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Dressing Cosets: The account of the Poisson-Lie T-duality is presented for the case when the
action of the duality group on a target is not free. At the same time a
generalization of the picture is given when the duality group does not even act
on $\si$-model targets but only on their phase spaces. The outcome is a huge
class of dualizable targets generically having no local isometries or
Poisson-Lie symmetries whatsoever. | hep-th |
Holographic Interpretation of Relative State Complexity: We investigate a large-$N$ CFT in a high-energy pure state coupled to a small
auxiliary system of $M$ weakly-interacting degrees of freedom, and argue the
relative state complexity of the auxiliary system is holographically dual to an
effective low-energy notion of computational cost in the bulk, \textit{i.e.} to
the minimal depth of the quantum circuit required to decode its gravitational
dual. In light of this, using Nielsen's approach, a new measure of quantum
chaos in terms of the evolution of circuit complexity is proposed. It suggests
that studying the evolution of circuit complexity of the auxiliary system can
teach us about the chaotic properties of the large-$N$ CFT. This new diagnostic
for quantum chaos has important implications for the interior dynamics of
evaporating black holes as it implies the radiated Hawking cloud is
pseudorandom. | hep-th |
Is N = 8 Supergravity Ultraviolet Finite?: Conventional wisdom holds that no four-dimensional gravity field theory can
be ultraviolet finite. This understanding is based mainly on power counting.
Recent studies confirm that one-loop N = 8 supergravity amplitudes satisfy the
so-called `no-triangle hypothesis', which states that triangle and bubble
integrals cancel from these amplitudes. A consequence of this hypothesis is
that for any number of external legs, at one loop N = 8 supergravity and N = 4
super-Yang-Mills have identical superficial degrees of ultraviolet behavior in
D dimensions. We describe how the unitarity method allows us to promote these
one-loop cancellations to higher loops, suggesting that previous power counts
were too conservative. We discuss higher-loop evidence suggesting that N = 8
supergravity has the same degree of divergence as N = 4 super-Yang-Mills theory
and is ultraviolet finite in four dimensions. We comment on calculations needed
to reinforce this proposal, which are feasible using the unitarity method. | hep-th |
From 4d Ambitwistor Strings to On Shell Diagrams and Back: We investigate the relation between 4d ambitwistor string theory and on-shell
diagrams for planar N=4 super-Yang-Mills and N=8 supergravity, and deduce
several new results about their scattering amplitudes at tree-level and 1-loop.
In particular, we derive new Grassmannian integral formulae for tree-level
amplitudes and obtain new worldsheet formulae for 1-loop amplitudes which are
manifestly supersymmetric and supported on scattering equations refined by MHV
degree. | hep-th |
Fractional Strings in (p,q) 5-brane and Quiver Matrix String Theory: We study the (p,q)5-brane dynamics from the viewpoint of Matrix string theory
in the T-dualized ALE background. The most remarkable feature in the
(p,q)5-brane is the existence of ``fractional string'', which appears as the
instanton of 5-brane gauge theory. We approach to the physical aspects of
fractional string by means of the two types of Matrix string probes: One of
which is that given in hep-th/9710065. As the second probe we present the
Matrix string theory describing the fractional string itself. We calculate the
moduli space metrics in the respective cases and argue on the specific
behaviors of fractional string. Especially, we show that the ``joining''
process of fractional strings can be realized as the transition from the
Coulomb branch to the Higgs branch of the fractional string probe. In this
argument, we emphasize the importance of some monodromies related with the
theta-angle of the 5-brane gauge theory. | hep-th |
Higher Dimensional Supersymmetry: Higher dimensional super symmetry has been analyzed in terms of quaternion
variables and the theory of quaternion harmonic oscillator has been analyzed.
Supersymmertization of quaternion Dirac equation has been developed for
massless,massive and interacting cases including generalized electromagnetic
fields of dyons. Accordingly higher dimensional super symmetric gauge theories
of dyons are analyzed. | hep-th |
Matrix Theory, AdS/CFT and Higgs-Coulomb Equivalence: We discuss the relation between the Matrix theory definitions of a class of
decoupled theories and their AdS/CFT description in terms of the corresponding
near-horizon geometry. The near horizon geometry, naively part of the Coulomb
branch, is embedded in the Higgs branch via a natural change of variables. The
principles of the map apply to all DLCQ descriptions in terms of hyper-K\"ahler
quotients, such as the ADHM quantum mechanics for the D1-D5 system. We then
focus the (2,0) field theory, and obtain an explicit mapping from all states in
the $N_0=1$ momentum sector of $N_4$ M5-branes to states in (a DLCQ version of)
$AdS_7\times S^4$. We show that, even for a single D0-brane, the space-time
coordinates become non-commuting variables, suggesting an inherent
non-commutativity of space-time in the presence of field strengths even for
theories with gravity. | hep-th |
Four-dimensional $N=1$ theories, S-fold constraints on T-branes, and
behaviors in IR and UV: We analyze four-dimensional (4d) $N=1$ superconformal field theories (SCFTs)
obtained as deformations of 4d $N=2$ SCFTs on S-folds by tilting 7-branes.
Geometric compatibility with the structures of S-folds constrains the forms of
T-branes. As a result, brane monodromies are constrained. We also discuss two
4d $N=1$ theories on probe D3-branes, where the two theories behave identically
in IR, but they originate from different theories in UV. Studying the global
structure of their geometry is useful in constructing these two theories. | hep-th |
Holographic Geometric Entropy at Finite Temperature from Black Holes in
Global Anti de Sitter Spaces: Using a holographic proposal for the geometric entropy we study its behavior
in the geometry of Schwarzschild black holes in global $AdS_p$ for $p=3,4,5$.
Holographically, the entropy is determined by a minimal surface. On the gravity
side, due to the presence of a horizon on the background, generically there are
two solutions to the surfaces determining the entanglement entropy. In the case
of $AdS_3$, the calculation reproduces precisely the geometric entropy of an
interval of length $l$ in a two dimensional conformal field theory with
periodic boundary conditions. We demonstrate that in the cases of $AdS_{4}$ and
$AdS_{5}$ the sign of the difference of the geometric entropies changes,
signaling a transition. Euclideanization implies that various embedding of the
holographic surface are possible. We study some of them and find that the
transitions are ubiquitous. In particular, our analysis renders a very
intricate phase space, showing, for some ranges of the temperature, up to three
branches. We observe a remarkable universality in the type of results we obtain
from $AdS_4$ and $AdS_5$. | hep-th |
Quantized Noncommutative Geometry from Multitrace Matrix Models: In this article the geometry of quantum gravity is quantized in the sense of
being noncommutative (first quantization) but it is also quantized in the sense
of being emergent (second quantization). A new mechanism for quantum geometry
is proposed in which noncommutative geometry can emerge from "one-matrix
multitrace scalar matrix models" by probing the statistical physics of
commutative phases of matter. This is in contrast to the usual mechanism in
which noncommutative geometry emerges from "many-matrix singletrace Yang-Mills
matrix models" by probing the statistical physics of noncommutative phases of
gauge theory. In this novel scenario quantized geometry emerges in the form of
a transition between the two phase diagrams of the real quartic matrix model
and the noncommutative scalar phi-four field theory. More precisely, emergence
of the geometry is identified here with the emergence of the uniform-ordered
phase and the corresponding commutative (Ising) and noncommutative (stripe)
coexistence lines. The critical exponents and the Wigner's semicircle law are
used to determine the dimension and the metric respectively. Arguments from the
saddle point equation, from Monte Carlo simulation and from the matrix
renormalization group equation are provided in support of this scenario. | hep-th |
Conformal graphs as twisted partition functions: We show that a class of $L$-loop conformal ladder graphs correspond to
twisted partition functions of free massive complex scalars in $d=2L+1$
dimensions. The graphs arise as four-point functions in certain two- and
four-dimensional conformal fishnet models. The twisted thermal two-point
function of the scalars is a generator of such conformal graphs for all loops.
