differ
only by factor 3/4 if compare with perturbative result. Considering HD gravity
as bosonic sector of some (compactified) HD supergravity we suggest new version
of AdS/CFT conjecture and successfully test it on the level of free energies
for ${\cal N}=2,4$ SCFTs. |
Spectrum of the Hypereclectic Spin Chain and Pólya Counting: In earlier work we proposed a generating function that encodes the Jordan
block spectrum of the integrable Hypereclectic spin chain, related to the
one-loop dilatation operator of the dynamical fishnet quantum field theory. We
significantly improve the expressions for these generating functions, rendering
them much more explicit and elegant. In particular, we treat the case of the
full spin chain without imposing any cyclicity constraints on the states, as
well as the case of cyclic states. The latter involves the P\'olya enumeration
theorem in conjunction with q-binomial coefficients. | Scattering of Topological Solitons on Barriers and Holes of Deformed
Sine-Gordon Models: We study scattering properties of topological solitons in two classes of
models, which are generalizations of the Sine-Gordon model and which have
recently been proposed by Bazeia et al. These two classes of models depend on
an integer parameter n which, when n=2(for the first class) and n=1 (for the
second class), reduce to the Sine-Gordon model. We take the soliton solutions
of these models (generalizations of the 'kink' solution of the Sine-Gordon
model) and consider their scattering on potential holes and barriers. We
present our results for n=1,...6. We find that, like in the Sine Gordon models,
the scattering on the barrier is very elastic while the scattering on the hole
is inelastic and can at times, lead to a reflection. We discuss the dependence
of our results on n and find that the critical velocity for the transmission
through the hole is lowest for n=3. |
Understanding the Cancelation of Double Poles in the Pfaffian of
CHY-formulism: For a physical field theory, the tree-level amplitudes should possess only
single poles. However, when computing amplitudes with Cachazo-He-Yuan (CHY)
formulation, individual terms in the intermediate steps will contribute
higher-order poles. In this paper, we investigate the cancelation of
higher-order poles in CHY formula with Pfaffian as the building block. We
develop a diagrammatic rule for expanding the reduced Pfaffian. Then by
organizing diagrams in appropriate groups and applying the cross-ratio
identities, we show that all potential contributions to higher-order poles in
the reduced Pfaffian are canceled out, i.e., only single poles survive in
Yang-Mills theory and gravity. Furthermore, we show the cancelations of
higher-order poles in other field theories by introducing appropriate
truncations, based on the single pole structure of Pfaffian. | On the number of relevant operators in asymptotically safe gravity: The asymptotic safety scenario of gravity conjectures that (i) the quantum
field theory of gravity exists thanks to the presence of a non-trivial
ultraviolet fixed point of the renormalization group, and that (ii) the fixed
point has only a finite number of relevant perturbations, i.e. a finite number
of UV-stable directions (or in other words, a finite number of free parameters
to be fixed experimentally). Within the f(R) approximation of the functional
renormalization group equation of gravity, we show that assuming the first half
of the conjecture to be true, the remaining half follows from general
arguments, that is, we show that assuming the existence of a non-trivial fixed
point, the fact that the number of relevant directions is finite is a general
consequence of the structure of the equations. |
Higher Spin Gauge Theory and Holography: The Three-Point Functions: In this paper we calculate the tree level three-point functions of Vasiliev's
higher spin gauge theory in AdS4 and find agreement with the correlators of the
free field theory of N massless scalars in three dimensions in the O(N) singlet
sector. This provides substantial evidence that Vasiliev theory is dual to the
free field theory, thus verifying a conjecture of Klebanov and Polyakov. We
also find agreement with the critical O(N) vector model, when the bulk scalar
field is subject to the alternative boundary condition such that its dual
operator has classical dimension 2. | QCD Flux Tubes and Anomaly Inflow: We apply the Callan-Harvey anomaly inflow mechanism to the study of QCD
(chromoelectric) flux tubes, quark (pair)-creation and chiral magnetic effect,
using new variables from the Cho-Faddeev-Niemi decomposition of the gauge
potential. A phenomenological description of chromoelectric flux tubes is
obtained by studying a gauged Nambu-Jona-Lasinio effective Lagrangian, derived
from the original QCD Lagrangian. At the quantum level, quark condensates in
the QCD vacuum may form a vortex-like structure in a chromoelectric flux tube.
Quark zero modes trapped in the vortex are chiral and lead to a two-dimensional
gauge anomaly. To cancel it an effective Chern-Simons coupling is needed and
hence a topological charge density term naturally appears. |
Towards S matrices on flat space and pp waves from SYM: We analyze the possibility of extracting S matrices on pp waves and flat
space from SYM correlators. For pp waves, there is a subtlety in defining S
matrices, but we can certainly obtain observables. Only extremal correlators
survive the pp wave limit. A first quantized string approach is inconclusive,
producing in the simplest form results that vanish in the pp wave limit. We
define a procedure to get S matrices from SYM correlators, both for flat space
and for pp waves, generalizing a procedure due to Giddings. We analyze
nonrenormalized correlators: 2 and 3 -point functions and extremal correlators.
For the extremal 3-point function, the SYM and AdS results for the S matrix
match for the angular dependence, but the energy dependence doesn't. | Toward a Quantum theory of Gravity and a Resolution of the Time paradox: One of the major issues confronting theoretical physics is finding a quantum
theory of gravity and a resolution to the cosmological constant problem. It is
believed that a true quantum theory of gravity will lead to a solution to the
this problem. Finding a quantum theory of gravity has been a difficult issue
mainly because of the high energy scale required for testing quantum gravity
which is far the reach of current accelerators. Also general relativity does
not possess a natural time variable thus the nature of time is not clear in
quantum gravity, a problem called the time paradox. The two main approaches are
string theory and loop quantum gravity. String theory unifies all interaction
but provides a perturbative background dependent formulation which violates
general covariance. Loop quantum gravity provides a non-perturbative approach
but does not provide a unified theory of interactions, which most physicist
believe should be the case at Planck scale energies. It doesn't also seem to
connect with low energy phenomena.
