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Euclidean 4d exact solitons in a Skyrme type model: We introduce a Skyrme type, four dimensional Euclidean field theory made of a
triplet of scalar fields n, taking values on the sphere S^2, and an additional
real scalar field phi, which is dynamical only on a three dimensional surface
embedded in R^4. Using a special ansatz we reduce the 4d non-linear equations
of motion into linear ordinary differential equations, which lead to the
construction of an infinite number of exact soliton solutions with vanishing
Euclidean action. The theory possesses a mass scale which fixes the size of the
solitons in way which differs from Derrick's scaling arguments. The model may
be relevant to the study of the low energy limit of pure SU(2) Yang-Mills
theory.
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On nonequilibrium states in QFT model with boundary interaction: We prove that certain nonequilibrium expectation values in the boundary
sine-Gordon model coincide with associated equilibrium-state expectation values
in the systems which differ from the boundary sine-Gordon in that certain extra
boundary degrees of freedom (q-oscillators) are added. Applications of this
result to actual calculation of nonequilibrium characteristics of the boundary
sine-Gordon model are also discussed.
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Conformal Models of Magnetohydrodynamic Turbulence: Following the previous work of Ferretti and Yang on the role of magnetic
fields in the theory of conformal turbulence, we show that non-unitary minimal
model solutions to 2-dimensional magnetohydrodynamics (MHD) obtained by
dimensional reduction from 3-dimensions exist under different (and more
restrictive) conditions. From a 3-dimensional point of view, these conditions
are equivalent to perpendicular flow, in which the magnetic and velocity fields
are orthogonal. We also extend the analysis to the finite conductivity case and
present some approximate solutions, whose connection to the exact ones of the
infinite conductivity case is also discussed.
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AdS2 D-branes in AdS3 spacetime: I review some recent progress in understanding the properties of AdS2 branes
in AdS3. Different methods - classical string motion, Born-Infeld dynamics,
boundary states - are evocated and compared.
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Algebraic Quantization on the Torus and Modular Invariance: New features of systems with non-trivial topology such as fractional quantum
numbers, inequivalent quantizations, good operators, topological anomalies,
etc. are described in the framework of an algebraic quantization procedure on a
group. Modular invariance naturally appears as a subgroup of good operators in
the particular case of the torus.
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Ghost-Matter Mixing and Feigenbaum Universality in String Theory: Brane-like vertex operators, defining backgrounds with the ghost-matter
mixing in NSR superstring theory, play an important role in a world-sheet
formulation of D-branes and M theory, being creation operators for extended
objects in the second quantized formalism. In this paper we show that dilaton's
beta function in ghost-matter mixing backgrounds becomes stochastic. The
renormalization group (RG) equations in ghost-matter mixing backgrounds lead to
non-Markovian Fokker-Planck equations which solutions describe superstrings in
curved space-times with brane-like metrics.We show that Feigenbaum universality
constant $\delta=4,669...$ describing transitions from order to chaos in a huge
variety of dynamical systems, appears analytically in these RG equations. We
find that the appearance of this constant is related to the scaling of relative
space-time curvatures at fixed points of the RG flow. In this picture the fixed
points correspond to the period doubling of Feigenbaum iterational schemes.
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Instantons and Matter in N=1/2 Supersymmetric Gauge Theory: We extend the instanton calculus for N=1/2 U(2) supersymmetric gauge theory
by including one massless flavor. We write the equations of motion at leading
order in the coupling constant and we solve them exactly in the
non(anti)commutativity parameter C. The profile of the matter superfield is
deformed through linear and quadratic corrections in C. Higher order
corrections are absent because of the fermionic nature of the back-reaction.
The instanton effective action, in addition to the usual 't Hooft term,
includes a contribution of order C^2 and is N=1/2 invariant. We argue that the
N=1 result for the gluino condensate is not modified by the presence of the new
term in the effective action.
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Release of physical modes from unphysical fields: We present a basic idea and a toy model that physical modes originate from
unobservable fields. The model is defined on a higher-dimensional space-time
and has fermionic symmetries that make fields unphysical, and observable modes
can appear through a dimensional reduction.
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Time evolution of the chiral phase transition during a spherical
expansion: We examine the non-equilibrium time evolution of the hadronic plasma produced
in a relativistic heavy ion collision, assuming a spherical expansion into the
vacuum. We study the $O(4)$ linear sigma model to leading order in a large-$N$
expansion. Starting at a temperature above the phase transition, the system
expands and cools, finally settling into the broken symmetry vacuum state. We
consider the proper time evolution of the effective pion mass, the order
parameter $\langle \sigma \rangle$, and the particle number distribution. We
examine several different initial conditions and look for instabilities
(exponentially growing long wavelength modes) which can lead to the formation
of disoriented chiral condensates (DCCs). We find that instabilities exist for
proper times which are less than 3 fm/c. We also show that an experimental
signature of domain growth is an increase in the low momentum spectrum of
outgoing pions when compared to an expansion in thermal equilibrium. In
comparison to particle production during a longitudinal expansion, we find that
in a spherical expansion the system reaches the ``out'' regime much faster and
more particles get produced. However the size of the unstable region, which is
related to the domain size of DCCs, is not enhanced.
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Holographic measurement and quantum teleportation in the SYK thermofield
double: According to holography, entanglement is the building block of spacetime;
therefore, drastic changes of entanglement will lead to interesting transitions
in the dual spacetime. In this paper, we study the effect of projective
measurements on the Sachdev-Ye-Kitaev (SYK) model's thermofield double state,
dual to an eternal black hole in Jackiw-Teitelboim (JT) gravity. We calculate
the (Renyi-2) mutual information between the two copies of the SYK model upon
projective measurement of a subset of fermions in one copy. We propose a dual
JT gravity model that can account for the change of entanglement due to
measurement, and observe an entanglement wedge phase transition in the von
Neumann entropy. The entanglement wedge for the unmeasured side changes from
the region outside the horizon to include the entire time reversal invariant
slice of the two-sided geometry as the number of measured Majorana fermions
increases. Therefore, after the transition, the bulk information stored in the
measured subsystem is not entirely lost upon projection in one copy of the SYK
model, but rather teleported to the other copy. We further propose a decoding
protocol to elucidate the teleportation interpretation, and connect our
analysis to the physics of traversable wormholes.
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Generalisation of the Yang-Mills Theory: We suggest an extension of the gauge principle which includes tensor gauge
fields. In this extension of the Yang-Mills theory the vector gauge boson
becomes a member of a bigger family of gauge bosons of arbitrary large integer
spins. The proposed extension is essentially based on the extension of the
Poincar\'e algebra and the existence of an appropriate transversal
representations. The invariant Lagrangian is expressed in terms of new
higher-rank field strength tensors. It does not contain higher derivatives of
tensor gauge fields and all interactions take place through three- and
four-particle exchanges with a dimensionless coupling constant. We calculated
the scattering amplitudes of non-Abelian tensor gauge bosons at tree level, as
well as their one-loop contribution into the Callan-Symanzik beta function.
This contribution is negative and corresponds to the asymptotically free
theory. Considering the contribution of tensorgluons of all spins into the beta
function we found that it is leading to the theory which is conformally
invariant at very high energies. The proposed extension may lead to a natural
inclusion of the standard theory of fundamental forces into a larger theory in
which vector gauge bosons, leptons and quarks represent a low-spin subgroup. We
consider a possibility that inside the proton and, more generally, inside
hadrons there are additional partons - tensorgluons, which can carry a part of
the proton momentum. The extension of QCD influences the unification scale at
which the coupling constants of the Standard Model merge, shifting its value to
lower energies.
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Gauge Transformations in String Field Theory and canonical
Transformation in String Theory: We study how canonical transfomations in first quantized string theory can be
understood as gauge transformations in string field theory. We establish this
fact by working out some examples. As a by product, we could identify some of
the fields appearing in string field theory with their counterparts in the
$\sigma$-model.
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E(11)-extended spacetime and gauged supergravities: We formulate all the five dimensional gauged maximal supergravity theories as
non-linear realisations of the semi-direct product of E_{11} and a set of
generators which transform according to the first fundamental representation l
of E_{11}. The latter introduces a generalised space-time which plays a crucial
role for these theories. We derive the E_{11} and l transformations of all the
form fields and their dynamics. We also formulate the five dimensional gauged
supergravity theories using the closure of the supersymmetry algebra. We show
that this closes on the bosonic field content predicted by E_{11} and we derive
the field transformations and the dynamics of this theory. The results are in
precise agreement with those found from the E_{11} formulation. This provides a
very detailed check of E_{11} and also the first substantial evidence for the
generalised space-time. The results can be generalised to all gauged maximal
supergravities, thus providing a unified framework of all these theories as
part of E_{11}.
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Semigroup Expansion and M-Supergravity in Eleven Dimensions: This thesis deals with the construction of an eleven-dimensional gauge
theory, off-shell invariant, for the M Algebra. The theory is built using a
Transgression Form as a Lagrangian.
In order to accomplish this, one must first analyze the general construction
of Transgression Gauge Field Theories, for an arbitrary symmetry group (Chapter
3). Some interesting results regarding this point are (1) the calculation of
Noether Charges which are off-shell conserved, (2) the association of the
double connection structure of the Transgression Form with both orientations of
the basis manifold and (3) the Subspace Separation Method, which allows us to
divide the action in bulk and boundary terms, and to split them in terms which
reflect the physics corresponding to a symmetry group choice.