We argue that this correspondence is seeded by a system of two decoupled
harmonic oscillators twisted by an imaginary chemical potential. We find a
number of algebraic and differential relations among the conformal graphs which
mirror the underlying free dynamics. | hep-th |
A Resummable beta-Function for Massless QED: Within the set of schemes defined by generalized, manifestly gauge invariant
exact renormalization groups for QED, it is argued that the beta-function in
the four dimensional massless theory cannot possess any nonperturbative power
corrections. Consequently, the perturbative expression for the beta-function
must be resummable. This argument cannot be extended to flows of the other
couplings or to the anomalous dimension of the fermions and so perturbation
theory does not define a unique trajectory in the critical surface of the
Gaussian fixed point. Thus, resummability of the beta-function is not
inconsistent with the expectation that a non-trivial fixed point does not
exist. | hep-th |
Reflected entropy in Galilean conformal field theories and flat
holography: We obtain the reflected entropy for bipartite states in a class of
$(1+1)$-dimensional Galilean conformal field theories ($GCFT_{1+1}$) through a
replica technique. Furthermore we compare our results with the entanglement
wedge cross section (EWCS) obtained for the dual (2+1) dimensional
asymptotically flat geometries in the context of flat holography. We find that
our results are consistent with the duality between the reflected entropy and
the bulk EWCS for flat holographic scenarios. | hep-th |
Scattering in Twisted Yangians: We study the bulk and boundary scattering of the sl(N) twisted Yangian spin
chain via the solution of the Bethe ansatz equations in the thermodynamic
limit. Explicit expressions for the scattering amplitudes are obtained and the
factorization of the bulk scattering is shown. The issue of defects in twisted
Yangians is also briefly discussed. | hep-th |
Tunneling Mechanism in Kerr-Newman Black Hole and Dimensional Reduction
near the Horizon: It is shown that the derivation of the Hawking radiation from a rotating
black hole on the basis of the tunneling mechanism is greatly simplified by
using the technique of the dimensional reduction near the horizon. This
technique is illustrated for the original derivation by Parikh and Wilczek, but
it is readily applied to a variant of the method such as suggested by Banerjee
and Majhi. | hep-th |
Conformal multi-Regge theory: We propose and explore the Regge limit for correlation functions of five
local primary operators in conformal field theories. After reviewing some
features of Regge theory for flat-space scattering amplitudes, we analyse the
analytic structure of conformal blocks both in position and Mellin space in the
Regge limit and propose an extension of conformal Regge theory for five-point
functions. As a byproduct of our analysis we also introduce a new basis of
three-point correlation functions for operators with spin and the associated
Euclidean conformal blocks. | hep-th |
Holographic Entanglement Entropy for the Most General Higher Derivative
Gravity: The holographic entanglement entropy for the most general higher derivative
gravity is investigated. We find a new type of Wald entropy, which appears on
entangling surface without the rotational symmetry and reduces to usual Wald
entropy on Killing horizon. Furthermore, we obtain a formal formula of HEE for
the most general higher derivative gravity and work it out exactly for some
squashed cones. As an important application, we derive HEE for gravitational
action with one derivative of the curvature when the extrinsic curvature
vanishes. We also study some toy models with non-zero extrinsic curvature. We
prove that our formula yields the correct universal term of entanglement
entropy for 4d CFTs. Furthermore, we solve the puzzle raised by Hung, Myers and
Smolkin that the logarithmic term of entanglement entropy derived from Weyl
anomaly of CFTs does not match the holographic result even if the extrinsic
curvature vanishes. We find that such mismatch comes from the `anomaly of
entropy' of the derivative of curvature. After considering such contributions
carefully, we resolve the puzzle successfully. In general, we need to fix the
splitting problem for the conical metrics in order to derive the holographic
entanglement entropy. We find that, at least for Einstein gravity, the
splitting problem can be fixed by using equations of motion. How to derive the
splittings for higher derivative gravity is a non-trivial and open question.
For simplicity, we ignore the splitting problem in this paper and find that it
does not affect our main results. | hep-th |
Bound states in the three dimensional phi^4 model: We discuss the spectrum of the three dimensional phi^4 theory in the broken
symmetry phase. In this phase the effective potential between the elementary
quanta of the model is attractive and bound states of two or more of them may
exist. We give theoretical and numerical evidence for the existence of these
bound states. Looking in particular at the Ising model realization of the phi^4
theory we show, by using duality, that these bound states are in one-to-one
correspondence with the glueball states of the gauge Ising model. We discuss
some interesting consequences of this identification. | hep-th |
Black holes on cylinders are not algebraically special: We give a Petrov classification for five-dimensional metrics. We classify
Ricci-flat metrics that are static, have an SO(3) isometry group and have
Petrov type 22. We use this classification to look for the metric of a black
hole on a cylinder, i.e. a black hole with asymptotic geometry four-dimensional
Minkowski space times a circle. Although a black string wrapped around the
circle and the five-dimensional black hole are both algebraically special, it
turns out that the black hole on a cylinder is not. | hep-th |
Matching gluon scattering amplitudes and Wilson loops in off-shell
regularization: We construct a regularization for light-like polygonal Wilson loops in ${\cal
N}=4$ SYM, which matches them to the off-shell MHV gluon scattering amplitudes.
Explicit calculations are performed for the 1-loop four gluon case. The off
light cone extrapolation has to be based on the local supersymmetric Wilson
loop. The observed matching concerns Feynman gauge. Furthermore, the leading
infrared divergent term is shown to be gauge parameter independent on 1-loop
level. | hep-th |
An Alternative to Compactification: Conventional wisdom states that Newton's force law implies only four
non-compact dimensions. We demonstrate that this is not necessarily true in the
presence of a non-factorizable background geometry. The specific example we
study is a single 3-brane embedded in five dimensions. We show that even
without a gap in the Kaluza-Klein spectrum, four-dimensional Newtonian and
general relativistic gravity is reproduced to more than adequate precision. | hep-th |
Superconformally covariant operators and super W algebras: We study superdifferential operators of order $2n+1$ which are covariant with
respect to superconformal changes of coordinates on a compact super Riemann
surface. We show that all such operators arise from super M\"obius covariant
ones. A canonical matrix representation is presented and applications to
classical super W algebras are discussed. | hep-th |
Two-Dimensional Quantum PoincarÉ Group: Quantum Poincar\'e-Weyl group in two dimensional quantum Minkowski space-time
is considered and an appriopriate relativistic kinematics is investigated. It
is claimed that a consistent approach to the above questions demands a kind of
a ``quantum geometry'' in the $q$-deformed space-time. | hep-th |
Exact Results in 5D from Instantons and Deconstruction: We consider non-perturbative effects in theories with extra dimensions and
the deconstructed versions of these theories. We establish the rules for
instanton calculations in 5D theories on the circle, and use them for an
explicit one-instanton calculation in a supersymmetric gauge theory. The
results are then compared to the known exact Seiberg-Witten type solution for
this theory, confirming the validity both of the exact results and of the rules
for instanton calculus for extra dimensions introduced here. Next we consider
the non-perturbative results from the perspective of deconstructed extra
dimensions. We show that the non-perturbative results of the deconstructed
theory do indeed reproduce the known results for the continuum extra
dimensional theory, thus providing the first non-perturbative evidence in favor
of deconstruction. This way deconstruction also allows us to make exact
predictions in higher dimensional theories which agree with earlier results,
and helps to clarify the interpretation of 5D instantons. | hep-th |
Higher derivative corrections to DBI action at $ α'^2$ order: We use the compatibility of D-brane action with linear off-shell T-duality
and linear on-shell S-duality as guiding principles to find all world volume
couplings of one massless closed and three massless open strings at order
$\alpha'^2$ in type II superstring theories in flat space-time. | hep-th |
Covariant - tensor method for quantum groups and applications I:
$SU(2)_{q}$: A covariant - tensor method for $SU(2)_{q}$ is described. This tensor method
is used to calculate q - deformed Clebsch - Gordan coefficients. The connection
with covariant oscillators and irreducible tensor operators is established.
This approach can be extended to other quantum groups. | hep-th |
Comments on gauge invariant overlaps for marginal solutions in open
string field theory: We calculate the gauge invariant overlaps for
Schnabl/Kiermaier-Okawa-Rastelli-Zwiebach's marginal solution with nonsingular
current. The obtained formula is the same as that for
Fuchs-Kroyter-Potting/Kiermaier-Okawa's marginal solution, which was already
computed by Ellwood. Our result is consistent with the expectation that they
may be gauge equivalent. We also comment on a gauge invariant overlap for
rolling tachyon solutions in cubic open string field theory. | hep-th |
Interactions of Charged Spin-2 Fields: In light of recent progress in ghost-free theories of massive gravity and
multi-gravity, we reconsider the problem of constructing a ghost-free theory of
an interacting spin-2 field charged under a U(1) gauge symmetry. Our starting
point is the theory originally proposed by Federbush, which is essentially
Fierz-Pauli generalized to include a minimal coupling to a U(1) gauge field. We
show the Federbush theory with a dynamical U(1) field is in fact ghost-free and
can be treated as a healthy effective field theory to describe a massive
charged spin-2 particle. It can even potentially have healthy dynamics above
its strong-coupling scale. We then construct candidate gravitational extensions
to the Federbush theory both by using Dimensional Deconstruction, and by
constructing a general non-linear completion. However, we find that the U(1)
symmetry forces us to modify the form of the Einstein-Hilbert kinetic term. By
performing a constraint analysis directly in the first-order form, we show that
these modified kinetic terms inevitably reintroduce the Boulware-Deser ghost.