In this note I look at how quantum cosmology provides useful inference toward
a quantum gravity theory by merging inputs from the perturbative and the
non-perturbative approaches, and resolving the time paradox issue. |
Closed strings in Misner space: a toy model for a Big Bounce ?: Misner space, also known as the Lorentzian orbifold $R^{1,1}/boost$, is one
of the simplest examples of a cosmological singularity in string theory. In
this lecture, we review the semi-classical propagation of closed strings in
this background, with a particular emphasis on the twisted sectors of the
orbifold. Tree-level scattering amplitudes and the one-loop vacuum amplitude
are also discussed. | Sphaleron on $S^{3}$: An exactly solvable sphaleron model in $3+1$ spacetime dimensions is
described |
4+1 dimensional homogeneous anisotropic string cosmological models: We present exact solutions of string cosmological models characterized by
five dimensional metrics (with four-dimensional real Lie groups as isometry
groups), space independent dilaton and vanishing torsion. As an example we
consider VII 0 \oplus R model and show that it is equivalent to the (4
+1)-dimensional cosmological model coupled to perfect fluid with negative
deceleration parameters (accelerating universe). | IR-deformed thermodynamics of quantum bouncers and the issue of
dimensional reduction: We probe the low-temperature behavior of a system of quantum bouncers as a
theoretical model for ultracold neutrons within a low energy modified version
of the standard quantum mechanics, due to the gravitational effects. Working in
one dimension, the energy spectrum and bound states of a deformed quantum
bouncer are obtained using the first-order WKB approximation, granted the very
low energy regime of the particle. In this manner, we can study energy levels
of a system of ultracold neutrons as an informative probe towards exploring the
low energy manifestation of semi-classical quantum gravitational effects. Our
calculated energy levels of ultracold neutrons are in accordance with the
observed energy levels, as obtained in the famous Nesvizhevsky \emph{et al.}
experiment, with a negative constant deformation, as dependent on the
deformation parameter. In advance, we tackle modified thermodynamics of a
system of quantum bouncers in the infrared regime via an ensemble theory both
in one dimension and also three dimensions, to seek for any trace of an
effective, thermodynamic dimensional reduction in this low energy regime of
semi-classical quantum gravity. While the issue of dimensional reduction has
been essentially assigned to the high energy regime, here we show that there is
a trace of an effective, thermodynamic dimensional reduction in infrared regime
with one important difference: in the high energy regime, the dimensional
reduction effectively occurs from $D=3$ to $D=1$, but here, in this low energy
regime, there is a trace of thermodynamic dimensional reduction from $D=3$ to
$D=2$. |
Higher Representations Duals: We uncover novel solutions of the 't Hooft anomaly matching conditions for
scalarless gauge theories with matter transforming according to higher
dimensional representations of the underlying gauge group. We argue that, if
the duals exist, they are gauge theories with fermions transforming according
to the defining representation of the dual gauge group. The resulting conformal
windows match the one stemming from the all-orders beta function results when
taking the anomalous dimension of the fermion mass to be unity which are also
very close to the ones obtained using the Schwinger-Dyson approximation. We use
the solutions to gain useful insight on the conformal window of the associated
electric theory. A consistent picture emerges corroborating previous results
obtained via different analytic methods and in agreement with first principle
lattice explorations. | UV stable, Lorentz-violating dark energy with transient phantom era: Phantom fields with negative kinetic energy are often plagued by the vacuum
quantum instability in the ultraviolet region. We present a Lorentz-violating
dark energy model free from this problem and show that the crossing of the
cosmological constant boundary w=-1 to the phantom equation of state is
realized before reaching a de Sitter attractor. Another interesting feature is
a peculiar time-dependence of the effective Newton's constant; the magnitude of
this effect is naturally small but may be close to experimental limits. We also
derive momentum scales of instabilities at which tachyons or ghosts appear in
the infrared region around the present Hubble scale and clarify the conditions
under which tachyonic instabilities do not spoil homogeneity of the
present/future Universe. |
Higher derivative effects on eta/s at finite chemical potential: We examine the effects of higher derivative corrections on eta/s, the ratio
of shear viscosity to entropy density, in the case of a finite R-charge
chemical potential. In particular, we work in the framework of five-dimensional
N =2 gauged supergravity, and include terms up to four derivatives,
representing the supersymmetric completion of the Chern-Simons term A \wedge Tr
(R \wedge R). The addition of the four-derivative terms yields a correction
which is a 1/N effect, and in general gives rise to a violation of the eta/s
bound. Furthermore, we find that, once the bound is violated, turning on the
chemical potential only leads to an even larger violation of the bound. | Fibers add Flavor, Part II: 5d SCFTs, Gauge Theories, and Dualities: In arXiv:1906.11820 and arXiv:1907.05404 we proposed an approach based on
graphs to characterize 5d superconformal field theories (SCFTs), which arise as
compactifications of 6d $\mathcal{N}= (1,0)$ SCFTs. The graphs, so-called
combined fiber diagrams (CFDs), are derived using the realization of 5d SCFTs
via M-theory on a non-compact Calabi--Yau threefold with a canonical
singularity. In this paper we complement this geometric approach by connecting
the CFD of an SCFT to its weakly coupled gauge theory or quiver descriptions
and demonstrate that the CFD as recovered from the gauge theory approach is
consistent with that as determined by geometry. To each quiver description we
also associate a graph, and the embedding of this graph into the CFD that is
associated to an SCFT provides a systematic way to enumerate all possible
consistent weakly coupled gauge theory descriptions of this SCFT. Furthermore,
different embeddings of gauge theory graphs into a fixed CFD can give rise to
new UV-dualities for which we provide evidence through an analysis of the
prepotential, and which, for some examples, we substantiate by constructing the
M-theory geometry in which the dual quiver descriptions are manifest. |
Constraining GUP Models Using Limits on SME Coefficients: Generalized uncertainty principles (GUP) and, independently, Lorentz symmetry
violations are two common features in many candidate theories of quantum
gravity. Despite that, the overlap between both has received limited attention
so far. In this brief paper, we carry out further investigations on this topic.
At the nonrelativistic level and in the realm of commutative spacetime
coordinates, a large class of both isotropic and anisotropic GUP models is
shown to produce signals experimentally indistinguishable from those predicted
by the Standard Model Extension (SME), the common framework for studying
Lorentz-violating phenomena beyond the Standard Model. This identification is
used to constrain GUP models using current limits on SME coefficients. In
particular, bounds on isotropic GUP models are improved by a factor of $10^{7}$
compared to current spectroscopic bounds and anisotropic models are constrained
for the first time. | Non-Renormalization For Non-Supersymmetric Black Holes: We analyze large logarithmic corrections to 4D black hole entropy and relate
them to the Weyl anomaly. We use duality to show that counter-terms in
Einstein-Maxwell theory can be expressed in terms of geometry alone, with no
dependence on matter terms. We analyze the two known $\mathcal{N} = 2$
supersymmetric invariants for various non-supersymmetric black holes and find
that both reduce to the Euler invariant. The $c$-anomaly therefore vanishes in
these theories and the coefficient of the large logarithms becomes topological.
It is therefore independent of continuous black hole parameters, such as the
mass, even far from extremality. |
Membrane paradigm and RG flows for anomalous holographic theories: Holographic RG flows can be better understood with the help of radially
conserved charges. It was shown by various authors that the bulk gauge and
diffeomorphism symmetries lead to the conservation of the zero mode of the
holographic U(1) current and, if the spacetime is stationary, to that of the
holographic heat current. In describing dual theories with \'t Hooft anomalies
the bulk gauge invariance is broken by Chern-Simons terms. We show that
conservation laws can still be derived and used to characterize the anomalous
transport in terms of membrane currents at the horizon. We devote particular
attention to systems with gravitational anomalies. These are known to be
problematic due to their higher derivative content. We show that this feature
alters the construction of the membrane currents in a way which is deeply tied
with the anomalous gravitational transport. | Phase transition in the 3-D massive Gross-Neveu model: We consider the 3-dimensional massive Gross-Neveu model at finite temperature
as an effective theory for strong interactions. Using the Matsubara imaginary
time formalism, we derive a closed form for the renormalized $T$-dependent
four-point function. This gives a singularity, suggesting a phase transition.