To construct the gauge theory explicitly, it is necessary to buid a new
mathematical tool, called S-Expansion procedure. Analyzing the M Algebra under
the light of this method, it is possible to construct an invariant tensor for
it. This method is developed in a general way and, given a Lie algebra and an
Abelian, finite semigroup, it allows us to generate new Lie algebras
(S-Expanded Algebras, Resonant Subalgebras, Resonant Forced Algebras).
Applying this tool, an invariant tensor for the M Algebra is constructed,
which serves as the basis upon which a Transgression Gauge Field Theory for the
M Algebra (Chapter 5) is constructed. The relationship between the
four-dimensional dynamics from this theory and the eleven-dimensional torsion
is also considered. Finally, we close with an analysis of the possible
applications of the developed tools, in the context of Cosmology, Supergravity
and String Theory.
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Star product and the general Leigh-Strassler deformation: We extend the definition of the star product introduced by Lunin and
Maldacena to study marginal deformations of N=4 SYM. The essential difference
from the latter is that instead of considering U(1)xU(1) non-R-symmetry, with
charges in a corresponding diagonal matrix, we consider two Z_3-symmetries
followed by an SU(3) transformation, with resulting off-diagonal elements. From
this procedure we obtain a more general Leigh-Strassler deformation, including
cubic terms with the same index, for specific values of the coupling constants.
We argue that the conformal property of N=4 SYM is preserved, in both beta-
(one-parameter) and gamma_{i}-deformed (three-parameters) theories, since the
deformation for each amplitude can be extracted in a prefactor. We also
conclude that the obtained amplitudes should follow the iterative structure of
MHV amplitudes found by Bern, Dixon and Smirnov.
|
Argyres-Douglas Theories in Class S Without Irregularity: We make a preliminary investigation into twisted $A_{2n}$ theories of class
S. Contrary to a common piece of folklore, we establish that theories of this
type realise a variety of models of Argyres-Douglas type while utilising only
regular punctures. We present an in-depth analysis of all twisted $A_2$ trinion
theories, analyse their interrelations via partial Higgsing, and discuss some
of their generalised S-dualities.
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Unitarity, Lorentz invariance and causality in Lee-Wick theories: An
asymptotically safe completion of QED: We revisit the previously unsolved problems of ensuring Lorentz invariance
and non-perturbative unitarity in Lee-Wick theories. We base our discussion on
an ultraviolet completion of QED by Lee-Wick ghost fields, which is argued to
be asymptotically safe. We argue that as long as the state space is based upon
a suitable choice of distributions of a type invented by Gel'fand and Shilov,
the Lee-Wick ghosts can be eliminated while preserving Lorentz invariance to
produce a unitary theory. The method for eliminating ghosts is in principle
non-perturbatively well-defined, in contrast with some previous proposals. We
also point out a second, independent mechanism for producing a unitary theory,
based on a covariant constraint on the maximum four-momentum, which would imply
an amusing connection, based on naturalness, between the coupling constant and
the hierarchy of scales in the theory. We further emphasize that the resulting
theory is causal, and point out some analogies between between the behaviour of
Lee-Wick ghost degrees of freedom and black holes.
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Quantum Moduli Space of the Cascading Sp(p+M) x Sp(p) Gauge Theory: We extend the detailed analysis of the quantum moduli space of the cascading
SU(p+M) x SU(p) gauge theory in the recent paper of Dymarsky, Klebanov, and
Seiberg for the Sp(p+M) x Sp(p) cascading gauge theory, which lives on the
world volume of p D3-branes and M fractional D3-branes at the tip of the
orientifolded conifold. As in their paper, we also find in this case that the
ratio of the deformation parameters of the quantum constraint on the different
branches in the gauge theory can be reproduced by the ratio of the deformation
parameters of the conifold with different numbers of mobile D3-branes.
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Hamiltonian Formulation of Open WZW Strings: Using a Hamiltonian approach, we construct the classical and quantum theory
of open WZW strings on a strip. (These are the strings which end on WZW
branes.) The development involves non-abelian generalized Dirichlet images in
an essential way. At the classical level, we find a new non-commutative
geometry in which the equal-time coordinate brackets are non-zero at the
world-sheet boundary, and the result is an intrinsically non-abelian effect
which vanishes in the abelian limit. Using the classical theory as a guide to
the quantum theory, we also find the operator algebra and the analogue of the
Knizhnik-Zamolodchikov equations for the the conformal field theory of open WZW
strings.
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Modular Hamiltonian of Excited States in Conformal Field Theory: We present a novel replica trick that computes the relative entropy of two
arbitrary states in conformal field theory. Our replica trick is based on the
analytic continuation of partition functions that break the replica Z_n
symmetry. It provides a method for computing arbitrary matrix elements of the
modular Hamiltonian corresponding to excited states in terms of correlation
functions. We show that the quantum Fisher information in vacuum can be
expressed in terms of two-point functions on the replica geometry. We perform
sample calculations in two-dimensional conformal field theories.
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Matching branches of non-perturbative conformal block at its singularity
divisor: Conformal block is a function of many variables, usually represented as a
formal series, with coefficients which are certain matrix elements in the
chiral (e.g. Virasoro) algebra. Non-perturbative conformal block is a
multi-valued function, defined globally over the space of dimensions, with many
branches and, perhaps, additional free parameters, not seen at the perturbative
level. We discuss additional complications of non-perturbative description,
caused by the fact that all the best studied examples of conformal blocks lie
at the singularity locus in the moduli space (at divisors of the coefficients
or, simply, at zeroes of the Kac determinant). A typical example is the
Ashkin-Teller point, where at least two naive non-perturbative expressions are
provided by elliptic Dotsenko-Fateev integral and by the celebrated
Zamolodchikov formula in terms of theta-constants, and they are different. The
situation is somewhat similar at the Ising and other minimal model points.
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Real-time gravitational replicas: Low dimensional examples: We continue the study of real-time replica wormholes initiated in
arXiv:2012.00828. Previously, we had discussed the general principles and had
outlined a variational principle for obtaining stationary points of the
real-time gravitational path integral. In the current work we present several
explicit examples in low-dimensional gravitational theories where the dynamics
is amenable to analytic computation. We demonstrate the computation of R\'enyi
entropies in the cases of JT gravity and for holographic two-dimensional CFTs
(using the dual gravitational dynamics). In particular, we explain how to
obtain the large central charge result for subregions comprising of disjoint
intervals directly from the real-time path integral.
|
4-Spinors and 5D Spacetime: We revisit the subject exploring maps from the space of 4-spinors to 3+1
space-time that commute with the Lorentz transformation. All known mappings
have a natural embedding in a higher five dimensional spacetime, and can be
succinctly expressed as products of quaternions, or split-quaternions,
depending on the signature of the embedding 5D spacetime. It is in this sense
that we may view the geometry of 4-spinors as being related to the `square
root' of five dimensional spacetime. In particular, a point in 5D spacetime may
be identified with a corresponding 4-spinor that is uniquely determined up to a
quaternionic - or split-quaternionic - phase.
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N-Complexes and Higher Spin Gauge Fields: $N$-complexes have been argued recently to be algebraic structures relevant
to the description of higher spin gauge fields. $N$-complexes involve a linear
operator $d$ that fulfills $d^N = 0$ and that defines a generalized cohomology.
Some elementary properties of $N$-complexes and the evidence for their
relevance to the description of higher spin gauge fields are briefly reviewed.
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A Test Of The Chiral E8 Current Algebra On A 6D Non-Critical String: Compactifying the $E_8$ non-critical string in 6D down to 5D the 6D strings
give rise to particles and strings in 5D. Using the dual M-theory description
compactified on an elliptically fibered Calabi-Yau we compare some of the 5D
BPS states to what one expects from non-critical strings with an $E_8$ chiral
current algebra. The $E_8$ multiplets of particle states comprise of 2-branes
wrapping on irreducible curves together with bound states of several 2-branes.
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BCFW-type recurrent relations for tree amplitudes of D=11 supergravity: We propose the on-shell superfield description for tree amplitudes of D=11
supergravity and the BCFW (Britto-Cachazo-Feng-Witten)-type recurrent relations
for these superamplitudes.
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General Procedure of Gauge Fixings and Ghosts: We revisit the general procedure of gauge fixings and ghosts based on BRST
invariance principle. It is shown that when this is applied to the
higher-derivative gauge fixings, it gives the correct structure of gauge
fixings and ghosts including "third ghost", previously derived at one-loop
level. This procedure is solely based on the symmetry principle and is valid at
full order.
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On the equivalence of two definitions of conformal primary fields in d >
2 dimensions: Conformal primary fields are of central importance in a conformal field
theory with d > 2 spacetime dimensions. They can be defined in two ways. A
first definition involves commutators between the field and the generators of
the conformal group; a second definition characterizes a primary field
according to its behavior under a finite conformal transformation. In the
existing literature, the proof of the equivalence of the definitions is either
omitted or carried out with little details. In this paper we present a clear
and concise review of the two definitions and provide a simple and detailed
proof for their equivalence, using some minimal results from quantum field
theory and basic properties of conformal transformations. The paper is intended
as a tutorial for an introductory lecture course in conformal field theory.