As a by-product of our analysis, we present a new proof for ghost-freedom of
bi-gravity in 2+1 dimensions (also known as Zwei-Dreibein gravity). We also
give a complementary algebraic argument that the Einstein-Hilbert kinetic term
is incompatible with a U(1) symmetry, for a finite number of gravitons. | hep-th |
Comments on Perturbative Dynamics of Non-Commutative Yang-Mills Theory: We study the U(N) non-commutative Yang-Mills theory at the one-loop
approximation. We check renormalizability and gauge invariance of the model and
calculate the one-loop beta function. The interaction of the SU(N) gauge bosons
with the U(1) gauge boson plays an important role in the consistency check. In
particular, the SU(N) theory by itself is not consistent. We also find that the
theta --> 0 limit of the U(N) theory does not converge to the ordinary SU(N) x
U(1) commutative theory, even at the planar limit. Finally, we comment on the
UV/IR mixing. | hep-th |
From positive geometries to a coaction on hypergeometric functions: It is well known that Feynman integrals in dimensional regularization often
evaluate to functions of hypergeometric type. Inspired by a recent proposal for
a coaction on one-loop Feynman integrals in dimensional regularization, we use
intersection numbers and twisted homology theory to define a coaction on
certain hypergeometric functions. The functions we consider admit an integral
representation where both the integrand and the contour of integration are
associated with positive geometries. As in dimensionally-regularized Feynman
integrals, endpoint singularities are regularized by means of exponents
controlled by a small parameter $\epsilon$. We show that the coaction defined
on this class of integral is consistent, upon expansion in $\epsilon$, with the
well-known coaction on multiple polylogarithms. We illustrate the validity of
our construction by explicitly determining the coaction on various types of
hypergeometric ${}_{p+1}F_p$ and Appell functions. | hep-th |
The Berry-Tabor conjecture for spin chains of Haldane-Shastry type: According to a long-standing conjecture of Berry and Tabor, the distribution
of the spacings between consecutive levels of a "generic'' integrable model
should follow Poisson's law. In contrast, the spacings distribution of chaotic
systems typically follows Wigner's law. An important exception to the
Berry-Tabor conjecture is the integrable spin chain with long-range
interactions introduced by Haldane and Shastry in 1988, whose spacings
distribution is neither Poissonian nor of Wigner's type. In this letter we
argue that the cumulative spacings distribution of this chain should follow the
"square root of a logarithm'' law recently proposed by us as a characteristic
feature of all spin chains of Haldane-Shastry type. We also show in detail that
the latter law is valid for the rational counterpart of the Haldane-Shastry
chain introduced by Polychronakos. | hep-th |
Lessons from All Logs Summation in Yukawa Theories: Some features of old results in the total summation of all logarithmic
contributions of all diagrams in Yukawa theory are presented. We discuss some
lessons from this picture for the description of Pomeron, odderon, etc. in QCD. | hep-th |
Fermion vacuum energies in brane world models: The fermion representations and boundary conditions in five dimensional anti
de Sitter space are described in detail. In each case the one loop effective
action is calculated for massless fermions. The possibility of topological or
Wilson loop symmetry breaking is discussed. | hep-th |
Linear $r$-matrix algebra for classical separable systems: We consider a hierarchy of the natural type Hamiltonian systems of $n$
degrees of freedom with polynomial potentials separable in general ellipsoidal
and general paraboloidal coordinates. We give a Lax representation in terms of
$2\times 2$ matrices for the whole hierarchy and construct the associated
linear $r$-matrix algebra with the $r$-matrix dependent on the dynamical
variables. A Yang-Baxter equation of dynamical type is proposed. Using the
method of variable separation we provide the integration of the systems in
classical mechanics conctructing the separation equations and, hence, the
explicit form of action variables. The quantisation problem is discussed with
the help of the separation variables. | hep-th |
Detecting topological sectors in continuum Yang-Mills theory and the
fate of BRST symmetry: In this work, motivated by Laplacian type center gauges in the lattice,
designed to avoid the Gribov problem, we introduce a new family of gauge
fixings for pure Yang-Mills theories in the continuum. This procedure separates
the partition function into partial contributions associated with different
sectors, containing center vortices and correlated monopoles. We show that, on
each sector, the gauge fixed path-integral displays a BRST symmetry, however,
it cannot be globally extended due to sector dependent boundary conditions on
the ghost fields. These are nice features as they would permit to discuss the
independence of the partial contributions on gauge parameters,, while opening a
window for the space of quantum states to be different from the perturbative
one, which would be implied if topological configurations were removed. | hep-th |
Opers and TBA: In this note we study the "conformal limit" of the TBA equations which
describe the geometry of the moduli space of four-dimensional N=2 gauge
theories compactified on a circle. We argue that the resulting conformal TBA
equations describe a generalization of the oper submanifold in the space of
complex flat connections on a Riemann surface. In particular, the conformal TBA
equations for theories in the A1 class produce solutions of the Schr\"odinger
equation with a rational potential. | hep-th |
On the canonical structure and extra mode of generalized unimodular
gravity: We consider a recently proposed generalization of unimodular gravity, where
the lapse function is constrained to be equal to a function of the determinant
of the spatial metric $f(h)$, as a potential origin of a dark fluid with a
generally $h$-dependent equation of state parameter. We establish the
Hamiltonian analysis and the canonical path integral for the theory. All the
special cases that do not match unimodular gravity involve violation of general
covariance, and consequently the physical content of the theory is changed
significantly. Particularly, the case of a constant function $f$ is shown to
contain an extra physical degree of freedom in each point of space. Physical
consequences of the extra degree of freedom are studied in a linearized theory,
where the extra mode is carried by the trace of the metric perturbation. The
trace mode does not propagate as a wave, since it satisfies an elliptic partial
differential equation in spacetime. Consequently, the trace perturbation is
shown to grow exponentially with time, which implies instability. The case of a
general $f(h)$ involves additional second-class constraints, which implies the
presence of an extra global degree of freedom that depends only on time
(instead of the extra local degree of freedom in the case of a constant $f$). | hep-th |
Higgs Phenomenon for 4-D Gravity in Anti de Sitter Space: We show that standard Einstein gravity coupled to a free conformal field
theory (CFT) in Anti de Sitter space can undergo a Higgs phenomenon whereby the
graviton acquires a nonzero mass (and three extra polarizations). We show that
the essential ingredients of this mechanism are the discreteness of the energy
spectrum in AdS space, and unusual boundary conditions on the elementary fields
of the CFT. These boundary conditions can be interpreted as implying the
existence of a 3-d defect CFT living at the boundary of the AdS space. Our
free-field computation sheds light on the essential, model-independent features
of AdS that give rise to massive gravity. | hep-th |
Non-Einstein geometries in Chiral Gravity: We analyze the asymptotic solutions of Chiral Gravity (Topologically Massive
Gravity at \mu l = 1 with Brown-Henneaux boundary conditions) focusing on
non-Einstein metrics. A class of such solutions admits curvature singularities
in the interior which are reflected as singularities or infinite bulk energy of
the corresponding linear solutions. A non-linear solution is found exactly. The
back-reaction induces a repulsion of geodesics and a shielding of the
singularity by an event horizon but also introduces closed timelike curves. | hep-th |
Fermion scattering on topological solitons in the $\mathbb{CP}^{N-1}$
model: The scattering of Dirac fermions in the background fields of topological
solitons of the $(2+1)$-dimensional $\mathbb{CP}^{N-1}$ model is studied using
analytical and numerical methods. It is shown that the exact solutions for
fermionic wave functions can be expressed in terms of the confluent Heun
functions. The question of the existence of bound states for the
fermion-soliton system is then investigated. General formulae describing
fermion scattering are obtained, and a symmetry property for the partial phase
shifts is derived. The amplitudes and cross-sections of the fermion-soliton
scattering are obtained in an analytical form within the framework of the Born
approximation, and the symmetry properties and asymptotic forms of the Born
amplitudes are investigated. The dependences of the first few partial phase
shifts on the fermion momentum are obtained by numerical methods, and some of
their properties are investigated and discussed. | hep-th |
Non-Abelian tensor gauge fields and new topological invariants: In this article we shall consider the tensor gauge fields which are possible
to embed into the existing framework of generalized YM theory and therefore
allows to construct the gauge invariant and metric independent forms in 2n+4
and 2n+2 dimensions. These new forms are analogous to the
Pontryagin-Chern-Simons densities in YM gauge theory and to the corresponding
series of densities in 2n+3 dimensions constructed recently in arXiv:1205.0027. | hep-th |
Flux-Induced Baryon Asymmetry: I propose that the primordial baryon asymmetry of the universe was induced by
the presence of a non-vanishing antisymmetric field background H_ijk across the
three space dimensions. This background creates a dilute (B-L)-number density
in the universe cancelling the contribution from baryons and leptons. This
situation naturally appears if the U(1)_{B-L} symmetry is gauged and the
corresponding gauge boson gets a Stuckelberg mass by combining with an
antisymmetric field B_ij. All these ingredients are present in D-brane models
of particle physics. None of the Sakharov conditions are required. | hep-th |
Mesoscopic Fluctuations in Stochastic Spacetime: Mesoscopic effects associated with wave propagation in spacetime with metric
stochasticity are studied. We show that the scalar and spinor waves in a
stochastic spacetime behave similarly to the electrons in a disordered system.