Considering the free energy we obtain the $T$-dependent mass, which goes to
zero for some temperature. These results lead us to the conclusion that there
is a second-order phase transition. |
Matter waves in terms of the unitary representations of the Lorentz
group: In a generalized Heisenberg/Schroedinger picture, the unitary representations
of the Lorentz group may, for a massive relativistic particle, be used to
attribute to waves an extra wavelength that is longer than the de Broglie
wavelength. Propagators are defined as spacetime transitions between states
with different eigenvalues of the first or the second Casimir operator of the
Lorentz algebra. | Non-Abelian Gravitoelectromagnetism and applications at finite
temperature: Studies about a formal analogy between the gravitational and the
electromagnetic fields lead to the notion of Gravitoelectromagnetism (GEM) to
describe gravitation. In fact, the GEM equations correspond to the weak field
approximation of gravitation field. Here a non-abelian extension of the GEM
theory is considered. Using the Thermo Field Dynamics (TFD) formalism to
introduce temperature effects some interesting physical phenomena are
investigated. The non-abelian GEM Stefan-Boltzmann law and the Casimir effect
at zero and finite temperature for this non-abelian field are calculated. |
3-Cocycles, Non-Associative Star-Products and the Magnetic Paradigm of
R-Flux String Vacua: We consider the geometric and non-geometric faces of closed string vacua
arising by T-duality from principal torus bundles with constant H-flux and pay
attention to their double phase space description encompassing all toroidal
coordinates, momenta and their dual on equal footing. We construct a
star-product algebra on functions in phase space that is manifestly duality
invariant and substitutes for canonical quantization. The 3-cocycles of the
Abelian group of translations in double phase space are seen to account for
non-associativity of the star-product. We also provide alternative
cohomological descriptions of non-associativity and draw analogies with the
quantization of point-particles in the field of a Dirac monopole or other
distributions of magnetic charge. The magnetic field analogue of the R-flux
string model is provided by a constant uniform distribution of magnetic charge
in space and non-associativity manifests as breaking of angular symmetry. The
Poincare vector comes to rescue angular symmetry as well as associativity and
also allow for quantization in terms of operators and Hilbert space only in the
case of charged particles moving in the field of a single magnetic monopole. | Finite size effects in integrable quantum field theory: the sine-Gordon
model with boundaries: In this thesis we review recent progresses on Nonlinear Integral Equation
approach to finite size effects in two dimensional integrable quantum field
theory with boundaries, with emphasis to sine-Gordon model with Dirichlet
boundary conditions. Exact calculations of the dependence of the energy
spectrum on the size and on boundary conditions are presented for vacuum and
many excited states. |
Flavoured Large N Gauge Theory on a Compact Space with an External
Magnetic Field: The phase structure of flavoured N=2 SYM on a three sphere in an external
magnetic field is studied. The pairing effect of the magnetic field competes
with the dissociating effect of the Casimir free energy, leading to an
interesting phase structure of confined and deconfined phases separated by a
critical curve of a first order quantum phase transition. At vanishing magnetic
field the phase transition is of a third order. For sufficiently strong
magnetic field, the only stable phase is the confined phase and magnetic
catalysis of chiral symmetry breaking is realized. The meson spectra of the
theory exhibit Zeeman splitting and level crossing and feature a finite jump at
the phase transition between the confined and deconfined phases. At strong
magnetic field the ground state has a massless mode corresponding to the
Goldstone boson associated with the spontaneously broken U(1) R-symmetry
analogous to the eta' meson in QCD. | A dynamical formulation of ghost-free massive gravity: We present a formulation of ghost-free massive gravity with flat reference
metric that exhibits the full non-linear constraint algebraically, in a way
that can be directly implemented for numerical simulations. Motivated by the
presence of higher order operators in the low-energy effective description of
massive gravity, we show how the inclusion of higher-order gradient
(dissipative) terms leads to a well-posed formulation of its dynamics. While
the formulation is presented for a generic combination of the minimal and
quadratic mass terms on any background, for concreteness, we then focus on the
numerical evolution of the minimal model for spherically symmetric
gravitational collapse of scalar field matter. This minimal model does not
carry the relevant interactions to switch on an active Vainshtein mechanism, at
least in spherical symmetry, thus we do not expect to recover usual GR
behaviour even for small graviton mass. Nonetheless we may ask what the outcome
of matter collapse is for this gravitational theory. Starting with small
initial data far away from the centre, we follow the matter through a
non-linear regime as it falls towards the origin. For sufficiently weak data
the matter disperses. However for larger data we generally find that the
classical evolution breaks down due to the theory becoming infinitely strongly
coupled without the presence of an apparent horizon shielding this behaviour
from an asymptotic observer. |
A non-rational CFT with c=1 as a limit of minimal models: We investigate the limit of minimal model conformal field theories where the
central charge approaches one. We conjecture that this limit is described by a
non-rational CFT of central charge one. The limiting theory is different from
the free boson but bears some resemblance to Liouville theory. Explicit
expressions for the three point functions of bulk fields are presented, as well
as a set of conformal boundary states. We provide analytic and numerical
arguments in support of the claim that this data forms a consistent CFT. | Gravity and the Crossed Product: Recently Leutheusser and Liu [1,2] identified an emergent algebra of Type
III$_1$ in the operator algebra of ${\mathcal N}=4$ super Yang-Mills theory for
large $N$. Here we describe some $1/N$ corrections to this picture and show
that the emergent Type III$_1$ algebra becomes an algebra of Type II$_\infty$.
The Type II$_\infty$ algebra is the crossed product of the Type III$_1$ algebra
by its modular automorphism group. In the context of the emergent Type
II$_\infty$ algebra, the entropy of a black hole state is well-defined up to an
additive constant, independent of the state. This is somewhat analogous to
entropy in classical physics. |
Exact M-Theory Solutions, Integrable Systems, and Superalgebras: In this paper, an overview is presented of the recent construction of fully
back-reacted half-BPS solutions in 11-dimensional supergravity which correspond
to near-horizon geometries of M2 branes ending on, or intersecting with, M5 and
M5$'$ branes along a self-dual string. These solutions have space-time manifold
${\rm AdS}_3 \times S^3 \times S^3$ warped over a Riemann surface $\Sigma$, and
are invariant under the exceptional Lie superalgebra $D(2,1;\gamma) \oplus
D(2,1;\gamma)$, where $\gamma $ is a real continuous parameter and $|\gamma|$
is governed by the ratio of the number of M5 and M5$'$ branes. The construction
proceeds by mapping the reduced BPS equations onto an integrable field theory
on $\Sigma$ which is of the Liouville sine-Gordon type. Families of regular
solutions are distinguished by the sign of $\gamma$, and include a
two-parameter Janus solution for $\gamma >0$, and self-dual strings on M5 as
well as asymptotically ${\rm AdS}_4/{\mathbb Z}_2$ solutions for $\gamma <0$. | BPS spectra from BPS graphs: I present a simple graphical method to find the BPS spectra of $A_1$ theories
of class S. BPS graphs provide a bridge between spectral networks and BPS
quivers, the two main frameworks for the study of BPS states. Here I show how
to essentially read off from a BPS graph the quantum spectrum generator (or BPS
monodromy), expressed as a product of quantum dilogarithms. Thanks to the
framed wall-crossing phenomenon for line defects, the determination of the BPS
spectrum reduces to the computation of quantum parallel transport across the
edges of the BPS graph. |
Renormalization-group Method for Reduction of Evolution Equations;
invariant manifolds and envelopes: The renormalization group (RG) method as a powerful tool for reduction of
evolution equations is formulated in terms of the notion of invariant
manifolds. We start with derivation of an exact RG equation which is analogous
to the Wilsonian RG equations in statistical physics and quantum field theory.