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*-Structures on Braided Spaces: $*$-structures on quantum and braided spaces of the type defined via an
R-matrix are studied. These include $q$-Minkowski and $q$-Euclidean spaces as
additive braided groups. The duality between the $*$-braided groups of vectors
and covectors is proved and some first applications to braided geometry are
made.
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Phase structures of the black D$p$-D$(p+4)$-brane system in various
ensembles I: thermal stability: When the D$(p+4)$-brane ($p=0,1,2$) with delocalized D$p$ charges is put into
equilibrium with a spherical thermal cavity, the two kinds of charges can be
put into canonical or grand canonical ensemble independently by setting
different conditions at the boundary. Using the thermal stability condition, we
discuss the phase structures of various ensembles of this system formed in this
way and find out the situations that the black brane could be the final stable
phase in these ensembles. In particular, van der Waals-like phase transitions
can happen when D0 and D4 charges are in different kinds of ensembles.
Furthermore, our results indicate that the D$(p+4)$-branes and the delocalized
D$p$-branes are equipotent.
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QUANTUM DISSIPATION AND QUANTUM GROUPS: We discuss the r\^ole of quantum deformation of Weyl-Heisenberg algebra in
dissipative systems and finite temperature systems. We express the time
evolution generator of the damped harmonic oscillator and the generator of
thermal Bogolubov transformations in terms of operators of the quantum
Weyl-Heisenberg algebra. The quantum parameter acts as a label for the
unitarily inequivalent representations of the canonical commutation relations
in which the space of the states splits in the infinite volume limit.
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The complex sinh-Gordon model: form factors of descendant operators and
current-current perturbations: We study quasilocal operators in the quantum complex sinh-Gordon theory in
the form factor approach. The free field procedure for descendant operators is
developed by introducing the algebra of screening currents and related
algebraic objects. We work out null vector equations in the space of operators.
Further we apply the proposed algebraic structures to constructing form factors
of the conserved currents $T_k$ and $\Theta_k$. We propose also form factors of
current-current operators of the form $T_kT_{-l}$. Explicit computations of the
four-particle form factors allow us to verify the recent conjecture of Smirnov
and Zamolodchikov about the structure of the exact scattering matrix of an
integrable theory perturbed by a combination of irrelevant operators. Our
calculations confirm that such perturbations of the complex sinh-Gordon model
and of the $\mathbb Z_N$ symmetric Ising models result in extra CDD factors in
the $S$ matrix.
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Variations on vacuum decay: the scaling Ising and tricritical Ising
field theories: We study the decay of the false vacuum in the scaling Ising and tricritical
Ising field theories using the Truncated Conformal Space Approach and compare
the numerical results to theoretical predictions in the thin wall limit. In the
Ising case, the results are consistent with previous studies on the quantum
spin chain and the $\varphi^4$ quantum field theory; in particular we confirm
that while the theoretical predictions get the dependence of the bubble
nucleation rate on the latent heat right, they are off by a model dependent
overall coefficient. The tricritical Ising model allows us on the other hand to
examine more exotic vacuum degeneracy structures, such as three vacua or two
asymmetric vacua, which leads us to study several novel scenarios of false
vacuum decay by lifting the vacuum degeneracy using different perturbations.
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Implications of ANEC for SCFTs in four dimensions: We explore consequences of the Averaged Null Energy Condition (ANEC) for
scaling dimensions $\Delta$ of operators in four-dimensional $\mathcal{N}=1$
superconformal field theories. We show that in many cases the ANEC bounds are
stronger than the corresponding unitarity bounds on $\Delta$. We analyze in
detail chiral operators in the $(\frac12 j,0)$ Lorentz representation and prove
that the ANEC implies the lower bound $\Delta\ge\frac32j$, which is stronger
than the corresponding unitarity bound for $j>1$. We also derive ANEC bounds on
$(\frac12 j,0)$ operators obeying other possible shortening conditions, as well
as general $(\frac12 j,0)$ operators not obeying any shortening condition. In
both cases we find that they are typically stronger than the corresponding
unitarity bounds. Finally, we elucidate operator-dimension constraints that
follow from our $\mathcal{N}=1$ results for multiplets of $\mathcal{N}=2,4$
superconformal theories in four dimensions. By recasting the ANEC as a convex
optimization problem and using standard semidefinite programming methods we are
able to improve on previous analyses in the literature pertaining to the
nonsupersymmetric case.
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Poisson-Lie T-Duality in Double Field Theory: We present a formulation of Double Field Theory with a Drinfeld double as
extended spacetime. It makes Poisson-Lie T-duality (including abelian and
non-abelian T-duality as special cases) manifest. This extends the scope of
possible applications of the theory, which so far captured abelian T-duality
only, considerably. The full massless bosonic subsector (NS/NS and R/R) of type
II string theories is covered.
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Sum Rule for the ADM Mass and Tensions in Planar AdS Spacetimes: An asymptotically planar AdS spacetimes is characterized by its ADM mass and
tensions. We define an additional ADM charge Q associated with the scaling
Killing vector of AdS, show that Q is given by a certain sum over the ADM mass
and tensions and that Q vanishes on solutions to the Einstein equation with
negative cosmological constant. The sum rule for the mass and tensions thus
established corresponds in an AdS/CFT context to the vanishing of the trace of
the boundary stress tensor. We also show that an analogous sum rule holds for
local planar sources of stress-energy sources in AdS. In a simple model
consisting of a static, plane symmetric source we find that the perturbative
stress-energy tensor must be tracefree.
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Positroid Stratification of Orthogonal Grassmannian and ABJM Amplitudes: A novel understanding of scattering amplitudes in terms of on-shell diagrams
and positive Grassmannian has been recently established for four dimensional
Yang-Mills theories and three dimensional Chern-Simons theories of ABJM type.
We give a detailed construction of the positroid stratification of orthogonal
Grassmannian relevant for ABJM amplitudes. On-shell diagrams are classified by
pairing of external particles. We introduce a combinatorial aid called `OG
tableaux' and map each equivalence class of on-shell diagrams to a unique
tableau. The on-shell diagrams related to each other through BCFW bridging are
naturally grouped by the OG tableaux. Introducing suitably ordered BCFW bridges
and positive coordinates, we construct the complete coordinate charts to cover
the entire positive orthogonal Grassmannian for arbitrary number of external
particles. The graded counting of OG tableaux suggests that the positive
orthogonal Grassmannian constitutes a combinatorial polytope.
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Secondary graviton spectra, second-order correlations and Bose-Einstein
enhancement: Primary graviton spectra, produced via stimulated emission from an initial
Bose-Einstein distribution, are enhanced for typical scales larger than the
redshifted thermal wavelength. A mixed state of phonons induces a secondary
graviton spectrum which is hereunder computed in terms of three parameters
(i.e. the number of phonon species, the tensor-to-scalar ratio and the thermal
wavelengths of the mixture). The primary and secondary graviton spectra are
shown to be sensitive, respectively, to the first-order and second-order
correlation properties of the initial quantum mixture so that the semiclassical
theory is argued to be generally inadequate in this context. For particular
values of the parameters the secondary contribution may turn out to be
comparable with the primary spectrum over large-scales.
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On the definition of Quantum Free Particle on Curved Manifolds: A selfconsistent definition of quantum free particle on a generic curved
manifold emerges naturally by restricting the dynamics to submanifolds of
co-dimension one.
PACS 0365 0240
|
Beta deformed sigma model and strong deformation coupling limit: We study the beta deformation of the superstring in $AdS_5\times S^5$ at all
orders in the deformation parameter, using the pure spinor formalism. This is
necessary to study the regime of strong deformation parameter, which in the
field side is related to fishnet theories. We compare the pure spinor sigma
model approach to the previously known supergravity description. We find a
complete agreement. Moreover, the BRST structure of the worldsheet model
provides a natural explanation of the peculiar features of the worldsheet model
in the fishnet limit. In particular, we study the degeneracy of the sigma model
Lagrangian. We show that the BRST structure is responsible for a particularly
"tame" degeneration of the fishnet sigma-model.
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Gravitation \& Cosmology in $(1+1)$-dimensional Dilaton Gravity: The properties of a string-inspired two-dimensional theory of gravity are
studied. The post-Newtonian and weak-field approximations, `stellar' structure
and cosmological solutions of this theory are developed. Some qualitative
similarities to general relativity are found, but there are important
differences.
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N-photon amplitudes in a plane-wave background: We use the worldline formalism to derive master formulas for the one-loop
N-photon amplitudes in a plane-wave background, for both scalar and spinor QED.
This generalises previous work by Ilderton and Torgrimsson for the vacuum
polarisation case, although with some change in methodology since, instead of
evaluating the path integral on the semi-classical trajectory, we use the
special kinematics of the plane-wave background to uncover the crypto-gaussian
character of this type of worldline path integral.