Viewing this as the quantum transport problem, mesoscopic fluctuations in such
a spacetime are discussed. The conductance and its fluctuations are expressed
in terms of a nonlinear sigma model in the closed time path formalism. We show
that the conductance fluctuations are universal, independent of the volume of
the stochastic region and the amount of stochasticity. | hep-th |
Matching three-point functions of BMN operators at weak and strong
coupling: The agreement between string theory and field theory is demonstrated in the
leading order by providing the first calculation of the correlator of three
two-impurity BMN states with all non-zero momenta. The calculation is performed
in two completely independent ways: in field theory by using the large-$N$
perturbative expansion, up to the terms subleading in finite-size, and in
string theory by using the Dobashi-Yoneya 3-string vertex in the leading order
of the Penrose expansion. The two results come out to be completely identical. | hep-th |
Winding Tachyons and Stringy Black Holes: We study string theory on $\mathbb{R}^d\times \mathbb{S}^1$. For applications
to thermodynamics, the circumference of the $\mathbb{S}^1$ is the inverse
temperature, $\beta$. We show that for $d=6$, the low energy effective field
theory at the inverse Hagedorn temperature, $\beta=\beta_H$, has a one
parameter family of normalizable spherically symmetric solutions that break the
winding symmetry around the $\mathbb{S}^1$. The resulting backgrounds exhibit
an enhanced symmetry, with the symmetry breaking pattern $SU(2)_L\times
SU(2)_R\to SU(2)_{\rm diagonal}$. The effective field theory analysis of these
backgrounds is reliable for some range of parameters. More generally, they are
described by a worldsheet CFT, which corresponds to the free theory on
$\mathbb{R}^6\times \mathbb{S}^1$ perturbed by a non-abelian Thirring
deformation with an $r$-dependent coupling. We propose that, in a certain
scaling limit, string theory in these backgrounds is described by the
$SL(2,\mathbb{R})/U(1)$ cigar, and provides a thermodynamic description of
weakly coupled highly excited fundamental strings. We also discuss the relation
of these backgrounds to Euclidean black holes with near-Hagedorn Hawking
temperature, and possible generalizations to other $d$. | hep-th |
Transverse Goldstone mode in holographic fluids with broken translations: In this paper we investigate the low energy shear modes in fluid systems with
spontaneously broken translations by a specific holographic model. In absence
of momentum relaxation, we find that there exist two decoupled gapless modes in
the transverse channel, one of which is purely diffusive and the other
corresponds to vortex like excitations. The diffusive mode is associated with
the conservation of momentum and the vortex mode can be viewed as the Goldstone
mode of the spontaneous symmetry breaking. Switching on an external source
which breaks the translations explicitly but weakly, the would-be gapless modes
both get relaxed and acquire a tiny mass gap. Finally, in the strong momentum
relaxation regime, we find a (pseudo-)diffusive-to-sound crossover that is set
by a momentum gap. | hep-th |
Unification of Gravity, Gauge and Higgs Fields by Confined Quantum
Fields II -Effective Theory-: Dynamics of quantized free fields ( of spin 0 and 1/2 ) contained in a
subspace $V_*$ of an N+4 dimensional flat space $V$ is studied. The space $V_*$
is considered as a neighborhood of a four dimensional submanifold $M$
arbitrarily embedded into $V$. We show that Einstein SO(N)-Yang-Mills Higgs
theory is induced as a low energy effective theory of the system. Gravity,
SO(N) gauge fields and Higgs fields are obtained from embedding functions of
$M$. | hep-th |
Exotic Dark Spinor Fields: Exotic dark spinor fields are introduced and investigated in the context of
inequivalent spin structures on arbitrary curved spacetimes, which induces an
additional term on the associated Dirac operator, related to a Cech cohomology
class. For the most kinds of spinor fields, any exotic term in the Dirac
operator can be absorbed and encoded as a shift of the electromagnetic vector
potential representing an element of the cohomology group H^1(M, Z_2). The
possibility of concealing such an exotic term does not exist in case of dark
(ELKO) spinor fields, as they cannot carry electromagnetic charge, so that the
full topological analysis must be evaluated. Since exotic dark spinor fields
also satisfy Klein-Gordon propagators, the dynamical constraints related to the
exotic term in the Dirac equation can be explicitly calculated. It forthwith
implies that the non-trivial topology associated to the spacetime can
drastically engender --- from the dynamics of dark spinor fields ---
constraints in the spacetime metric structure. Meanwhile, such constraints may
be alleviated, at the cost of constraining the exotic spacetime topology.
Besides being prime candidates to the dark matter problem, dark spinor fields
are shown to be potential candidates to probe non-trivial topologies in
spacetime, as well as probe the spacetime metric structure. | hep-th |
The Overall Coefficient of the Two-loop Superstring Amplitude Using Pure
Spinors: Using the results recently obtained for computing integrals over
(non-minimal) pure spinor superspace, we compute the coefficient of the
massless two-loop four-point amplitude from first principles. Contrasting with
the mathematical difficulties in the RNS formalism where unknown normalizations
of chiral determinant formulae force the two-loop coefficient to be determined
only indirectly through factorization, the computation in the pure spinor
formalism can be smoothly carried out. | hep-th |
Multivalued Fields on the Complex Plane and Conformal Field Theories: In this paper a class of conformal field theories with nonabelian and
discrete group of symmetry is investigated. These theories are realized in
terms of free scalar fields starting from the simple $b-c$ systems and scalar
fields on algebraic curves. The Knizhnik-Zamolodchikov equations for the
conformal blocks can be explicitly solved. Besides of the fact that one obtains
in this way an entire class of theories in which the operators obey a
nonstandard statistics, these systems are interesting in exploring the
connection between statistics and curved space-times, at least in the two
dimensional case. | hep-th |
Novel Analysis of Spinor Interactions and non-Riemannian Geometry: A novel analysis of the gauge theory of the local Lorentz group is
implemented both in flat and in curved space-time, and the resulting dynamics
is analyzed in view of the geometrical interpretation of the gauge potential.
The Yang-Mills picture of local Lorentz transformations is first approached in
a second-order formalism. For the Lagrangian approach to reproduce the second
Cartan structure equation as soon as the Lorentz gauge connections are
identified with the contortion tensor, an interaction term between the Lorentz
gauge fields and the spin connections has to be postulated. The full picture
involving gravity, torsion and spinors is described by a coupled set of field
equations, which allows one to interpret both gravitational spin connections
and matter spin density as the source term for the Yang-Mills equations. The
contortion tensor acquires a propagating character, because of its non-Abelian
feature, and the pure contact interaction is restored in the limit of vanishing
Lorentz connections. | hep-th |
On the integrability of Wilson loops in AdS_5 x S^5: Some periodic
ansatze: Wilson loops are calculated within the AdS/CFT correspondence by finding a
classical solution to the string equations of motion in AdS_5 x S^5 and
evaluating its action. An important fact is that this sigma-model used to
evaluate the Wilson loops is integrable, a feature that has gained relevance
through the study of spinning strings carrying large quantum numbers and
spin-chains. We apply the same techniques used to solve the equations for
spinning strings to find the minimal surfaces describing a wide class of Wilson
loops. We focus on different cases with periodic boundary conditions on the
AdS_5 and S^5 factors and find a rich array of solutions. We examine the
different phases that appear in the problem and comment on the applicability of
integrability to the general problem. | hep-th |
Black Holes and U-duality in Diverse Dimensions: In this paper we review some properties of BPS black holes of supergravities
with n=32,16 supersymmetries. The BPS condition, a condition on the eigenvalues
of the central charge matrix, can be shown to be U-duality invariant. We
explicitly work out D=4, N=8 and D=5, N=4 supergravities. | hep-th |
Quantum Field Theory of Topological Defects as Inhomogeneous Condensates: In the framework of the Closed-Time-Path formalism, we show how topological
defects may arise in Quantum Field Theory as result of a localized
(inhomogeneous) condensation of particles. We demonstrate our approach on two
examples; kinks in the $2D \lambda \psi^{4}$ theory (both at zero and finite
temperature) and vortices in the complex $4D \lambda \psi^{4} $ theory. | hep-th |
Derivation of String Field Theory from the Large N BMN Limit: We continue the development of a systematic procedure for deriving closed
string pp wave string field theory from the large N
Berenstein-Maldacena-Nastase limit. In the present paper the effects of the
Yang-Mills interaction are considered in detail for general BMN states. The SFT
interaction with the appropriate operator insertion at the interaction point is
demonstrated. | hep-th |
Renormalization and asymptotic safety in truncated quantum Einstein
gravity: A perturbative quantum theory of the 2-Killing vector reduction of general
relativity is constructed. Although non-renormalizable in the standard sense,
we show that to all orders of the loop expansion strict cut-off independence
can be achieved in a space of Lagrangians differing only by a field dependent
conformal factor. In particular the Noether currents and the quantum
constraints can be defined as finite composite operators. The form of the field
dependence in the conformal factor changes with the renormalization scale and a
closed formula is obtained for the beta functional governing its flow. The flow
possesses a unique fixed point at which the trace anomaly is shown to vanish.