It is clarified that the perturbative RG method constructs invariant manifolds
successively as the initial value of evolution equations, thereby the meaning
to set $t_0=t$ is naturally understood where $t_0$ is the arbitrary initial
time. We show that the integral constants in the unperturbative solution
constitutes natural coordinates of the invariant manifold when the linear
operator $A$ in the evolution equation has no Jordan cell; when $A$ has a
Jordan cell, a slight modification is necessary because the dimension of the
invariant manifold is increased by the perturbation. The RG equation determines
the slow motion of the would-be integral constants in the unperturbative
solution on the invariant manifold. We present the mechanical procedure to
construct the perturbative solutions hence the initial values with which the RG
equation gives meaningful results. The underlying structure of the reduction by
the RG method as formulated in the present work turns out to completely fit to
the universal one elucidated by Kuramoto some years ago. We indicate that the
reduction procedure of evolution equations has a good correspondence with the
renormalization procedure in quantum field theory; the counter part of the
universal structure of reduction elucidated by Kuramoto may be the Polchinski's
theorem for renormalizable field theories. We apply the method to interface
dynamics such as kink-anti-kink and soliton-soliton interactions in the latter
of which a linear operator having a Jordan-cell structure appears. | Bootstrapping Pions at Large $N$: We revisit from a modern bootstrap perspective the longstanding problem of
solving QCD in the large $N$ limit. We derive universal bounds on the effective
field theory of massless pions by imposing the full set of positivity
constraints that follow from $2 \to 2$ scattering. Some features of our
exclusion plots have intriguing connections with hadronic phenomenology. The
exclusion boundary exhibits a sharp kink, raising the tantalizing scenario that
large $N$ QCD may sit at this kink. We critically examine this possibility,
developing in the process a partial analytic understanding of the geometry of
the bounds. |
T-duality for boundary-non-critical point-particle and string quantum
mechanics: It is observed that some structures recently uncovered in the study of
Calogero-Sutherland models and anyons are close analogs of well-known
structures of boundary conformal field theory. These examples of ``boundary
conformal quantum mechanics'', in spite of their apparent simplicity, have a
rather reach structure, including some sort of T-duality, and could provide
useful frameworks for testing general properties of boundary conformal
theories. Of particular interest are the duality properties of anyons and
Calogero-Sutherland particles in presence of boundary-violations of conformal
invariance; these are here briefly analyzed leading to the conjecture of a
general interconnection between (deformed) boundary conformal quantum
mechanics, T-type duality, and (``exchange'' or ``exclusion'') exotic
statistics. These results on the point-particle quantum-mechanics side are
compared with recent results on the action of T-duality on open strings that
satisfy conformal-invariance-violating boundary conditions. Moreover, it is
observed that some of the special properties of anyon and Calogero-Sutherland
quantum mechanics are also enjoyed by the M(atrix) quantum mechanics which has
recently attracted considerable attention. | Localization and Reference Frames in $κ$-Minkowski Spacetime: We study the limits to the localizability of events and reference frames in
the $\kappa$-Minkowski quantum spacetime. Our main tool will be a
representation of the $\kappa$-Minkowski commutation relations between
coordinates, and the operator and measurement theory borrowed from ordinary
quantum mechanics. Spacetime coordinates are described by operators on a
Hilbert space, and a complete set of commuting observables cannot contain the
radial coordinate and time at the same time. The transformation between the
complete sets turns out to be the Mellin transform, which allows us to discuss
the localizability properties of states both in space and time. We then discuss
the transformation rules between inertial observers, which are described by the
quantum $\kappa$-Poincar\'e group. These too are subject to limitations in the
localizability of states, which impose further restrictions on the ability of
an observer to localize events defined in a different observer's reference
frame. |
Operads, homotopy algebra and iterated integrals for double loop spaces: This paper provides some background to the theory of operads, used in the
first author's papers on 2d topological field theory (hep-th/921204, CMP 159
(1994), 265-285; hep-th/9305013). It is intended for specialists. | OPE formulae for deformed super-Virasoro algebras: We show the OPE formulae for three types of deformed super-Virasoro algebras:
Chaichian-Presnajder's deformation, Belov-Chaltikhian's one and its modified
version. Fundamental (anti-)commutation relations toward a ghost realization of
deformed super-Virasoro algebra are also discussed. |
Holographic Constraints on a Vector Boson: We show that holography poses non-trivial restrictions on various couplings
of an interacting field. For a vector boson in the AdS Reissner-Nordstrom
background, the dual boundary theory is pathological unless its electromagnetic
and gravitational multipole moments are constrained. Among others, a generic
dipole moment afflicts the dual CFT with superluminal modes, whose remedy
bounds the gyromagnetic ratio in a range around the natural value g=2. We
discuss the CFT implications of our results, and argue that similar
considerations can shed light on how massive higher-spin fields couple to
electromagnetism and gravity. | Descent equations of Yang--Mills anomalies in noncommutative geometry: Consistent Yang--Mills anomalies $\int\om_{2n-k}^{k-1}$ ($n\in\N$, $ k=1,2,
\ldots ,2n$) as described collectively by Zumino's descent equations
$\delta\om_{2n-k}^{k-1}+\dd\om_{2n-k-1}^{k}=0$ starting with the Chern
character $Ch_{2n}=\dd\om_{2n-1}^{0}$ of a principal $\SU(N)$ bundle over a
$2n$ dimensional manifold are considered (i.e.\ $\int\om_{2n-k}^{k-1}$ are the
Chern--Simons terms ($k=1$), axial anomalies ($k=2$), Schwinger terms ($k=3$)
etc.\ in $(2n-k)$ dimensions). A generalization in the spirit of Connes'
noncommutative geometry using a minimum of data is found. For an arbitrary
graded differential algebra $\CC=\bigoplus_{k=0}^\infty \CC^{(k)}$ with
exterior differentiation $\dd$, form valued functions $Ch_{2n}: \CC^{(1)}\to
\CC^{(2n)}$ and $\om_{2n-k}^{k-1}: \underbrace{\CC^{(0)}\times\cdots \times
\CC^{(0)}}_{\mbox{{\small $(k-1)$ times}}} \times \CC^{(1)}\to \CC^{(2n-k)}$
are constructed which are connected by generalized descent equations
$\delta\om_{2n-k}^{k-1}+\dd\om_{2n-k-1}^{k}=(\cdots)$. Here $Ch_{2n}= (F_A)^n$
where $F_A=\dd(A)+A^2$ for $A\in\CC^{(1)}$, and $(\cdots)$ is not zero but a
sum of graded commutators which vanish under integrations (traces). The problem
of constructing Yang--Mills anomalies on a given graded differential algebra is
thereby reduced to finding an interesting integration $\int$ on it. Examples
for graded differential algebras with such integrations are given and thereby
noncommutative generalizations of Yang--Mills anomalies are found. |
A Gravity Dual of the Chiral Anomaly: We study effects associated with the chiral anomaly for a cascading
$SU(N+M)\times SU(N)$ gauge theory using gauge/gravity duality. In the gravity
dual the anomaly is a classical feature of the supergravity solution, and the
breaking of the U(1) R-symmetry down to ${\bf Z}_{2M}$ proceeds via the Higgs
mechanism. | BPS states and the P=W conjecture: A string theoretic framework is presented for the work of Hausel and
Rodriguez-Vilegas as well as de Cataldo, Hausel and Migliorini on the
cohomology of character varieties. The central element of this construction is
an identification of the cohomology of the Hitchin moduli space with BPS states
in a local Calabi-Yau threefold. This is a summary of several talks given
during the Moduli Space Program 2011 at Isaac Newton Institute. |
Complete integration-by-parts reductions of the non-planar hexagon-box
via module intersections: We present the powerful module-intersection integration-by-parts (IBP)
method, suitable for multi-loop and multi-scale Feynman integral reduction.