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On the resurgent structure of quantum periods: Quantum periods appear in many contexts, from quantum mechanics to local
mirror symmetry. They can be described in terms of topological string free
energies and Wilson loops, in the so-called Nekrasov-Shatashvili limit. We
consider the trans-series extension of the holomorphic anomaly equations
satisfied by these quantities, and we obtain exact multi-instanton solutions
for these trans-series. Building on this result, we propose a unified
perspective on the resurgent structure of quantum periods. We show for example
that the Delabaere-Pham formula, which was originally obtained in quantum
mechanical examples, is a generic feature of quantum periods. We illustrate our
general results with explicit calculations for the double-well in quantum
mechanics, and for the quantum mirror curve of local $\mathbb{P}^2$.
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Black Hole S-matrix for a scalar field: We describe a unitary scattering process, as observed from spatial infinity,
of massless scalar particles on an asymptotically flat Schwarzschild black hole
background. In order to do so, we split the problem in two different regimes
governing the dynamics of the scattering process. The first describes the
evolution of the modes in the region away from the horizon and can be analysed
in terms of the effective Regge-Wheeler potential. In the near horizon region,
where the Regge-Wheeler potential becomes insignificant, the WKB geometric
optics approximation of Hawking's is replaced by the near-horizon gravitational
scattering matrix that captures non-perturbative soft graviton exchanges near
the horizon. We perform an appropriate matching for the scattering solutions of
these two dynamical problems and compute the resulting Bogoliubov relations,
that combines both dynamics. This allows us to formulate an S-matrix for the
scattering process that is manifestly unitary. We discuss the analogue of the
(quasi)-normal modes in this setup and the emergence of gravitational echoes
that follow an original burst of radiation as the excited black hole relaxes to
equilibrium.
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Multi-particle Correlations in Quaternionic Quantum Systems: We investigate the outcomes of measurements on correlated, few-body quantum
systems described by a quaternionic quantum mechanics that allows for regions
of quaternionic curvature. We find that a multi-particle interferometry
experiment using a correlated system of four nonrelativistic, spin-half
particles has the potential to detect the presence of quaternionic curvature.
Two-body systems, however, are shown to give predictions identical to those of
standard quantum mechanics when relative angles are used in the construction of
the operators corresponding to measurements of particle spin components.
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Brane Decay and Death of Open Strings: We show how open strings cease to propagate when unstable D-branes decay. The
information on the propagation is encoded in BSFT two-point functions for
arbitrary profiles of open string excitations. We evaluate them in tachyon
condensation backgrounds corresponding to (i) static spatial tachyon kink (=
lower dimensional BPS D-brane) and (ii) homogeneous rolling tachyon. For (i)
the propagation is restricted to the directions along the tachyon kink, while
for (ii) all the open string excitations cease to propagate at late time and
are subject to a collapsed light cone characterized by Carrollian contraction
of Lorentz group.
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Dual Bosonic Thermal Green Function and Fermion Correlators of the
Massive Thirring Model at a Finite Temperature: The Euclidian thermal Green function of the two-dimensional (2D) free
massless scalar field in coordinate space is written as the real part of a
complex analytic function of a variable that conformally maps the infinite
strip $-\infty<x<\infty$ ($0<\tau<\beta$) of the $z=x+i\tau$ ($\tau$: imaginary
time) plane into the upper-half-plane. Using this fact and the Cauchy-Riemann
conditions, we identify the dual thermal Green function as the imaginary part
of that function. Using both the thermal Green function and its dual, we obtain
an explicit series expression for the fermionic correlation functions of the
massive Thirring model (MTM) at a finite temperature.
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Monopoles, vortices and kinks in the framework of non-commutative
geometry: Non-commutative differential geometry allows a scalar field to be regarded as
a gauge connection, albeit on a discrete space. We explain how the underlying
gauge principle corresponds to the independence of physics on the choice of
vacuum state, should it be non-unique. A consequence is that Yang-Mills-Higgs
theory can be reformulated as a generalised Yang-Mills gauge theory on
Euclidean space with a $Z_2$ internal structure. By extending the Hodge star
operation to this non-commutative space, we are able to define the notion of
self-duality of the gauge curvature form in arbitrary dimensions. It turns out
that BPS monopoles, critically coupled vortices, and kinks are all self-dual
solutions in their respective dimensions. We then prove, within this unified
formalism, that static soliton solutions to the Yang-Mills-Higgs system exist
only in one, two and three spatial dimensions.
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Finite temperature properties of the Dirac operator with bag boundary
conditions: We study the finite temperature free energy and fermion number for Dirac
fields in a one-dimensional spatial segment, under local boundary conditions
compatible with the presence of a spectral asymmetry. We discuss in detail the
contribution of this part of the spectrum to the determinant. We evaluate the
finite temperature properties of the theory for arbitrary values of the
chemical potential.
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Topologically Massive Abelian Gauge Theory From BFT Hamiltonian
Embedding of A First-order Theory: We start with a new first order gauge non-invariant formulation of massive
spin-one theory and map it to a reducible gauge theory viz; abelian
$B{\wedge}F$ theory by the Hamiltonian embedding procedure of Batalin, Fradkin
and Tyutin(BFT). This equivalence is shown from the equations of motion of the
embedded Hamiltonian. We also demonstrate that the original gauge non-invariant
model and the topologically massive gauge theory can both be obtained by
suitable choice of gauges, from the phase space partition function of the
emebedded Hamiltonian, proving their equivalence. Comparison of the first order
formulation with the other known massive spin-one theories is also discussed.
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Induced cosmological constant in braneworlds with warped internal spaces: We investigate the vacuum energy density induced by quantum fluctuations of a
bulk scalar field with general curvature coupling parameter on two codimension
one parallel branes in a $(D+1)$-dimensional background spacetime
${\mathrm{AdS}}_{D1+1}\times \Sigma $ with a warped internal space $\Sigma $.
It is assumed that on the branes the field obeys Robin boundary conditions.
Using the generalized zeta function technique in combination with contour
integral representations, the surface energies on the branes are presented in
the form of the sums of single brane and second brane induced parts. For the
geometry of a single brane both regions, on the left (L-region) and on the
right (R-region), of the brane are considered. The surface densities for
separate L- and R-regions contain pole and finite contributions. For an
infinitely thin brane taking these regions together, in odd spatial dimensions
the pole parts cancel and the total surface energy is finite. The parts in the
surface densities generated by the presence of the second brane are finite for
all nonzero values of the interbrane separation. The contribution of the
Kaluza-Klein modes along $\Sigma $ is investigated in various limiting cases.
It is shown that for large distances between the branes the induced surface
densities give rise to an exponentially suppressed cosmological constant on the
brane. In the higher dimensional generalization of the Randall-Sundrum
braneworld model, for the interbrane distances solving the hierarchy problem,
the cosmological constant generated on the visible brane is of the right order
of magnitude with the value suggested by the cosmological observations.
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Soliton S matrices for the critical A_{N-1}^(1) chain: We compute by Bethe Ansatz both bulk and boundary hole scattering matrices
for the critical A_{N-1}^(1) quantum spin chain. The bulk S matrix coincides
with the soliton S matrix for the A_{N-1}^(1) Toda field theory with imaginary
coupling. We verify our result for the boundary S matrix using a generalization
of the Ghoshal-Zamolodchikov boundary crossing relation.
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Classifying Supersymmetric Solutions in 3D Maximal Supergravity: String theory contains various extended objects. Among those, objects of
codimension two (such as the D7-brane) are particularly interesting.
Codimension two objects carry non-Abelian charges which are elements of a
discrete U-duality group and they may not admit a simple space-time
description, in which case they are known as exotic branes. A complete
classification of consistent codimension two objects in string theory is
missing, even if we demand that they preserve some supersymmetry. As a step
toward such a classification, we study the supersymmetric solutions of 3D
maximal supergravity, which can be regarded as approximate description of the
geometry near codimension two objects. We present a complete classification of
the types of supersymmetric solutions that exist in this theory. We found that
this problem reduces to that of classifying nilpotent orbits associated with
the U-duality group, for which various mathematical results are known. We show
that the only allowed supersymmetric configurations are 1/2, 1/4, 1/8, and 1/16
BPS, and determine the nilpotent orbits that they correspond to. One example of
1/16 BPS configurations is a generalization of the MSW system, where momentum
runs along the intersection of seven M5-branes. On the other hand, it turns out
exceedingly difficult to translate this classification into a simple criterion
for supersymmetry in terms of the non-Abelian (monodromy) charges of the
objects. For example, it can happen that a supersymmetric solution exists
locally but cannot be extended all the way to the location of the object. To
illustrate the various issues that arise in constructing supersymmetric
solutions, we present a number of explicit examples.
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Noncommutative gauge fields coupled to noncommutative gravity: We present a noncommutative (NC) version of the action for vielbein gravity
coupled to gauge fields. Noncommutativity is encoded in a twisted star product
between forms, with a set of commuting background vector fields defining the
(abelian) twist. A first order action for the gauge fields avoids the use of
the Hodge dual. The NC action is invariant under diffeomorphisms and twisted
gauge transformations. The Seiberg-Witten map, adapted to our geometric setting
and generalized for an arbitrary abelian twist, allows to re-express the NC
action in terms of classical fields: the result is a deformed action, invariant
under diffeomorphisms and usual gauge transformations. This deformed action is
a particular higher derivative extension of the Einstein-Hilbert action coupled
to Yang-Mills fields, and to the background vector fields defining the twist.