The approach to the fixed point adheres to Weinberg's ``asymptotic safety''
scenario, both in the gravitational wave/cosmological sector and in the
stationary sector. | hep-th |
An equivalence of two mass generation mechanisms for gauge fields: Two mass generation mechanisms for gauge theories are studied. It is proved
that in the abelian case the topological mass generation mechanism introduced
in hep-th/9301060, hep-th/9512216 is equivalent to the mass generation
mechanism defined in hep-th/0510240, hep-th/0605050 with the help of
``localization'' of a nonlocal gauge invariant action. In the nonabelian case
the former mechanism is known to generate a unitary renormalizable quantum
field theory describing a massive vector field. | hep-th |
Anti-de Sitter Space, Thermal Phase Transition, And Confinement In Gauge
Theories: The correspondence between supergravity (and string theory) on $AdS$ space
and boundary conformal field theory relates the thermodynamics of ${\cal N}=4$
super Yang-Mills theory in four dimensions to the thermodynamics of
Schwarzschild black holes in Anti-de Sitter space. In this description, quantum
phenomena such as the spontaneous breaking of the center of the gauge group,
magnetic confinement, and the mass gap are coded in classical geometry. The
correspondence makes it manifest that the entropy of a very large $AdS$
Schwarzschild black hole must scale ``holographically'' with the volume of its
horizon. By similar methods, one can also make a speculative proposal for the
description of large $N$ gauge theories in four dimensions without
supersymmetry. | hep-th |
Integrable N=2 Supersymmetric Field Theories: Some additional references are included on the last 3 pages. | hep-th |
Supersymmetric field theories and geometric Langlands: The other side of
the coin: This note announces results on the relations between the approach of
Beilinson and Drinfeld to the geometric Langlands correspondence based on
conformal field theory, the approach of Kapustin and Witten based on $N=4$ SYM,
and the AGT-correspondence. The geometric Langlands correspondence is described
as the Nekrasov-Shatashvili limit of a generalisation of the AGT-correspondence
in the presence of surface operators. Following the approaches of Kapustin -
Witten and Nekrasov - Witten we interpret some aspects of the resulting picture
using an effective description in terms of two-dimensional sigma models having
Hitchin's moduli spaces as target-manifold. | hep-th |
Algebraic inversion of the Dirac equation for the vector potential in
the non-abelian case: We study the Dirac equation for spinor wavefunctions minimally coupled to an
external field, from the perspective of an algebraic system of linear equations
for the vector potential. By analogy with the method in electromagnetism, which
has been well-studied, and leads to classical solutions of the Maxwell-Dirac
equations, we set up the formalism for non-abelian gauge symmetry, with the
SU(2) group and the case of four-spinor doublets. An extended isospin-charge
conjugation operator is defined, enabling the hermiticity constraint on the
gauge potential to be imposed in a covariant fashion, and rendering the
algebraic system tractable. The outcome is an invertible linear equation for
the non-abelian vector potential in terms of bispinor current densities. We
show that, via application of suitable extended Fierz identities, the solution
of this system for the non-abelian vector potential is a rational expression
involving only Pauli scalar and Pauli triplet, Lorentz scalar, vector and axial
vector current densities, albeit in the non-closed form of a Neumann series. | hep-th |
Collective Motion of Micro-organisms from Field Theoretical Viewpoint: We analyze the collective motion of micro-organisms in the fluid and consider
the problem of the red tide. The red tide is produced by the condensation of
the micro-organisms, which might be a similar phenomenon to the condensation of
the strings. We propose a model of the generation of the red tide. By
considering the interaction between the micro- organisms mediated by the
velocity fields in the fluid, we derive the Van der Waals type equation of
state, where the generation of the red tide can be regarded as a phase
transition from the gas of micro-organisms to the liquid. (The number density
of micro-organisms which generates the red tide is order estimated.) | hep-th |
Momentum space topology of QCD: We discuss the possibility to consider quark matter as the topological
material. We consider hadronic phase (HP), the quark - gluon plasma phase
(QGP), and the hypothetical color - flavor locking (CFL) phase. In those phases
we identify the relevant topological invariants in momentum space. The
formalism is developed, which relates those invariants and massless fermions
that reside on vortices and at the interphases. This formalism is illustrated
by the example of vortices in the CFL phase. | hep-th |
Stability of the quantum supermembrane in a manifold with boundary: We point out an effect which may stabilize a supersymmetric membrane moving
on a manifold with boundary, and lead to a light-cone Hamiltonian with a
discrete spectrum of eigenvalues. The analysis is carried out explicitly for a
closed supermembrane in the regularized $SU(N)$ matrix model version. | hep-th |
Aspects of critical O$(N)$ model with boundary and defect: In this thesis, we explore the critical phenomena in the presence of extended
objects, which we call defects, aiming for a better understanding of the
properties of non-local objects ubiquitous in our world and a more practical
and realistic study of criticality. To this end, we study the statistical
O$(N)$ vector model in $(4-\epsilon)$ dimensions with three kinds of defects: a
line defect constructed by smearing an O$(N)$ vector field along one direction
and Dirichlet and Neumann boundaries. A conventional approach to critical
phenomena would be to perform perturbative calculations using Feynman diagrams
and doing renormalization group analysis. But we here also take a different but
complementary approach based on three axioms that include conformal symmetry of
the theory at the criticality. We apply this axiomatic framework to the
critical O$(N)$ model with a defect and reproduce the perturbative results at
the leading non-trivial order in $\epsilon$, substantiating the validity of our
approach. Along the way, we develop and refine the axiomatic framework to
derive anomalous dimensions of the composite operators on the defect that have
not been accessible in the existing literature by focusing on the analyticity
of the correlation functions. | hep-th |
Observations on Integral and Continuous U-duality Orbits in N=8
Supergravity: One would often like to know when two a priori distinct extremal black
p-brane solutions are in fact U-duality related. In the classical supergravity
limit the answer for a large class of theories has been known for some time.
However, in the full quantum theory the U-duality group is broken to a discrete
subgroup and the question of U-duality orbits in this case is a nuanced matter.
In the present work we address this issue in the context of N=8 supergravity in
four, five and six dimensions. The purpose of this note is to present and
clarify what is currently known about these discrete orbits while at the same
time filling in some of the details not yet appearing in the literature. To
this end we exploit the mathematical framework of integral Jordan algebras and
Freudenthal triple systems. The charge vector of the dyonic black string in D=6
is SO(5,5;Z) related to a two-charge reduced canonical form uniquely specified
by a set of two arithmetic U-duality invariants. Similarly, the black hole
(string) charge vectors in D=5 are E_{6(6)}(Z) equivalent to a three-charge
canonical form, again uniquely fixed by a set of three arithmetic U-duality
invariants. The situation in four dimensions is less clear: while black holes
preserving more than 1/8 of the supersymmetries may be fully classified by
known arithmetic E_{7(7)}(Z) invariants, 1/8-BPS and non-BPS black holes yield
increasingly subtle orbit structures, which remain to be properly understood.
However, for the very special subclass of projective black holes a complete
classification is known. All projective black holes are E_{7(7)}(Z) related to
a four or five charge canonical form determined uniquely by the set of known
arithmetic U-duality invariants. Moreover, E_{7(7)}(Z) acts transitively on the
charge vectors of black holes with a given leading-order entropy. | hep-th |
The Search for the Origins of M Theory : Loop Quantum Mechanics,
Loops/Strings and Bulk/Boundary Dualities: The construction of a $covariant$ Loop Wave functional equation in a 4D
spacetime is attained by introducing a generalized $eleven$ dimensional
categorical {\bf C}-space comprised of $8\times 8$ antisymmetric matrices. The
latter matrices encode the generalized coordinates of the histories of points,
loops and surfaces $combined$. Spacetime Topology change and the Holographic
principle are natural consequences of imposing the principle of $covariance$ in
{\bf C}-space. The Planck length is introduced as a necessary rescaling
parameter to establish the correspondence limit with the physics of
point-histories in ordinary Minkowski space, in the limit $l_P\to 0$. Spacetime
quantization should appear in discrete units of Planck length, area, volume
,....All this seems to suggest that the generalized principle of covariance,
representing invariance of proper $area$ intervals in {\bf C}-space, under
matrix-coordinate transformations, could be relevant in discovering the
underlying principle behind the origins of $M$ theory. We construct an ansatz
for the $SU(\infty)$ Yang-Mills vacuum wavefunctional as a solution of the
Schroedinger Loop Wave equation associated with the Loop Quantum Mechanical
formulation of the Eguchi-Schild String . The Strings/Loops ($SU(\infty)$ gauge
field) correspondence implements one form of the Bulk/Boundary duality
conjecture in this case. | hep-th |
Some aspects of quantum correlations and decoherence in the cosmological
spacetimes: This thesis presents a theoretical investigation into the quantum field
theoretic aspects of quantum correlations and decoherence in the cosmological
spacetimes. We shall focus on the inflationary or dark energy dominated phase
of the universe, and we shall take the spacetime background to be de Sitter.