Utilizing modern computational algebraic geometry techniques, this new method
successfully trims traditional IBP systems dramatically to much simpler
integral-relation systems on unitarity cuts. We demonstrate the power of this
method by explicitly carrying out the complete analytic reduction of two-loop
five-point non-planar hexagon-box integrals, with degree-four numerators, to a
basis of $73$ master integrals. | Dimensional regularization for N=1 susy sigma models and the worldline
formalism: We generalize the worldline formalism to include spin 1/2 fields coupled to
gravity. To this purpose we first extend dimensional regularization to
supersymmetric nonlinear sigma models in one dimension. We consider a finite
propagation time and find that dimensional regularization is a manifestly
supersymmetric regularization scheme, since the classically supersymmetric
action does not need any counterterm to preserve worldline supersymmetry. We
apply this regularization scheme to the worldline description of Dirac fermions
coupled to gravity. We first compute the trace anomaly of a Dirac fermion in 4
dimensions, providing an additional check on the regularization with finite
propagation time. Then we come to the main topic and consider the one-loop
effective action for a Dirac field in a gravitational background. We describe
how to represent this effective action as a worldline path integral and compute
explicitly the one- and two-point correlation functions, i.e. the spin 1/2
particle contribution to the graviton tadpole and graviton self-energy. These
results are presented for the general case of a massive fermion. It is
interesting to note that in the worldline formalism the coupling to gravity can
be described entirely in terms of the metric, avoiding the introduction of a
vielbein. Consequently, the fermion--graviton vertices are always linear in the
graviton, just like the standard coupling of fermions to gauge fields. |
Supersymmetric Wilson Loops in IIB Matrix Model: We show that the supersymmetric Wilson loops in IIB matrix model give a
transition operator from reduced supersymmetric Yang-Mills theory to
supersymmetric space-time theory. In comparison with Green-Schwarz superstring
we identify the supersymmetric Wilson loops with the asymptotic states of IIB
superstring. It is pointed out that the supersymmetry transformation law of the
Wilson loops is the inverse of that for the vertex operators of massless modes
in the U(N) open superstring with Dirichlet boundary condition. | Gravity-mediated holography in fluid dynamics: For any spherically symmetric black hole spacetime with an ideal fluid
source, we establish a dual fluid system on a hypersurface near the black hole
horizon. The dual fluid is incompressible and obeys Navier-Stokes equation
subject to some external force. The force term in the fluid equation consists
in two parts, one comes from the curvature of the hypersurface, the other comes
from the stress-energy of the bulk fluid. |
Heating up Galilean holography: We embed a holographic description of a quantum field theory with Galilean
conformal invariance in string theory. The key observation is that such field
theories may be realized as conventional superconformal field theories with a
known string theory embedding, twisted by the R-symmetry in a light-like
direction. Using the Null Melvin Twist, we construct the appropriate dual
geometry and its non-extremal generalization. From the nonzero temperature
solution we determine the equation of state. We also discuss the hydrodynamic
regime of these non-relativistic plasmas and show that the shear viscosity to
entropy density ratio takes the universal value one over four pi typical of
strongly interacting field theories with gravity duals. | Born-Infeld Electrodynamics and Euler-Heisenberg-like Model: outstanding
examples of the lack of commutativity among quantized truncated actions and
truncated quantized actions: We calculate the lowest-order corrections to the static potential for both
the generalized Born-Infeld Electrodynamics and an Euler-Heisenberg-like model,
in the presence of a constant external magnetic field. Our analysis is carried
out within the framework of the gauge-invariant but path-dependent variables
formalism. The calculation reveals a long-range correction ($
{\raise0.7ex\hbox{$1$} \mathord{\left/ {\vphantom {1
{r^5}}}\right.\kern-\nulldelimiterspace} \lower0.7ex\hbox{${r^5}$}}$-type) to
the Coulomb potential for the generalized Born-Infeld Electrodynamics.