Here noncommutativity of the original NC action dictates the precise form of
this extension. We explicitly compute the first order correction in the NC
parameter of the deformed action, and find that it is proportional to cubic
products of the gauge field strength and to the symmetric anomaly tensor
D_{IJK}.
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On higher derivative gravity, c-theorems and cosmology: We consider higher derivative gravity lagrangians in 3 and 4 dimensions,
which admit simple c-theorems, including upto six derivative curvature
invariants. Following a suggestion by Myers, these lagrangians are restricted
such that the fluctuations around (anti) de Sitter spaces have second order
linearized equations of motion. We study c-theorems both in the context of
AdS/CFT and cosmology. In the context of cosmology, the monotonic function is
the entropy defined on the apparent horizon through Wald's formula. Exact black
hole solutions which are asymptotically (anti) de Sitter are presented. An
interesting lower bound for entropy is found in de Sitter space. Some aspects
of cosmology in both D=3 and D=4 are discussed.
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A Comment on Jones Inclusions with infinite Index: Given an irreducible inclusion of infinite von-Neumann-algebras $\cn \subset
\cm$ together with a conditional expectation $ E : \cm \rightarrow \cm $ such
that the inclusion has depth 2, we show quite explicitely how $\cn $ can be
viewed as the fixed point algebra of $\cm$ w.r.t. an outer action of a compact
Kac-algebra acting on $\cm$. This gives an alternative proof, under this
special setting of a more general result of M. Enock and R. Nest, [E-N], see
also S. Yamagami, [Ya2].
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Fermion number non-conservation and gravity: It is shown that in the Einstein-Yang-Mills (EYM) theory, as well as in the
pure flat space Yang-Mills (YM) theory, there always exists an opportunity to
pass over the potential barrier separating homotopically distinct vacuum
sectors, because the barrier height may be arbitrarily small. However, at low
energies all the overbarrier histories are suppressed by the destructive
interference. In the pure YM theory the situation remains the same for any
energies. In the EYM theory on the other hand, when the energy is large and
exceeds the ground state EYM sphaleron mass, the constructive interference
occurs instead. This means that in the extreme high energy limit the
exponential suppression of the fermion number violation in pure YM theory is
removed due to gravitational effects.
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Some Exact Results in QCD-like Theories: I propose a controlled approximation to QCD-like theories with massless
quarks by employing supersymmetric QCD perturbed by anomaly-mediated
supersymmetry breaking. They have identical massless particle contents. Thanks
to the ultraviolet-insensitivity of anomaly mediation, dynamics can be worked
out exactly when $m \ll \Lambda$, where $m$ is the size of supersymmetry
breaking and $\Lambda$ the dynamical scale of the gauge theory. I demonstrate
that chiral symmetry is dynamically broken for $N_{f} \leq \frac{3}{2} N_{c}$
while the theories lead to non-trivial infrared fixed points for larger number
of flavors. While there may be a phase transition as $m$ is increased beyond
$\Lambda$, qualitative agreements with expectations in QCD are encouraging and
suggest that two limits $m \ll \Lambda$ and $m \gg \Lambda$ may be in the same
universality class.
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Covariant action for M5 brane in nonrelativistic M-theory: We construct the nonrelativistic covariant world-volume action for a single
M5 brane of $ D=11 $ supergravity in M-theory. The corresponding non-Lorentzian
(NL) background possesses a codimension three foliation and is identified as
the Membrane Newton-Cartan manifold in the presence of background fluxes that
are suitably expanded in $ 1/c^2 $ expansion. We also expand the associated
world-volume fields in $ 1/c^2 $ expansion. The above procedure eventually
results into a well defined world-volume action that is coupled to Membrane
Newton-Cartan background.
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Modified Supergravity and Early Universe: the Meeting Point of Cosmology
and High-Energy Physics: We review the new theory of modified supergravity, dubbed F(\cal R)
supergravity, and some of its recent applications to inflation and reheating in
the early universe cosmology. The F(\cal R) supergravity is the N=1 locally
supersymmetric extension of the f(R) gravity in four space-time dimensions. A
manifestly supersymmetric formulation of the F(\cal R) supergravity exist in
terms of N=1 superfields, by using the (old) minimal Poincar'e supergravity in
curved superspace. We find the conditions for stability, the absence of ghosts
and tachyons. Three models of the F(\cal R) supergravity are studied. The first
example is devoted to a recovery of the standard (pure) N=1 supergravity with a
negative cosmological constant from the F(\cal R) supergravity. As the second
example, a generic {\cal R}^2-type supergravity is investigated, and the
existence of the AdS bound on the scalar curvature is found. As the third (and
most important) example, a simple viable realization of chaotic inflation in
supergravity is found. Our approach is {\it minimalistic} since it does not
introduce new exotic fields or new interactions, beyond those already present
in (super)gravity. The universal reheating mechanism is automatic. We establish
the consistency of our approach and also apply it to preheating and reheating
after inflation. The Higgs inflation and its correspondence to the Starobinsky
inflation is established in the context of supergravity. We briefly review
other relevant issues such as non-Gaussianity, CP-violation, origin of baryonic
asymmetry, lepto- and baryo-genesis. The F(\cal R) supergravity has promise for
possible solutions to those outstanding problems too.
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The effective potential of the confinement order parameter in the
Hamiltonian approach: The effective potential of the order parameter for confinement is calculated
for SU(N) Yang--Mills theory in the Hamiltonian approach. Compactifying one
spatial dimension and using a background gauge fixing, this potential is
obtained within a variational approach by minimizing the energy density for
given background field. In this formulation the inverse length of the
compactified dimension represents the temperature. Using Gaussian trial wave
functionals we establish an analytic relation between the propagators in the
background gauge at finite temperature and the corresponding zero-temperature
propagators in Coulomb gauge. In the simplest truncation, neglecting the ghost
and using the ultraviolet form of the gluon energy, we recover the Weiss
potential. We explicitly show that the omission of the ghost drastically
increases the transition temperature. From the full non-perturbative potential
(with the ghost included) we extract a critical temperature of the
deconfinement phase transition of 269 MeV for the gauge group SU(2) and 283 MeV
for SU(3).
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Bicovariant differential calculus on quantum groups from Poisson Lie
structures: The aim of this lecture is to give a pedagogical explanation of the notion of
a Poisson Lie structure on the external algebra of a Poisson Lie group which
was introduced in our previous papers. Using this notion as a guide we
construct quantum external algebras on $SL_q(N)$ with proper (classical)
dimension.
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Dissociation by acceleration: We show that mesons, described using rotating relativistic strings in a
holographic setup, undergo dissociation when their acceleration 'a' exceeds a
value which scales with the angular momentum 'J' as a_max ~ \sqrt{T_s/J}, where
'T_s' is the string tension.
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Sequential deconfinement and self-dualities in $4d$ $\mathcal{N}\!=\!1$
gauge theories: We apply the technique of sequential deconfinement to the four dimensional
$\mathcal{N}\!=\!1$ $Usp(2N)$ gauge theory with an antisymmetric field and $2F$
fundamentals. The fully deconfined frame is a length-$N$ quiver. We use this
deconfined frame to prove the known self-duality of $Usp(2N)$ with an
antisymmetric field and $8$ fundamentals. Along the way we encounter a
subtlety: in certain quivers with degenerate holomorphic operators, a naive
application of Seiberg duality rules leads to an incorrect superpotential or
chiral ring.
We also consider the reduction to $3d$ $\mathcal{N}\!=\!2$ theories,
recovering known fully deconfined duals of $Usp(2N)$ and $U(N)$ gauge theories,
and obtaining new ones.
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4d $\mathcal{N} = 1$/2d Yang-Mills Duality in Holography: We study the supergravity dual of four-dimensional ${\mathcal{N}=1}$
superconformal field theories arising from wrapping M5-branes on a K\"ahler
two-cycle inside a Calabi-Yau threefold. We derive an effective
three-dimensional theory living on the cobordism between the infrared and
ultraviolet Riemann surfaces, describing the renormalization group flows
between AdS$_7$ and AdS$_{5}$ as well as between different AdS$_{5}$ fixed
points. The realization of this system as an effective theory is convenient to
make connections to known theories, and we show that upon imposing (physical)
infrared boundary conditions, the effective three-dimensional theory further
reduces to two-dimensional $SU(2)$ Yang-Mills theory on the Riemann surface,
thus deriving a correspondence between the gravity duals of a class of
$\mathcal{N}=1$ superconformal field theories arising from wrapping M5-branes
on a Riemann surface and two-dimensional Yang-Mills theory on the same Riemann
surface.
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Quantum field theory in generalised Snyder spaces: We discuss the generalisation of the Snyder model that includes all possible
deformations of the Heisenberg algebra compatible with Lorentz invariance and
investigate its properties. We calculate peturbatively the law of addition of
momenta and the star product in the general case. We also undertake the
construction of a scalar field theory on these noncommutative spaces showing
that the free theory is equivalent to the commutative one, like in other models
of noncommutative QFT.