The primary objective of this thesis is to study the physics of the very early
universe and to gain insight into the interesting interplay among quantum
correlations, entanglement and decoherence which can affect the evolution of
our universe. | hep-th |
$θ$-diagram technique for $\mathcal{N}=1$, $d=4$ superfields: We describe a diagrammatic procedure to carry out the Grassmann integration
in super-Feynman diagrams of 4d theories expressed in terms of $\mathcal{N}=1$
superfields. This method is alternative to the well known $D$-algebra approach.
We develop it in detail for theories containing vector, chiral and anti-chiral
superfields, with the type of interactions which occur in $\mathcal{N}=2$ SYM
theories with massless matter, but it would be possible to extend it to other
cases. The main advantage is that this method is algorithmic; we implemented it
as a Mathematica program that, given the description of a super Feynman diagram
in momentum space, returns directly the polynomial in the momenta produced by
the Grassmann integration. | hep-th |
Holographic description of vacuum bubbles: We discuss a holographic description of vacuum bubbles, with possible
implications for a consistent description of the multiverse. In particular, we
elaborate on the recent observation by Maldacena, that the interior of AdS
bubbles can be described in terms of CFT degrees of freedom living on the
worldsheet of the bubble wall. We consider the scattering of bulk gravitons in
the ambient parent vacuum, off the bubble wall. In the dual description, the
transmission coefficient is interpreted as the probability that a graviton is
absorbed by the worldsheet CFT degrees of freedom. The result is in agreement
with intuitive expectations. Conformal invariance is not exact in this setup,
and the leading corrections due to the IR and UV cut-offs are displayed. Aside
from bulk scattering states, we find that when a bubble nucleates within a
parent dS vacuum, there is a zero mode of the graviton which describes lower
dimensional gravity with a finite Newton's constant. This massless graviton
lives within one Hubble radius away from the bubble wall. Possible implications
for a fully holographic description of the inflating multiverse are briefly
discussed. | hep-th |
Free Fermions at Finite Temperature: An Application of the
Non-Commutative Algebra: Charret et. al. applied the properties of the Grassmann generators to develop
a new method to calculate the coefficients of the high temperature expansion of
the grand canonical partition function of self-interacting fermionic models in
any d-dimensions (d>=1). The method explores the anti-commuting nature of
fermionic fields and avoids the calculation of the fermionic path integral. We
apply this new method to the relativistic free Dirac fermions and recover the
known results in the literature. | hep-th |
Cohomology of Lie Superalgebras: Forms, Pseudoforms, and Integral Forms: We study the cohomology of Lie superalgebras for the full complex of forms:
superforms, pseudoforms and integral forms. We use the technique of spectral
sequences to abstractly compute the Chevalley-Eilenberg cohomology. We first
focus on the superalgebra $\mathfrak{osp}(2|2)$ and show that there exist
non-empty cohomology spaces among pseudoforms related to sub-superalgebras. We
then extend some classical theorems by Koszul, as to include pseudoforms and
integral forms. Further, we conjecture that the algebraic Poincar\'e duality
extends to Lie superalgebras, as long as all the complexes of forms are taken
into account and we prove that this holds true for $\mathfrak{osp}(2|2)$. We
finally construct the cohomology representatives explicitly by using a
distributional realisation of pseudoforms and integral forms. On one hand,
these results show that the cohomology of Lie superalgebras is actually larger
than expected, whereas one restricts to superforms only; on the other hand, we
show the emergence of completely new cohomology classes represented by
pseudoforms. These classes realise as integral form classes of
sub-superstructures. | hep-th |
The extremal black hole bomb: We analyze the spectrum of massive scalar bound states in the background of
extremal Kerr black holes, focusing on modes in the superradiant regime, which
grow exponentially in time and quickly deplete the black hole's mass and spin.
Previous analytical estimates for the growth rate of this instability were
limited to the $\mu M\ll1$ and $\mu M\gg1$ regimes, where $\mu$ and $M$ denote
the scalar field and black hole masses, respectively. In this work, we discuss
an analytical method to compute the superradiant spectrum for generic values of
these parameters, namely in the phenomenologically interesting regime $\mu
M\sim 1$. To do this, we solve the radial mode equation in two overlapping
regions and match the solutions in their common domain of validity. We show
that matching the functional forms of these functions involves approximations
that are not valid for the whole range of scalar masses, exhibiting unphysical
poles that produce a large enhancement of the growth rate. Alternatively, we
match the functions at a single point and show that, despite the uncertainty in
the choice of the match point, this method eliminates the spurious poles and
agrees with previous numerical computations of the spectrum using a
continued-fraction method. | hep-th |
Discrete scale invariance in holography and an argument against the
complexity=action proposal: The AdS/CFT correspondence often motivates research on questions in
gravitational physics whose relevance might not be immediately clear from a
purely GR-perspective, but which are nevertheless interesting. In these
proceedings, we summarise two such results recently obtained by the author. One
concerns, broadly speaking, the possible isometry-groups of a spacetime sourced
by physical matter. The other one provides a possible argument against the
recently proposed complexity=action conjecture. | hep-th |
Positivity, low twist dominance and CSDR for CFTs: We consider a crossing symmetric dispersion relation (CSDR) for CFT four
point correlation with identical scalar operators, which is manifestly
symmetric under the cross-ratios $u,v$ interchange. This representation has
several features in common with the CSDR for quantum field theories. It enables
a study of the expansion of the correlation function around $u=v=1/4$, which is
used in the numerical conformal bootstrap program. We elucidate several
remarkable features of the dispersive representation using the four point
correlation function of $\Phi_{1,2}$ operators in 2d minimal models as a
test-bed. When the dimension of the external scalar operator ($\Delta_\sigma$)
is less than $\frac{1}{2}$, the CSDR gets contribution from only a single tower
of global primary operators with the second tower being projected out. We find
that there is a notion of low twist dominance (LTD) which, as a function of
$\Delta_\sigma$, is maximized near the 2d Ising model as well as the
non-unitary Yang-Lee model. The CSDR and LTD further explain positivity of the
Taylor expansion coefficients of the correlation function around the crossing
symmetric point and lead to universal predictions for specific ratios of these
coefficients. These results carry over to the epsilon expansion in $4-\epsilon$
dimensions. We also conduct a preliminary investigation of geometric function
theory ideas, namely the Bieberbach-Rogosinski bounds. | hep-th |
Spacetime Subsystem Symmetries: One characteristic feature of many fractonic lattice models, and a defining
property of the exotic field theories developed to describe them, are subsystem
symmetries including a conservation of not just net electric charge but also
electric dipole moments or charges living on submanifolds. So far all such
theories were based on internal subsystem symmetries. In this work we
generalize the notion of subsystem symmetries to system with subsystem
spacetime symmetries with locally conserved energies. | hep-th |
Eikonal phase matrix, deflection angle and time delay in effective field
theories of gravity: The eikonal approximation is an ideal tool to extract classical observables
in gauge theory and gravity directly from scattering amplitudes. Here we
consider effective theories of gravity where in addition to the
Einstein-Hilbert term we include non-minimal couplings of the type $R^3$, $R^4$
and $FFR$. In particular, we study the scattering of gravitons and photons of
frequency $\omega$ off heavy scalars of mass $m$ in the limit $m\gg \omega \gg
|\vec{q}\,|$, where $\vec{q}$ is the momentum transfer. The presence of
non-minimal couplings induces helicity-flip processes which survive the eikonal
limit, thereby promoting the eikonal phase to an eikonal phase matrix. We
obtain the latter from the relevant two-to-two helicity amplitudes that we
compute up to one-loop order, and confirm that the leading-order terms in
$\omega$ exponentiate \`{a} la Amati, Ciafaloni and Veneziano. From the
eigenvalues of the eikonal phase matrix we then extract two physical
observables, to 2PM order: the classical deflection angle and Shapiro time
delay/advance. Whenever the classical expectation of helicity conservation of
the massless scattered particle is violated, i.e. the eigenvalues of the
eikonal matrix are non-degenerate, causality violation due to time advance is a
generic possibility for small impact parameter. We show that for graviton
scattering in the $R^4$ and $FFR$ theories, time advance is circumvented if the
couplings of these interactions satisfy certain positivity conditions, while it
is unavoidable for graviton scattering in the $R^3$ theory and photon
scattering in the $FFR$ theory. The scattering processes we consider mimic the
deflection of photons and gravitons off spinless heavy objects such as
black~holes. | hep-th |
Classicalization and unitarization of wee partons in QCD and Gravity:
The CGC-Black Hole correspondence: We discuss a remarkable correspondence between the description of Black Holes
as highly occupied condensates of $N$ weakly interacting gravitons and that of
Color Glass Condensates (CGCs) as highly occupied gluon states. In both cases,
the dynamics of "wee partons" in Regge asymptotics is controlled by emergent
semi-hard scales that lead to perturbative unitarization and classicalization
of $2\rightarrow N$ particle amplitudes at weak coupling. In particular, they
attain a maximal entropy permitted by unitarity, bounded by the inverse
coupling $\alpha$ of the respective constituents. Strikingly, this entropy is
equal to the area measured in units of the Goldstone constant corresponding to
the spontaneous breaking of Poincar{\'{e}} symmetry by the corresponding
graviton or gluon condensate. In gravity, the Goldstone constant is the Planck
scale, and gives rise to the Bekenstein-Hawking entropy. Likewise, in the CGC,
the corresponding Goldstone scale is determined by the onset of gluon
screening. We point to further similarities in Black Hole formation,
thermalization and decay, to that of the Glasma matter formed from colliding
CGCs in ultrarelativistic nuclear collisions, which decays into a Quark-Gluon
Plasma. | hep-th |
Twistorial monopoles & chiral algebras: We initiate the study of how the insertion of magnetically charged states in
4d self-dual gauge theories impacts the 2d chiral algebras supported on the
celestial sphere at asymptotic null infinity, from the point of view of the
4d/2d twistorial correspondence introduced by Costello and the second author.