Interestingly enough, in the Euler-Heisenberg-like model, the static potential
remains Coulombian. Therefore, contrary to popular belief, the quantized
truncated action and the truncated quantized action do not commute at all. |
The superconformal index of N=1 class S fixed points: We investigate the superconformal index of four-dimensional N=1
superconformal field theories that arise on coincident M5 branes wrapping a
holomorphic curve in a local Calabi-Yau three-fold. The structure of the index
is very similar to that which appears in the special case preserving N=2
supersymmetry. We first compute the index for the fixed points that admit a
known four-dimensional ultraviolet description and prove infrared equivalence
at the level of the index for all such constructions. These results suggest a
formulation of the index as a two-dimensional topological quantum field theory
that generalizes the one that computes the N=2 index. The TQFT structure leads
to an expression for the index of all class S fixed points in terms of the
index of the N=2 theories. Calculations of spectral data using the index
suggests a connection between these families of fixed points and the
mathematics of SU(2) Yang-Mills theory on the wrapped curve. | Small N=2 Extremal Black Holes in Special Geometry: We provide an intrinsic classification of the large and small orbits for N=2,
4D extremal black holes on symmetric spaces which does not depend on the
duality frame used for the charges or on the special coordinates. A coordinate
independent formula for the fake superpotential W, which (at infinity)
represents the black hole ADM mass, is given explicitly in terms of invariants
of the N=2 special geometry. |
Quantum Field Theory on the q-deformed Fuzzy Sphere: We discuss the second quantization of scalar field theory on the q-deformed
fuzzy sphere S^2_{q,N} for q \in \R, using a path-integral approach. We find
quantum field theories which are manifestly covariant under U_q(su(2)), have a
smooth limit q -> 1, and satisfy positivity and twisted bosonic symmetry
properties. Using a Drinfeld twist, they are equivalent to ordinary but
slightly "nonlocal" QFT's on the undeformed fuzzy sphere, which are covariant
under SU(2). | A $p$-Adic Matter in a Closed Universe: In this paper, we introduce a new type of matter that has origin in $p$-adic
strings, i.e., strings with a $p$-adic worldsheet. We investigate some
properties of this $p$-adic matter, in particular its cosmological aspects. We
start with crossing symmetric scattering amplitudes for $p$-adic open strings
and related effective nonlocal and nonlinear Lagrangian which describes tachyon
dynamics at the tree level. Then, we make a slight modification of this
Lagrangian and obtain a new Lagrangian for non-tachyonic scalar field. {Using
this new Lagrangian in the weak field approximation as a matter in Einstein
gravity with the cosmological constant, one obtains an exponentially expanding
FLRW closed universe.} At the end, we discuss the obtained results, i.e.,
computed mass of the scalar $p$-adic particle, estimated radius of related
closed universe and noted $p$-adic matter as a possible candidate for dark
matter. |
Regular collision of dilatonic inflating branes: We demonstrate that a two brane system with a bulk scalar field driving
power-law inflation on the branes has an instability in the radion. We solve
for the resulting trajectory of the brane, and find that the instability can
lead to collision. Brane quantities such as the scale factor are shown to be
regular at this collision. In addition we describe the system using a low
energy expansion. The low energy expansion accurately reproduces the known
exact solution, but also identifies an alternative solution for the bulk metric
and brane trajectory. | Mild Non-Gaussianities under Perturbative Control from Rapid-Turn
Inflation Models: Inflation can be supported in very steep potentials if it is generated by
rapidly turning fields, which can be natural in negatively curved field spaces.
The curvature perturbation, $\zeta$, of these models undergoes an exponential,
transient amplification around the time of horizon crossing, but can still be
compatible with observations at the level of the power spectrum. However, a
recent analysis (based on a proposed single-field effective theory with an
imaginary speed of sound) found that the trispectrum and other higher-order,
non-Gaussian correlators also undergo similar exponential enhancements. This
arguably leads to `hyper-large' non-Gaussianities in stark conflict with
observations, and even to the loss of perturbative control of the calculations.
In this paper, we provide the first analytic solution of the growth of the
perturbations in two-field rapid-turn models, and find it in good agreement
with previous numerical and single-field EFT estimates. We also show that the
nested structure of commutators of the in-in formalism has subtle and crucial
consequences: accounting for these commutators, we show analytically that the
naively leading-order piece (which indeed is exponentially large) cancels
exactly in all relevant correlators. The remaining non-Gaussianities of these
models are modest, and there is no problem with perturbative control from the
exponential enhancement of $\zeta$. Thus, rapid-turn inflation with negatively
curved field spaces remains a viable and interesting class of candidate
theories of the early universe. |
Marginal Deformations In the Open Bosonic String Field Theory for N
D0-branes: In this short note we give an example of the exact solution of the open
bosonic string field theory defined on the background of $N$ coincided
D0-branes. This solution leads to the change of the original background to the
background where D0-branes are localised in general positions. | Special Geometry of Euclidean Supersymmetry III: the local r-map,
instantons and black holes: We define and study projective special para-Kahler manifolds and show that
they appear as target manifolds when reducing five-dimensional vector
multiplets coupled to supergravity with respect to time. The dimensional
reductions with respect to time and space are carried out in a uniform way
using an epsilon-complex notation. We explain the relation of our formalism to
other formalisms of special geometry used in the literature. In the second part
of the paper we investigate instanton solutions and their dimensional lifting
to black holes. We show that the instanton action, which can be defined after
dualising axions into tensor fields, agrees with the ADM mass of the
corresponding black hole. The relation between actions via Wick rotation, Hodge
dualisation and analytic continuation of axions is discussed. |
Non-anticommutative N=2 supersymmetric SU(2) gauge theory: We calculate the component Lagrangian of a four-dimensional
non-anticommutative (with a singlet deformation parameter) and fully N=2
supersymmetric gauge field theory with the simple gauge group SU(2). We find
that the deformed (classical) scalar potential is unbounded from below, in
contrast to the undeformed case. | Exotic symmetry and monodromy equivalence in Schrodinger sigma models: We consider the classical integrable structure of two-dimensional non-linear
sigma models with target space three-dimensional Schrodinger spacetimes. There
are the two descriptions to describe the classical dynamics: 1) the left
description based on SL(2,R)_L and 2) the right description based on U(1)_R. We
have shown the sl(2,R)_L Yangian and q-deformed Poincare algebras associated
with them. We proceed to argue an infinite-dimensional extension of the
q-deformed Poincare algebra. The corresponding charges are constructed by using
a non-local map from the flat conserved currents related to the Yangian. The
exotic tower structure of the charges is revealed by directly computing the
classical Poisson brackets. Then the monodromy matrices in both descriptions
are shown to be gauge-equivalent via the relation between the spectral
parameters. We also give a simple Riemann sphere interpretation of this
equivalence. |
Holographic End-Point of Spatially Modulated Phase Transition: In the previous paper [arXiv:0911.0679], we showed that the
Reissner-Nordstrom black hole in the 5-dimensional anti-de Sitter space coupled
to the Maxwell theory with the Chern-Simons term is unstable when the
Chern-Simons coupling is sufficiently large. In the dual conformal field
theory, the instability suggests a spatially modulated phase transition. In
this paper, we construct and analyze non-linear solutions which describe the
end-point of this phase transition. In the limit where the Chern-Simons
coupling is large, we find that the phase transition is of the second order
with the mean field critical exponent. However, the dispersion relation with
the Van Hove singularity enhances quantum corrections in the bulk, and we argue
that this changes the order of the phase transition from the second to the
first. We compute linear response functions in the non-linear solution and find
an infinite off-diagonal DC conductivity in the new phase. | Black hole determinants and quasinormal modes: We derive an expression for functional determinants in thermal spacetimes as
a product over the corresponding quasinormal modes. As simple applications we
give efficient computations of scalar determinants in thermal AdS, BTZ black
hole and de Sitter spacetimes. We emphasize the conceptual utility of our
formula for discussing `1/N' corrections to strongly coupled field theories via
the holographic correspondence. |
Equivalence of Local Potential Approximations: In recent papers it has been noted that the local potential approximation of
the Legendre and Wilson-Polchinski flow equations give, within numerical error,
identical results for a range of exponents and Wilson-Fisher fixed points in
three dimensions, providing a certain ``optimised'' cutoff is used for the
Legendre flow equation. Here we point out that this is a consequence of an
exact map between the two equations, which is nothing other than the exact
reduction of the functional map that exists between the two exact
renormalization groups. We note also that the optimised cutoff does not allow a
derivative expansion beyond second order. | Classical Solutions for Two Dimensional QCD on the Sphere: We consider $U(N)$ and $SU(N)$ gauge theory on the sphere. We express the
problem in terms of a matrix element of $N$ free fermions on a circle. This
allows us to find an alternative way to show Witten's result that the partition
function is a sum over classical saddle points. We then show how the phase
transition of Douglas and Kazakov occurs from this point of view. By
generalizing the work of Douglas and Kazakov, we find other `stringy' solutions
for the $U(N)$ case in the large $N$ limit. Each solution is described by a net
$U(1)$ charge. We derive a relation for the maximum charge for a given area and
we also describe the critical behavior for these new solutions. Finally, we
describe solutions for lattice $SU(N)$ which are in a sense dual to the
continuum $U(N)$ solutions. (Parts of this paper were presented at the Strings
'93 Workshop, Berkeley, May 1993.) |
Integrality of instanton numbers and p-adic B-model: We study integrality of instanton numbers (genus zero Gopakumar - Vafa
invariants) for quintic and other Calabi-Yau manifolds. We start with the
analysis of the case when the moduli space of complex structures is
one-dimensional; later we show that our methods can be used to prove
integrality in general case. We give an expression of instanton numbers in
terms of Frobenius map on $p$-adic cohomology ; the proof of integrality is
based on this expression. | Comparing two definitions for gauge variations of dielectric D-branes: We compare two definitions of gauge variations in the case of non-Abelian
actions for multiple D-branes. Equivalence is proven for the R-R variations,
which shows that the action is invariant also under the easier, naive
variation. For the NS-NS variations however, the two definitions are not
equivalent, leaving the naive definition as the only valid one. |
Scale-invariant breaking of conformal symmetry: Known examples of unitary relativistic scale but not conformal-invariant
field theories (SFTs) can be embedded into conventional conformal field
theories (CFTs). We show that any SFT which is a subsector of a unitary CFT is
a free theory. Our discussion applies to an arbitrary number of spacetime
dimensions and explains triviality of known SFTs in four spacetime dimensions.