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Fermionic determinant with a linear domain wall in 2+1 dimensions: We consider a Dirac field in 2+1 Euclidean dimensions, in the presence of a
linear domain wall defect in its mass, and a constant electromagnetic field. We
evaluate the exact fermionic determinant for the situation where the defect is
assumed to be rectilinear, static, and the gauge field is minimally coupled to
the fermions. We discuss the dependence of the result on the (unique)
independent geometrical parameter of this system, namely, the relative
orientation of the wall and the direction of the external field. We apply the
result for the determinant to the evaluation of the vacuum energy.
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Classical String Solitons: We discuss some recent work in the field of classical solitonic solutions in
string theory. In particular, we construct instanton and monopole solutions and
discuss the dynamics of string-like solitons. Some of the motivation behind
this work is that instantons may provide a nonperturbative understanding of the
vacuum structure of string theory, while monopoles may appear in string
predictions for grand unification. The string-like solitons represent extended
states of fundamental strings. The essential role of supersymmetry in both the
saturation of the Bogomol'nyi bound and in the cancellation of higher order
corrections is emphasized. (Talk given at the International Workshop: ``Recent
Advances in the Superworld'', Houston Advanced Research Center, The Woodlands,
TX, April 14-16, 1993.)
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Finitely Many Dirac-Delta Interactions on Riemannian Manifolds: This work is intended as an attempt to study the non-perturbative
renormalization of bound state problem of finitely many Dirac-delta
interactions on Riemannian manifolds, S^2, H^2 and H^3. We formulate the
problem in terms of a finite dimensional matrix, called the characteristic
matrix. The bound state energies can be found from the characteristic equation.
The characteristic matrix can be found after a regularization and
renormalization by using a sharp cut-off in the eigenvalue spectrum of the
Laplacian, as it is done in the flat space, or using the heat kernel method.
These two approaches are equivalent in the case of compact manifolds. The heat
kernel method has a general advantage to find lower bounds on the spectrum even
for compact manifolds as shown in the case of S^2. The heat kernels for H^2 and
H^3 are known explicitly, thus we can calculate the characteristic matrix.
Using the result, we give lower bound estimates of the discrete spectrum.
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Casimir effect in rugby-ball type flux compactifications: As a continuation of the work in \cite{mns}, we discuss the Casimir effect
for a massless bulk scalar field in a 4D toy model of a 6D warped flux
compactification model,to stabilize the volume modulus. The one-loop effective
potential for the volume modulus has a form similar to the Coleman-Weinberg
potential. The stability of the volume modulus against quantum corrections is
related to an appropriate heat kernel coefficient. However, to make any
physical predictions after volume stabilization, knowledge of the derivative of
the zeta function, $\zeta'(0)$ (in a conformally related spacetime) is also
required. By adding up the exact mass spectrum using zeta function
regularization, we present a revised analysis of the effective potential.
Finally, we discuss some physical implications, especially concerning the
degree of the hierarchy between the fundamental energy scales on the branes.
For a larger degree of warping our new results are very similar to the previous
ones \cite{mns} and imply a larger hierarchy. In the non-warped (rugby-ball)
limit the ratio tends to converge to the same value, independently of the bulk
dilaton coupling.
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Massive spin-2 particles via embedment of the Fierz-Pauli equations of
motion: Here we obtain alternative descriptions of massive spin-2 particles by an
embedding procedure of the Fierz-Pauli equations of motion. All models are free
of ghosts at quadratic level although most of them are of higher order in
derivatives. The models that we obtain can be nonlinearly completed in terms of
a dynamic and a fixed metric. They include some $f(R)$ massive gravities
recently considered in the literature. In some cases there is an infrared (no
derivative) modification of the Fierz-Pauli mass term altogether with higher
order terms in derivatives. The analytic structure of the propagator of the
corresponding free theories is not affected by the extra terms in the action as
compared to the usual second order Fierz-Pauli theory.
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The string-junction picture of multiquark states: an update: We recall and update, both theoretically and phenomenologically, our (nearly)
forty-years-old proposal of a string-junction as a necessary complement to the
conventional classification of hadrons based just on their quark-antiquark
constituents. In that proposal single (though in general metastable) hadronic
states are associated with "irreducible" gauge-invariant operators consisting
of Wilson lines (visualized as strings of color flux tubes) that may either end
on a quark or an antiquark, or annihilate in triplets at a junction $J$ or an
anti-junction $\bar{J}$. For the junction-free sector (ordinary $q\, \bar{q}$
mesons and glueballs) the picture is supported by large-$N$ (number of colors)
considerations as well as by a lattice strong-coupling expansion. Both imply
the famous OZI rule suppressing quark-antiquark annihilation diagrams. For
hadrons with $J$ and/or $\bar{J}$ constituents the same expansions support our
proposal, including its generalization of the OZI rule to the suppression of
$J-\bar{J}$ annihilation diagrams. Such a rule implies that hadrons with
junctions are "mesophobic" and thus unusually narrow if they are below
threshold for decaying into as many baryons as their total number of junctions
(two for a tetraquark, three for a pentaquark). Experimental support for our
claim, based on the observation that narrow multiquark states typically lie
below (well above) the relevant baryonic (mesonic) thresholds, will be
presented.
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Localization of scalar fields on self-gravitating thick branes: The model of a domain wall ("thick" brane) in noncompact five-dimensional
space-time is considered with geometries of $AdS_5$ type generated by
self-interacting scalar matter. The scalar matter is composed of two fields
with O(2) symmetric self interaction. One of them is mixed with gravity scalar
modes and plays role of the brane formation mode (due to a kink background) and
another one is of a Higgs-field type. The interplay between soft breaking of
O(2) symmetry and gravity influence is thoroughly investigated around the
critical point of spontaneous $\tau$ symmetry breaking when the v.e.v. of the
Higgs-type scalar field occurs. The possibility of (quasi)localization of
scalar modes on such thick branes is examined.
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Perturbative study of the QCD phase diagram for heavy quarks at nonzero
chemical potential: We investigate the phase diagram of QCD with heavy quarks at finite
temperature and chemical potential in the context of background field methods.
In particular, we use a massive extension of the Landau-DeWitt gauge which is
motivated by previous studies of the deconfinement phase transition in pure
Yang-Mills theories. We show that a simple one-loop calculation is able to
capture the richness of the phase diagram in the heavy quark region, both at
real and imaginary chemical potential. Moreover, dimensionless ratios of
quantities directly measurable in numerical simulations are in good agreement
with lattice results.
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Gravitational Forces on a Codimension-2 Brane: We compute the gravitational response of six dimensional gauged, chiral
supergravity to localized stress energy on one of two space-filling branes,
including the effects of compactifying the extra dimensions and brane
back-reaction. We find a broad class of exact solutions, including various
black-brane solutions. Several approximate solutions are also described, such
as the near-horizon geometry of a small black hole which is argued to be
approximately described by a 6D Schwarzschild (or Kerr) black hole, with event
horizon appropriately modified to encode the brane back-reaction. The general
linearized far-field solutions are found in the 4D regime very far from the
source, and all integration constants are related to physical quantities
describing the branes and the localized energy source. The localized source
determines two of these, corresponding to the source mass and the size of the
strength of a coupling to a 4D scalar mode whose mass is parametrically smaller
than the KK scale. At large distances the solutions agree with those of 4D
general relativity, but for an intermediate range of distances (larger than the
KK scale) the solutions better fit a Brans-Dicke theory. For a realistic choice
of parameters the KK scale could lie at a micron, while the crossover to
Brans-Dicke behaviour could occur at around 10 microns. While allowed by
present data this points to potentially measurable changes to Newton's Law
arising at distances larger than the KK scale.
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Exact solution of the $A^{(1)}_{n-1}$ trigonometric vertex model with
non-diagonal open boundaries: The $A^{(1)}_{n-1}$ trigonometric vertex model with {\it generic
non-diagonal} boundaries is studied. The double-row transfer matrix of the
model is diagonalized by algebraic Bethe ansatz method in terms of the
intertwiner and the corresponding face-vertex relation. The eigenvalues and the
corresponding Bethe ansatz equations are obtained.
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Black Hole Nilpotent Orbits and Tits Satake Universality Classes: In this paper we consider the problem of classification of nilpotent orbits
for the pseudo-quaternionic coset manifolds U/H* obtained in the time-like
dimensional reduction of N = 2 supergravity models based on homogeneous
symmetric special geometries. Within the D=3 approach this classification
amounts to a classification of regular and singular extremal black hole
solutions of supergravity. We show that the pattern of such orbits is a
universal property depending only on the Tits-Satake universality class of the
considered model, the number of such classes being five. We present a new
algorithm for the classification and construction of the nilpotent orbits for
each universality class which is based on an essential use of the Weyl group W
of the Tits Satake subalgebra U_{TS} of U and on a certain subgroup W_H
thereof. The splitting of orbits of the full group Uinto suborbits with respect
to the stability subgroup H* is shown to be governed by the structure of the
discrete coset W/W_H. For the case of the universality class SO(4,5) /[SO(2,3)
x SO(2,2)] we derive the complete list of nilpotent orbits which happens to
contain 37 elements. We also show how the universal orbits are regularly
embedded in all the members of the class that are infinite in number. As a
matter of check we apply our new algorithm also to the Tits Satake class
G_(2,2)/[SL(2)x SL(2)] confirming the previously obtained result encompassing 7
nilpotent orbits. Perspectives for future developments based on the obtained
results are outlined.