By reducing the 6d twistorial theory to a 3d holomorphic-topological theory
with suitable boundary conditions, we can motivate certain non-perturbative
enhancements of the celestial chiral algebra corresponding to extensions by
modules arising from 3d boundary monopole operators. We also identify the
insertion of 4d (non-abelian) monopoles with families of spectral flow
automorphisms of the celestial chiral algebra. | hep-th |
Accelerating Black Holes and Spinning Spindles: We study solutions in the Pleba\'nski--Demia\'nski family which describe an
accelerating, rotating and dyonically charged black hole in $AdS_4$. These are
solutions of $D=4$ Einstein-Maxwell theory with a negative cosmological
constant and hence minimal $D=4$ gauged supergravity. It is well known that
when the acceleration is non-vanishing the $D=4$ black hole metrics have
conical singularities. By uplifting the solutions to $D=11$ supergravity using
a regular Sasaki-Einstein $7$-manifold, $SE_7$, we show how the free parameters
can be chosen to eliminate the conical singularities. Topologically, the $D=11$
solutions incorporate an $SE_7$ fibration over a two-dimensional weighted
projective space, $\mathbb{WCP}^1_{[n_-,n_+]}$, also known as a spindle, which
is labelled by two integers that determine the conical singularities of the
$D=4$ metrics. We also discuss the supersymmetric and extremal limit and show
that the near horizon limit gives rise to a new family of regular
supersymmetric $AdS_2\times Y_9$ solutions of $D=11$ supergravity, which
generalise a known family by the addition of a rotation parameter. We calculate
the entropy of these black holes and argue that it should be possible to derive
this from certain ${\cal N}=2$, $d=3$ quiver gauge theories compactified on a
spinning spindle with appropriate magnetic flux. | hep-th |
Algebraic deformations of toric varieties II. Noncommutative instantons: We continue our study of the noncommutative algebraic and differential
geometry of a particular class of deformations of toric varieties, focusing on
aspects pertinent to the construction and enumeration of noncommutative
instantons on these varieties. We develop a noncommutative version of twistor
theory, which introduces a new example of a noncommutative four-sphere. We
develop a braided version of the ADHM construction and show that it
parametrizes a certain moduli space of framed torsion free sheaves on a
noncommutative projective plane. We use these constructions to explicitly build
instanton gauge bundles with canonical connections on the noncommutative
four-sphere that satisfy appropriate anti-selfduality equations. We construct
projective moduli spaces for the torsion free sheaves and demonstrate that they
are smooth. We define equivariant partition functions of these moduli spaces,
finding that they coincide with the usual instanton partition functions for
supersymmetric gauge theories on C^2. | hep-th |
A Meandering Inflaton: If the cosmological inflationary scenario took place in the cosmic landscape
in string theory, the inflaton, the scalar mode responsible for inflation,
would have meandered in a complicated multi-dimensional potential. We show that
this meandering property naturally leads to many e-folds of inflation, a
necessary condition for a successful inflationary scenario. This behavior also
leads to fluctuations in the primordial power spectrum of the cosmic microwave
background radiation, which may be detected in a near future cosmic variance
limited experiment like PLANCK. | hep-th |
Structure of deformations in Jackiw-Teitelboim black holes with matter: We consider Jackiw-Teitelboim gravity with a massless matter field and turn
on bulk excitations leading to a nontrivial vev of the corresponding dual
boundary operator. To leading order, we realize the corresponding deformation
of thermofield double state by explicitly identifying their Hilbert space. The
deformed state can be prepared with an operator insertion at the mid-point of
the Euclidean time evolution in the context of Hartle-Hawking construction. We
show that the inserted operators form an SL(2,{\bf R}) representation. We
construct a specific orthonormal basis that is directly related to the operator
basis of the vev deformations. If we include the higher order corrections, the
bulk geometry is no longer left-right symmetric. We argue that, classically,
the mode coefficients in the bulk deformation cannot be fully recovered from
the data collected along the boundary cutoff
trajectories. Then the bulk seems to contain more information than the cutoff
boundary, and this might be responsible for nontrivial behind-horizon degrees
of freedom. | hep-th |
$L_\infty$ algebras and Tensor Hierarchies in Exceptional Field Theory
and Gauged Supergravity: We show how the gauge and field structure of the tensor hierarchies in Double
and $E_{7(7)}$ Exceptional Field Theory fits into $L_\infty$ algebras. Special
attention is paid to redefinitions, the role of covariantly constrained fields
and intertwiners. The results are connected to Gauged Supergravities through
generalized Scherk-Schwarz reductions. We find that certain gauging-dependent
parameters generate trivial gauge transformations, giving rise to novel
symmetries for symmetries that are absent in their ungauged counterparts. | hep-th |
How one can obtain unambiguous predictions for the S-matrix in
non-renormalizable theories: The usual Bogolyubov R-operation works in non-renormalizable theories in the
same way as in renormalizable ones. However, in the non-renormalizable case,
the counter-terms eliminating ultraviolet divergences do not repeat the
structure of the original Lagrangian but contain new terms with a higher degree
of fields and derivatives increasing from order to order of PT. If one does not
aim to obtain finite off-shell Green functions but limits oneself only to the
finiteness of the S-matrix, then one can use the equations of motion and
drastically reduce the number of independent counter-terms. For example, it is
possible to reduce all counter-terms to a form containing only operators with
four fields and an arbitrary number of derivatives. And although there will
still be infinitely many such counter-terms, in order to fix the arbitrariness
of the subtraction procedure, one can normalize the on-shell 4-point amplitude,
which must be known for arbitrary kinematics, plus the 6-point amplitude at one
point. All other multiparticle amplitudes will be calculated unambiguously.
Within the framework of perturbation theory, the number of independent
counter-terms in a given order is limited, so does the number of normalization
conditions. The constructed counter-terms are not absorbed into the
normalization of a single coupling constant, the Lagrangian contains an
infinite number of terms, but after fixing the arbitrariness, it allows one to
obtain unambiguous predictions for observables. | hep-th |
Pure Spinor Superstrings on Generic type IIA Supergravity Backgrounds: We derive the Free Differential Algebra for type IIA supergravity in 10
dimensions in the string frame. We provide all fermionic terms for all
curvatures. We derive the Green-Schwarz sigma model for type IIA superstring
based on the FDA construction and we check its invariance under kappa-symmetry.
Finally, we derive the pure spinor sigma model and we check the BRST
invariance. The present derivation has the advantage that the resulting sigma
model is constructed in terms of the superfields appearing in the FDA and
therefore one can directly relate a supergravity background with the
corresponding sigma model. The complete explicit form of the BRST
transformations is given and some new pure spinor constraints are obtained.
Finally, the explicit form of the action is given. | hep-th |
Vertex algebras and 4-manifold invariants: We propose a way of computing 4-manifold invariants, old and new, as chiral
correlation functions in half-twisted 2d $\mathcal{N}=(0,2)$ theories that
arise from compactification of fivebranes. Such formulation gives a new
interpretation of some known statements about Seiberg-Witten invariants, such
as the basic class condition, and gives a prediction for structural properties
of the multi-monopole invariants and their non-abelian generalizations. | hep-th |
Classical Gravity Coupled to Liouville Theory: We consider the two dimensional Jackiw-Teitelboim model of gravity. We first
couple the model to the Liouville action and $c$ scalar fields and show,
treating the combined system as a non linear sigma model, that the resulting
theory can be interpreted as a critical string moving in a target space of
dimension $D=c+2$. We then analyse perturbatively a generalised model
containing a kinetic term and an arbitrary potential for the auxiliary field.
We use the background field method and work with covariant gauges. We show that
the renormalisability of the theory depends on the form of the potential. For a
general potential, the theory can be renormalised as a non linear sigma model.