We comment on examples of unitary SFTs which are not captured by our
construction. | Boundary Liouville Field Theory: Boundary Three Point Function: Liouville field theory is considered on domains with conformally invariant
boundary conditions. We present an explicit expression for the three point
function of boundary fields in terms of the fusion coefficients which determine
the monodromy properties of the conformal blocks. |
New massive spin two model on curved space-time: We have proposed a new ghost-free model with interactions of massive spin two
particles in Phys.\ Rev.\ D {\bf 90} (2014) 043006 [arXiv:1402.5737 [hep-th]].
Although the model is ghost-free on the Minkowski space-time, it is not obvious
whether or not this desirable property is preserved on curved space-time. In
fact, Buchbinder et al. already pointed out that the Fierz-Pauli theory is not
ghost-free on curved space-time without non-minimal coupling terms. In this
paper, we construct a new theory of massive spin two particles with non-minimal
coupling on curved space-time and show that the model can be ghost-free.
Furthermore, we propose new non-minimal coupling terms. | Direct evidence for the Maldacena conjecture for N=(8,8) super
Yang-Mills theory in 1+1 dimensions: We solve N=(8,8) super Yang-Mills theory in 1+1 dimensions at strong coupling
to directly confirm the predictions of supergravity at weak coupling. We do our
calculations in the large-N_c approximation using Supersymmetric Discrete
Light-Cone Quantization with up to 3*10^{12} basis states. We calculate the
stress-energy correlator <T^{++}(r) T^{++}(0)> as a function of the separation
r and find that at intermediate values of r the correlator behaves as r^{-5} to
within errors as predicted by weak-coupling supergravity. We also present an
extension to significantly higher resolution of our earlier results for the
same correlator in the N=(2,2) theory and see that in this theory the
correlator has very different behavior at intermediate values of r. |
Background Independent Quantum Field Theory and the Cosmological
Constant Problem: We introduce the notion of background independent quantum field theory. The
distinguishing feature of this theory is that the dynamics can be formulated
without recourse to a background metric structure. We show in a simple model
how the metric properties of spacetime can be recovered from the dynamics.
Background independence is not only conceptually desirable but allows for the
resolution of a problem haunting ordinary quantum field theory: the
cosmological constant problem. | Degenerate Odd Poisson Bracket on Grassmann Variables: A linear degenerate odd Poisson bracket (antibracket) realized solely on
Grassmann variables is presented. It is revealed that this bracket has at once
three nilpotent $\Delta$-like differential operators of the first, the second
and the third orders with respect to the Grassmann derivatives. It is shown
that these $\Delta$-like operators together with the Grassmann-odd nilpotent
Casimir function of this bracket form a finite-dimensional Lie superalgebra. |
Ramond-Ramond Field Transformation: We find that the mixture of Ramond-Ramond fields and Neveu-Schwarz two form
are transformed as Majorana spinors under the T-duality group $O(d,d)$. The
Ramond-Ramond field transformation under the group $O(d,d)$ is realized in a
simple form by using the spinor representation. The Ramond-Ramond field
transformation rule obtained by Bergshoeff et al. is shown as a specific simple
example. We also give some explicit examples of the spinor representation. | Hidden Conformal Symmetry of Smooth Braneworld Scenarios: In this paper we generalize our previous model (arXiv: 1705.09331), on a
hidden conformal symmetry of smooth braneworld scenarios, to the case with two
real scalar fields non-minimally coupled to gravity. The gauge condition
reduces the action of the system to the action were gravity minimally couples
to one of the scalar fields, plus a cosmological constant. We show that,
depending on the internal symmetry of the scalar fields, the two possibilities,
$SO(2)$ or $SO(1,1)$, emerge. In the $SO(2)$ case we get a ghost-like scalar
field action, which can describe two models -- Standing Wave and Sine-Gordon
smooth braneworlds. For the $SO(1,1)$ case we get the standard sign for the
kinetic part of the scalar field. By breaking the $SO(1,1)$ symmetry (but
keeping the conformal one) we are able to get two Randall-Sundrum models, with
a non-minimal coupling and with a scalar field having hyperbolic potential. We
conclude that this method can be seen as a solution-generating technique and a
natural way to introduce non-trivial scalar fields that can provide smooth
braneworld models. |
The Holographic Entropy Cone: We initiate a systematic enumeration and classification of entropy
inequalities satisfied by the Ryu-Takayanagi formula for conformal field theory
states with smooth holographic dual geometries. For 2, 3, and 4 regions, we
prove that the strong subadditivity and the monogamy of mutual information give
the complete set of inequalities. This is in contrast to the situation for
generic quantum systems, where a complete set of entropy inequalities is not
known for 4 or more regions. We also find an infinite new family of
inequalities applicable to 5 or more regions. The set of all holographic
entropy inequalities bounds the phase space of Ryu-Takayanagi entropies,
defining the holographic entropy cone. We characterize this entropy cone by
reducing geometries to minimal graph models that encode the possible cutting
and gluing relations of minimal surfaces. We find that, for a fixed number of
regions, there are only finitely many independent entropy inequalities. To
establish new holographic entropy inequalities, we introduce a combinatorial
proof technique that may also be of independent interest in Riemannian geometry
and graph theory. | Inscribing geodesic circles on the face of the superstratum: We use families of circular null geodesics as probes of a family of
microstate geometries, known as $(1,0,n)$ superstrata. These geometries carry a
left-moving momentum wave and the behavior of some of the geodesic probes is
very sensitive to this background wave. The left-moving geodesics behave like
BPS particles and so can be placed in circular orbits anywhere in the geometry
and actually "float" at fixed radius and angle in the three-dimensional "capped
BTZ" geometry. The right-moving geodesics behave like non-BPS particles. We
show that they provide a simple geometric characterization of the black-hole
bound: when the momentum charge of the geometry is below this bound, such
geodesics can be placed anywhere, but exceeding the bound, even by a small
amount, means these geodesics are restricted to the deep interior of the
geometry. We also show that for left-moving string probes, the tidal forces
remain comparable with those of global AdS$_3$. Nevertheless, for some of these
probes, the "bumps" in the geometry induce an oscillatory mass term and we
discuss how this can lead to chaotic scrambling of the state of the string. |
Free fields via canonical transformations of matter-coupled 2D dilaton
gravity models: It is shown that the 1+1-dimensional matter-coupled Jackiw-Teitelboim model
and the model with an exponential potential can be converted by means of
appropriate canonical transformations into a bosonic string theory propagating
on a flat target space with an indefinite signature. This makes it possible to
consistently quantize these models in the functional Schroedinger
representation thus generalizing recent results on CGHS theory. | Asymptotic Safety Guaranteed at Four Loop: We investigate a family of four-dimensional quantum field theories with
weakly interacting ultraviolet fixed points up to four loop order in
perturbation theory. Key new ingredients are the three loop gauge contributions
to quartic scalar beta functions, which we compute in the
$\overline{\text{MS}}$ scheme for a template $SU(N_c)$ gauge theory coupled to
$N_f$ fundamental fermions and elementary scalars. We then determine fixed
point couplings, field and mass anomalous dimensions, and universal scaling
exponents up to the first three non-trivial orders in a small Veneziano
parameter. The phase diagram and UV-IR connecting trajectories are found and
contrasted with asymptotic freedom. Further, the size of the conformal window,
unitarity, and mechanisms leading to the loss of conformality are investigated.