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Hypercharge Flux in IIB and F-theory: Anomalies and Gauge Coupling
Unification: We analyse hypercharge flux GUT breaking in F-theory/Type IIB GUT models with
regards to its implications for anomaly cancellation and gauge coupling
unification. To this aim we exploit the Type IIB limit and consider 7-brane
configurations that for the first time are guaranteed to exhibit net
hypercharge flux restriction to matter curves. We show that local F-theory
models with anomalies of type U(1)_Y-U(1)^2 in the massless spectrum can be
consistent only if such additional U(1)s are globally geometrically massive (in
the sense that they arise from non-Kahler deformations of the Calabi-Yau
four-fold). Further, in such cases of geometrically massive U(1)s hypercharge
flux can induce new anomalies of type U(1)_Y^2-U(1) in the massless spectrum,
violating constraints in local models forbidding such anomalies. In particular
this implies that it is possible to construct models exhibiting a U(1)_{PQ}
global symmetry which have hypercharge flux doublet-triplet splitting and no
further exotics. We also show that the known hypercharge flux induced splitting
of the gauge couplings in IIB models at tree-level can be reduced by a factor
of 5 by employing a more F-theoretic twisting of U(1) flux by hypercharge flux
bringing it to well within MSSM 2-loop results. In the case of net restriction
of hypercharge flux to matter curves this tree-level splitting becomes more
involved, is tied to the vacuum expectation values of certain closed-string
fields, and therefore gauge coupling unification becomes tied to the question
of moduli stabilisation.
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Non-minimal derivative couplings and inflation in supergravity: In this article we motivate and review the embedding of the gravitationally
enhanced friction mechanism in supergravity. The very interesting feature is
that inflationary models which utilize this mechanism drive inflation for a
wider range of parameter values and predict lower values for the
tensor-to-scalar ratio.
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5d gauge theories on orbifolds and 4d 't Hooft line indices: We study indices for 5d gauge theories on S^1 \times S^4/Z_n. In the large
orbifold limit, n \rightarrow \infty, we find evidence that the indices become
4d indices in the presence of a 't Hooft line operator. The non-perturbative
part of the index poses some subtleties when being compared to the 4d monopole
bubbling which happens in the presence of 't Hooft line operators. We study
such monopole bubbling indices and find an interesting connection to the
Hilbert series of the moduli space of instantons on an auxiliary ALE space.
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Quantum Annihilation of Anti- de Sitter Universe: We discuss the role of conformal matter quantum effects (using large $N$
anomaly induced effective action) to creation-annihilation of an Anti-de Sitter
Universe. The arbitrary GUT with conformally invariant content of fields is
considered. On a purely gravitational (supersymmetric) AdS background, the
quantum effects act against an (already existing) AdS Universe. The
annihilation of such a Universe occurs, what is common for any conformal matter
theory. On a dilaton-gravitational background, where there is dilatonic
contribution to the induced effective action, the quantum creation of an AdS
Universe is possible assuming fine-tuning of the dilaton.
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WZW models as mutual super Poisson-Lie T-dual sigma models: A WZW model on the Lie supergroup (C3+A) is constructed. It is shown that
this model contains super Poisson-Lie symmetry with the dual Lie supergroup C3
+ A1,1|.i. Furthermore, we show that the dual model is also equivalent to the
WZW model on isomorphic Lie supergroup (C3+A).i. In this manner, because of
isomorphism of the (C3+A) with a Manin supertriple, it is shown that the
N=(2,2) structure is preserved under the super Poisson-Lie T-duality
transformation.
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Spectra of Coset Sigma Models: We compute the complete 1-loop spectrum of anomalous dimensions for the bulk
fields of non-linear sigma models on symmetric coset (super)spaces G/H, both
with and without world-sheet supersymmetry. In addition, we provide two new
methods for the construction of partition functions in the infinite radius
limit and demonstrate their efficiency in the case of (super)sphere sigma
models. Our results apply to a large number of target spaces including
superspheres and superprojective spaces such as the N=2 sigma model on CP(3|4).
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Cancellation of divergences up to three loops in exceptional field
theory: We consider the tetrahedral three-loop diagram in $E_d$ exceptional field
theory evaluated as a scalar diagram for four external gravitons. At lowest
order in momenta, this diagram contributes to the $\nabla^6 R^4$ term in the
low-energy effective action for M-theory. We evaluate explicitly the sums over
the discrete exceptional field theory loop momenta that become sums over
1/2-BPS states in the compact exceptional space. These sums can be rewritten as
Eisenstein series that solve the homogeneous differential equations that
supersymmetry implies for the $\nabla^6 R^4$ coupling. We also show how our
results, even though sums over 1/2-BPS states, are consistent with expected
1/4-BPS contributions to the couplings.
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Algebraic renormalization of N=2 Super Yang-Mills theories coupled to
matter: We study the algebraic renormalization of $N=2$ Supersymmetric Yang--Mills
theories coupled to matter. A regularization procedure preserving both the BRS
invariance and the supersymmetry is not known yet, therefore it is necessary to
adopt the algebraic method of renormalization, which does not rely on any
regularization scheme. The whole analysis is reduced to the solution of
cohomology problems arising from the generalized Slavnov operator which
summarizes all the symmetries of the model. Besides to unphysical
renormalizations of the quantum fields, we find that the only coupling constant
of $N=2$ SYMs can get quantum corrections. Moreover we prove that all the
symmetries defining the theory are algebraically anomaly--free.
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On Subleading Contributions to the AdS/CFT Trace Anomaly: In the context of the AdS/CFT correspondence, we perform a direct computation
in AdS_5 supergravity of the trace anomaly of a d=4, N=2 SCFT. We find
agreement with the field theory result up to next to leading order in the 1/N
expansion. In particular, the order N gravitational contribution to the anomaly
is obtained from a Riemann tensor squared term in the 7-brane effective action
deduced from heterotic - type I duality. We also discuss, in the AdS/CFT
context, the order N corrections to the trace anomaly in d=4, N=4 SCFTs
involving SO or Sp gauge groups.
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Landau-Khalatnikov-Fradkin transformation in three-dimensional quenched
QED: We study the gauge-covariance of the massless fermion propagator in
three-dimensional quenched Quantum Electrodynamics in the framework of
dimensional regularization in d=3-2\ep. Assuming the finiteness of the quenched
perturbative expansion, that is the existence of the limit \ep \to 0, we state
that, exactly in d=3, all odd perturbative coefficients, starting with the
third order one, should be zero in any gauge.
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Spinor-Vector Duality in Heterotic String Orbifolds: The three generation heterotic-string models in the free fermionic
formulation are among the most realistic string vacua constructed to date,
which motivated their detailed investigation. The classification of free
fermion heterotic string vacua has revealed a duality under the exchange of
spinor and vector representations of the SO(10) GUT symmetry over the space of
models. We demonstrate the existence of the spinor-vector duality using
orbifold techniques, and elaborate on the relation of these vacua to free
fermionic models.
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The Calabi-Yau Landscape: from Geometry, to Physics, to Machine-Learning: We present a pedagogical introduction to the recent advances in the
computational geometry, physical implications, and data science of Calabi-Yau
manifolds. Aimed at the beginning research student and using Calabi-Yau spaces
as an exciting play-ground, we intend to teach some mathematics to the budding
physicist, some physics to the budding mathematician, and some machine-learning
to both. Based on various lecture series, colloquia and seminars given by the
author in the past year, this writing is a very preliminary draft of a book to
appear with Springer, by whose kind permission we post to ArXiv for comments
and suggestions.
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Path integral action and Chern-Simons quantum mechanics in
noncommutative plane: In this paper, the connection between the path integral representation of
propagators in the coherent state basis with additional degrees of freedom
\cite{rohwer} and the one without any such degrees of freedom \cite{sgfgs} is
established. We further demonstrate that the path integral formalism developed
in the noncommutative plane using the coherent state basis leads to a quantum
mechanics involving a Chern-Simons term in momentum which is of noncommutative
origin. The origin of this term from the Bopp-shift point of view is also
investigated. A relativistic generalization of the action derived from the path
integral framework is then proposed. Finally, we construct a map from the
commutative quantum Hall system to a particle in a noncommutative plane moving
in a magnetic field. The value of the noncommutative parameter from this map is
then computed and is found to agree with previous results.
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Dynamics of Effective Gluons: Renormalized Hamiltonians for gluons are constructed using a perturbative
boost-invariant renormalization group procedure for effective particles in
light-front QCD, including terms up to third order. The effective gluons and
their Hamiltonians depend on the renormalization group parameter lambda, which
defines the width of momentum space form factors that appear in the
renormalized Hamiltonian vertices. Third-order corrections to the three-gluon
vertex exhibit asymptotic freedom, but the rate of change of the vertex with
lambda depends in a finite way on regularization of small-x singularities. This
dependence is shown in some examples, and a class of regularizations with two
distinct scales in x is found to lead to the Hamiltonian running coupling
constant whose dependence on lambda matches the known perturbative result from
Lagrangian calculus for the dependence of gluon three-point Green's function on
the running momentum scale at large scales. In the Fock space basis of
effective gluons with small lambda, the vertex form factors suppress
interactions with large kinetic energy changes and thus remove direct couplings
of low energy constituents to high energy components in the effective bound
state dynamics. This structure is reminiscent of parton and constituent models
of hadrons.