In the particular case of a Liouville-like potential, the theory is
renormalisable in the usual sense. | hep-th |
Semiclassical Bethe Ansatz and AdS/CFT: The Bethe ansatz can be used to compute anomalous dimensions in N=4 SYM
theory. The classical solutions of the sigma-model on AdS(5)xS(5) can also be
parameterized by an integral equation of Bethe type. In this note the
relationship between the two Bethe ansaetze is reviewed following
hep-th/0402207. | hep-th |
Rotating Rotated Branes: We present a class of spacetime rotations that preserve a proportion of
spacetime supersymmetry. We then give the rules for superposing these rotations
with various branes to construct rotating brane solutions which preserve exotic
fractions of supersymmetry. We also investigate the superposition of rotations
with intersecting branes at angles and we find new rotating intersecting branes
at angles configurations. We demonstrate this with two examples of such
solutions one involving intersecting NS-5-branes on a string at $Sp(2)$ angles
superposed with fundamental strings and pp-waves, and the other involving
intersecting M-5-branes on a string at $Sp(2)$ angles superposed with membranes
and pp-waves. We find that the geometry of some of these solutions near the
intersection region of every pair of 5-branes is $AdS_3\times S^3\times
S^3\times \bE$ and $AdS_3\times S^3\times S^3\times\bE^2$, respectively. We
also present a class of solutions that can be used for null string and M-theory
compactifications preserving supersymmetry. | hep-th |
$SO/Sp$ Chern-Simons Gauge Theories At Large $N$, $SO/Sp$ Penner Models
And The Gauge Group Volumes: We construct a deformed $SO/Sp$ Penner generating function responsible for
the close connection between $SO/Sp$ Chern-Simons gauge theories at large $N$
and the $SO/Sp$ Penner models. This construction is then shown to follow from a
sector of a Chern-Simons gauge theory with coupling constant $\lambda$. The
free energy and its continuum limit of the perturbative Chern-Simons gauge
theory are obtained from the Penner model. Finally, asymptotic expansions for
the logarithm of the gauge group volumes are given for every genus $g\geq 0$
and shown to be equivalent to the continuum limits of the $SO/Sp$ Chern-Simons
gauge theories and the $SO/Sp$ Penner models | hep-th |
Cancellation of soft and collinear divergences in noncommutative QED: In this paper, we investigate the behavior of non-commutative IR divergences
and will also discuss their cancellation in the physical cross sections. The
commutative IR (soft) divergences existing in the non-planar diagrams will be
examined in order to prove an all order cancellation of these divergences using
the Weinberg's method. In non-commutative QED, collinear divergences due to
triple photon splitting vertex, were encountered, which are shown to be
canceled out by the non-commutative version of KLN theorem. This guarantees
that there is no mixing between the Collinear, soft and non-commutative IR
divergences. | hep-th |
Fast scrambling in holographic Einstein-Podolsky-Rosen pair: We demonstrate that a holographic model of the Einstein-Podolsky-Rosen pair
exhibits fast scrambling. Strongly entangled quark and antiquark in
$\mathcal{N}=4$ super Yang-Mills theory are considered. Their gravity dual is a
fundamental string whose endpoints are uniformly accelerated in opposite
direction. We slightly increase the acceleration of the endpoint and show that
it quickly destroys the correlation between the quark and antiquark. The proper
time scale of the destruction is $\tau_\ast\sim \beta \ln S$ where $\beta$ is
the inverse Unruh temperature and $S$ is the entropy of the accelerating quark.
We also evaluate the Lyapunov exponent from correlation function as
$\lambda_L=2\pi/\beta$, which saturates the Lyapunov bound. Our results suggest
that the fast scrambling or saturation of the Lyapunov bound do not directly
imply the existence of an Einstein dual. When we slightly decrease the
acceleration, the quark and antiquark are causally connected and an "one-way
traversable wormhole" is created on the worldsheet. It causes the divergence of
the correlation function between the quark and antiquark. | hep-th |
Dual Path Integral: a non-perturbative approach to strong coupling: We develop a non-perturbative method for calculating partition functions of
strongly coupled quantum mechanical systems with interactions between
subsystems described by a path integral of a dual system. The dual path
integral is derived starting from non-interacting subsystems at zeroth order
and then by introducing couplings of increasing complexity at each order of an
iterative procedure. These orders of interactions play the role of a dual time
and the full quantum partition function is expressed as a transition amplitude
in the dual system. More precisely, it is expressed as a path integral from a
deformation-operators dependent initial state at zero time/order to the
inverse-temperature dependent final state at later time/order. We provide three
examples of strongly coupled systems with first-order, second-order and
higher-order interactions and discuss a possible emergence of space-time,
quantum field theories and general relativity in context of the dual path
integral. | hep-th |
S-matrix on effective string and compactified membrane: Expanding Nambu-Goto action near infinitely long string vacuum one can
compute scattering amplitudes of 2d massless fields representing transverse
string coordinates. As was shown in arXiv:1203.1054, the resulting S-matrix is
integrable, in agreement with the known free string spectrum and also with an
interpretation of the static-gauge NG action as a $T\bar T$ deformation of a
free massless theory. We consider a generalization of this computation to the
case of a membrane, expanding its 3d action near an infinite membrane vacuum
that has cylindrical $\mathbb R \times S^1$ shape (we refer to such membrane as
"compactified"). Representing 3d fields as Fourier series in $S^1$ coordinate
we get an effective 2d model in which the massless string modes are coupled to
an infinite KK tower of massive 2d modes. We find that the resulting 2d
S-matrix is not integrable already at the tree level. We also compute 1-loop
scattering amplitude of massless string modes with all compactified membrane
modes propagating in the loop. The result is UV finite and is a non-trivial
function of the kinematic variables. In the large momentum limit or when the
radius of $S^1$ is taken to infinity we recover the expression for the 1-loop
scattering amplitude of the uncompactified $\mathbb R^2$ membrane. We also
consider a 2d model which is the $T\bar T$ deformation to the free theory with
the same massless plus infinite massive tower of modes. The corresponding 2d
S-matrix is found, as expected, to be integrable. | hep-th |
The Conformal Limit of the 0A Matrix Model and String Theory on AdS(2): We analyze the conformal limit of the matrix model describing flux
backgrounds of two dimensional type 0A string theory. This limit is believed to
be dual to an AdS(2) background of type 0A string theory. We show that the
spectrum of this limit is identical to that of a free fermion on AdS(2),
suggesting that there are no closed string excitations in this background. | hep-th |
Quantum Mechanics on S^n and Meron Solution: A particle in quantum mechanics on manifolds couples to the induced
topological gauge field that characterises the possible inequivalent
quantizations. For instance, the gauge potential induced on $S^2$ is that of a
magnetic monopole located at the center of $S^2$. We find that the gauge
potential induced on $S^3$ ($S^{2n+1}$) is that of a meron (generalized meron)
also sitting at the center of $S^3$ ($S^{2n+1}$). | hep-th |
Finite-size effects of Membranes on AdS_4 x S_7: We consider semi-classical solution of membranes on the AdS_4 x S^7. This is
supposed to be dual to the N=6 super Chern-Simons theory with k=1 in a planar
limit recently proposed by Aharony, Bergmann, Jafferis, and Maldacena (ABJM).
We have identified giant magnon and single spike states on the membrane by
reducing them to the Neumamm - Rosochatius integrable system. We also connect
these to the complex sine-Gordon integrable model. Based on this approach, we
find finite-size membrane solutions and obtain their images in the complex
sine-Gordon system along with the leading finite-size corrections to the
energy-charge relations. | hep-th |
Hamiltonian structure of three-dimensional gravity in Vielbein formalism: Considering Chern-Simons like gravity theories in three dimensions as first
order systems, we analyze the Hamiltonian structure of three theories
Topological massive gravity, New massive gravity, and Zwei-Dreibein Gravity.We
show that these systems demonstrate a new feature of the constrained systems in
which a new kind of constraints emerge due to factorization of determinant of
the matrix of Poisson brackets of constraints. We find the desired number of
degrees of freedom as well as the generating functional of local Lorentz
transformations and diffeomorphism through canonical structure of the system.
We also compare the Hamiltonian structure of linearized version of the
considered models with the original ones. | hep-th |
Reflections on Virasoro circuit complexity and Berry phase: Recently, the notion of circuit complexity defined in symmetry group
manifolds has been related to geometric actions which generally arise in the
coadjoint orbit method in representation theory and play an important role in
geometric quantization. On the other hand, it is known that there exists a
precise relation between geometric actions and Berry phases defined in group
representations. Motivated by these connections, we elaborate on a relation
between circuit complexity and the group theoretic Berry phase. As the simplest
setup relevant for holography, we discuss the case of two dimensional conformal
field theories. In the large central charge limit, we identify the
computational cost function with the Berry connection in the unitary
representation of the Virasoro group. We then use the latter identification to
express the Berry phase in terms of the Virasoro circuit complexity. The former
can be seen as the holonomy of the Berry connection along the path in the group
manifold which defines the protocol. In addition, we derive a proportionality
relation between Virasoro circuit complexity and the logarithm of the inner
product between a particularly chosen reference state and the prepared target
state. In this sense, the logarithmic formula turns out to be approximating the
complexity up to some additive constant if the building blocks of the circuit
are taken to be the underlying symmetry gates. Predictions based on this
formula have recently been shown to coincide with the holographic complexity
proposals and the path integral optimization procedure. The found connections
may therefore help to better understand such coincidences. We also discuss that
our findings, put together with earlier observations, may suggest a connection
between the Virasoro Berry phase and the complexity measure in the path
integral optimization proposal. | hep-th |
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