Our results provide blueprints for concrete 4d non-supersymmetric conformal
field theories with standard model-like field content, and invite further model
building. |
Witten index in supersymmetric 3d theories revisited: We have performed a direct calculation of Witten index in N = 1,2,3
supersymmetric Yang-Mills Chern-Simons 3d theories. We do it in the framework
of Born-Oppenheimer (BO) approach by putting the system into a small spatial
box and studying the effective Hamiltonian depending on the zero field
harmonics. At the tree level, our results coincide with the results of Witten,
but there is a difference in the way the loop effects are implemented. In
Witten's approach, one has only take into account the fermion loops, which
bring about a negative shift of the (chosen positive at the tree level)
Chern-Simons coupling k. As a result, Witten index vanishes and supersymmetry
is broken at small k. In the effective BO Hamiltonian framework, fermion, gluon
and ghost loops contribute on an equal footing. Fermion loop contribution to
the effective Hamiltonian can be evaluated exactly, and their effect amounts to
the negative shift k -> k - h/2 for N =1 and k -> k - h for N = 2,3 in the
tree-level formulae for the index. In our approach, with rather natural
assumptions on the structure of bosonic corrections, the shift k -> k + h
brought about by the gluon loops also affects the index. Since the total shift
of k is positive or zero, Witten index appears to be nonzero at nonzero k, and
supersymmetry is not broken. We discuss possible reasons for such disagreement. | Super-de Sitter and alternative super-Poincaré symmetries: It is well-known that de Sitter Lie algebra $\mathfrak{o}(1,4)$ contrary to
anti-de Sitter one $\mathfrak{o}(2,3)$ does not have a standard
$\mathbb{Z}_2$-graded superextension. We show here that the Lie algebra
$\mathfrak{o}(1,4)$ has a superextension based on the
$\mathbb{Z}_2\times\mathbb{Z}_2$-grading. Using the standard contraction
procedure for this superextension we obtain an {\it alternative}
super-Poincar\'e algebra with the $\mathbb{Z}_2\times\mathbb{Z}_2$-grading. |
Decoherence and Vacuum Fluctuations: The interference pattern of coherent electrons is effected by coupling to the
quantized electromagnetic field. The amplitudes of the interference maxima are
changed by a factor which depends upon a double line integral of the photon
two-point function around the closed path of the electrons. The interference
pattern is sensitive to shifts in the vacuum fluctuations in regions from which
the electrons are excluded. Thus this effect combines aspects of both the
Casimir and the Aharonov-Bohm effects. The coupling to the quantized
electromagnetic field tends to decrease the amplitude of the interference
oscillations, and hence is a form of decoherence. The contributions due to
photon emission and to vacuum fluctuations may be separately identified. It is
to be expected that photon emission leads to decoherence, as it can reveal
which path an electron takes. It is less obvious that vacuum fluctuations also
can cause decoherence. What is directly observable is a shift in the
fluctuations due, for example, to the presence of a conducting plate. In the
case of electrons moving parallel to conducting boundaries, the dominant
decohering influence is that of the vacuum fluctuations. The shift in the
interference amplitudes can be of the order of a few percent, so experimental
verification of this effect may be possible. The possibility of using this
effect to probe the interior of matter, e.g., to determine the electrical
conductivity of a rod by means of electrons encircling it is discussed.
(Presented at the Conference on Fundamental Problems in Quantum Theory,
University of Maryland, Baltimore County, June 18-22, 1994.) | Electromagnetic field generated by a charge moving along a helical orbit
inside a dielectric cylinder: The electromagnetic field generated by a charged particle moving along a
helical orbit inside a dielectric cylinder immersed into a homogeneous medium
is investigated. Expressions are derived for the electromagnetic potentials,
electric and magnetic fields in the region inside the cylinder. The parts
corresponding to the radiation field are separated. The radiation intensity on
the lowest azimuthal mode is studied. |
Chaotic dynamics of a suspended string in a gravitational background
with magnetic field: We study the effects of a magnetic field on the chaotic dynamics of a string
with endpoints on the boundary of an asymptotically AdS$_5$ space with black
hole. We study Poincar\'e sections and compute the Lyapunov exponents for the
string perturbed from the static configuration, for two different orientations,
with position of the endpoints on the boundary orthogonal and parallel to the
magnetic field. We find that the magnetic field stabilizes the string dynamics,
with the largest Lyapunov exponent remaining below the
Maldacena-Shenker-Stanford bound. | Partial wave expansion and Wightman positivity in conformal field theory: A new method for computing exact conformal partial wave expansions is
developed and applied to approach the problem of Hilbert space (Wightman)
positivity in a non-perturbative four-dimensional quantum field theory model.
The model is based on the assumption of global conformal invariance on
compactified Minkowski space. Bilocal fields arising in the harmonic
decomposition of the operator product expansion prove to be a powerful
instrument in exploring the field content. In particular, in the theory of a
field of dimension 4 which has the properties of a (gauge invariant)
Lagrangian, the scalar field contribution to the 6-point function of the twist
2 bilocal field is analyzed with the aim to separate the free field part from
the nontrivial part. |
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