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Loop Equations for + and - Loops in c = 1/2 Non-Critical String Theory: New loop equations for all genera in $c = \frac{1}{2}$ non-critical string
theory are constructed. Our loop equations include two types of loops, loops
with all Ising spins up (+ loops) and those with all spins down ( $-$ loops).
The loop equations generate an algebra which is a certain extension of $W_3$
algebra and are equivalent to the $W_3$ constraints derived before in the
matrix-model formulation of 2d gravity. Application of these loop equations to
construction of Hamiltonian for $c = \frac{1}{2}$ string field theory is
considered.
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On exact correlation functions in SU(N) ${\cal N} = 2$ superconformal
QCD: We consider the exact coupling constant dependence of extremal correlation
functions of ${\cal N} = 2$ chiral primary operators in 4d ${\cal N} = 2$
superconformal gauge theories with gauge group SU(N) and N_f=2N massless
fundamental hypermultiplets. The 2- and 3-point functions, viewed as functions
of the exactly marginal coupling constant and theta angle, obey the tt*
equations. In the case at hand, the tt* equations form a set of complicated
non-linear coupled matrix equations. We point out that there is an ad hoc
self-consistent ansatz that reduces this set of partial differential equations
to a sequence of decoupled semi-infinite Toda chains, similar to the one
encountered previously in the special case of SU(2) gauge group. This ansatz
requires a surprising new non-renormalization theorem in ${\cal N} = 2$
superconformal field theories. We derive a general 3-loop perturbative formula
for 2- and 3-point functions in the ${\cal N} = 2$ chiral ring of the SU(N)
theory, and in all explicitly computed examples we find agreement with the tt*
equations, as well as the above-mentioned ansatz. This is suggestive evidence
for an interesting non-perturbative conjecture about the structure of the
${\cal N} = 2$ chiral ring in this class of theories. We discuss several
implications of this conjecture. For example, it implies that the holonomy of
the vector bundles of chiral primaries over the superconformal manifold is
reducible. It also implies that a specific subset of extremal correlation
functions can be computed in the SU(N) theory using information solely from the
S^4 partition function of the theory obtained by supersymmetric localization.
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Gravitational Wave Constraints on Multi-Brane Inflation: A class of non-canonical inflationary models is identified, where the
leading-order contribution to the non-Gaussianity of the curvature perturbation
is determined by the sound speed of the fluctuations in the inflaton field.
Included in this class of models is the effective action for multiple
coincident branes in the finite n limit. The action for this configuration is
determined using a powerful iterative technique, based upon the fundamental
representation of SU(2). In principle the upper bounds on the tensor-scalar
ratio that arise in the standard, single-brane DBI inflationary scenario can be
relaxed in such multi-brane configurations if a large and detectable
non-Gaussianity is generated. Moreover models with a small number of coincident
branes could generate a gravitational wave background that will be observable
to future experiments.
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On Gauge Enhancement and Singular Limits in $G_2$ Compactifications of
M-theory: We study the physics of singular limits of $G_2$ compactifications of
M-theory, which are necessary to obtain a compactification with non-abelian
gauge symmetry or massless charged particles. This is more difficult than for
Calabi-Yau compactifications, due to the absence of calibrated two-cycles that
would have allowed for direct control of W-boson masses as a function of
moduli. Instead, we study the relationship between gauge enhancement and
singular limits in $G_2$ moduli space where an associative or coassociative
submanifold shrinks to zero size; this involves the physics of topological
defects and sometimes gives indirect control over particle masses, even though
they are not BPS. We show how a lemma of Joyce associates the class of a
three-cycle to any $U(1)$ gauge theory in a smooth $G_2$ compactification. If
there is an appropriate associative submanifold in this class then in the limit
of nonabelian gauge symmetry it may be interpreted as a gauge theory
worldvolume and provides the location of the singularities associated with
non-abelian gauge or matter fields. We identify a number of gauge enhancement
scenarios related to calibrated submanifolds, including Coulomb branches and
non-isolated conifolds, and also study examples that realize them.
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Everything is Entangled: We show that big bang cosmology implies a high degree of entanglement of
particles in the universe. In fact, a typical particle is entangled with many
particles far outside our horizon. However, the entanglement is spread nearly
uniformly so that two randomly chosen particles are unlikely to be directly
entangled with each other -- the reduced density matrix describing any pair is
likely to be separable.
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Example of quantum systems reduction: To solve the quantum-mechanical problem the procedure of mapping onto linear
space $W$ of generators of the (sub)group violated by given classical
trajectory is formulated. The formalism is illustrated by the plane H-atom
model. The problem is solved noting conservation of the Runge-Lentz vector $n$
and reducing the 4-dimensional incident phase space $T$ to the 3-dimensional
linear subspace $W=T^* V\times R^1$, where $T^* V$ is the (angular momentum
($l$) - angle ($\vp$)) phase space and $R^1 =n$. It is shown explicitly that
(i) the motion in $R^1$ is pure classical as the consequence of the reduction,
(ii) motion in the $\vp$ direction is classical since the Kepler orbits are
closed independently from initial conditions and (iii) motion in the $l$
direction is classical since all corresponding quantum corrections are defined
on the bifurcation line ($l=\infty$) of the problem. In our terms the H-atom
problem is exactly quasiclassical and is completely integrable by this reasons.
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Large-N reduction for N=2 quiver Chern-Simons theories on S^3 and
localization in matrix models: We study reduced matrix models obtained by the dimensional reduction of N=2
quiver Chern-Simons theories on S^3 to zero dimension and show that if a
reduced model is expanded around a particular multiple fuzzy sphere background,
it becomes equivalent to the original theory on S^3 in the large-N limit. This
is regarded as a novel large-N reduction on a curved space S^3. We perform the
localization method to the reduced model and compute the free energy and the
vacuum expectation value of a BPS Wilson loop operator. In the large-N limit,
we find an exact agreement between these results and those in the original
theory on S^3.
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Canonical sectors of five-dimensional Chern-Simons theories: The dynamics of five-dimensional Chern-Simons theories is analyzed. These
theories are characterized by intricate self couplings which give rise to
dynamical features not present in standard theories. As a consequence, Dirac's
canonical formalism cannot be directly applied due to the presence of
degeneracies of the symplectic form and irregularities of the constraints on
some surfaces of phase space, obscuring the dynamical content of these
theories. Here we identify conditions that define sectors where the canonical
formalism can be applied for a class of non-Abelian Chern-Simons theories,
including supergravity. A family of solutions satisfying the canonical
requirements is explicitly found. The splitting between first and second class
constraints is performed around these backgrounds, allowing the construction of
the charge algebra, including its central extension.
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Renormalization in Coulomb gauge QCD: In the Coulomb gauge of QCD, the Hamiltonian contains a non-linear Christ-Lee
term, which may alternatively be derived from a careful treatment of ambiguous
Feynman integrals at 2-loop order. We investigate how and if UV divergences
from higher order graphs can be consistently absorbed by renormalization of the
Christ-Lee term. We find that they cannot.
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On the symmetry orbits of black holes in non-linear sigma models: Breitenlohner, Maison and Gibbons claimed some time ago that all bona-fide
four dimensional asymptotically flat non-degenerate black holes are in a
symmetry orbit of the Schwarzschild/Kerr black hole in a large set of theories
of gravity and matter. Their argument involved reducing the theory on a
time-like Killing vector field and analysing the resulting three dimensional
sigma model of maps to a symmetric space $G/H$. In the construction of their
proof, they conjectured the existence of a suitable $H$-transformation that
always remove the electromagnetic charges of the four dimensional black hole
solution. We show in this short note that such a transformation does not exist
in general, and discuss a set of boundary conditions on the horizon for the
scalar fields in the sigma model that yield black holes for which the result by
Breitenlohner, Maison and Gibbons can be applied.
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Holographic calculation of entanglement entropy in the presence of
boundaries: When a spacetime has boundaries, the entangling surface does not have to be
necessarily compact and it may have boundaries as well. Then there appear a
new, boundary, contribution to the entanglement entropy due to the intersection
of the entangling surface with the boundary of the spacetime. We study the
boundary contribution to the logarithmic term in the entanglement entropy in
dimensions $d=3$ and $d=4$ when the entangling surface is orthogonal to the
boundary. In particular, we compute a boundary term in the entropy of
${\mathcal{N}}=4$ super-gauge multiplet at weak coupling. This result is
compared with the holographic calculation of the entropy based on the
Ryu-Takayanagi proposal adapted appropriately to the present situation. We find
a complete agreement between these two calculations provided the boundary
conditions imposed on the gauge multiplet preserve $1/2$ of the supersymmetry
and the extension of the boundary into the AdS bulk is a minimal hypersurface.
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The dynamics of aloof baby Skyrmions: The aloof baby Skyrme model is a (2+1)-dimensional theory with solitons that
are lightly bound. It is a low-dimensional analogue of a similar Skyrme model
in (3+1)-dimensions, where the lightly bound solitons have binding energies
comparable to nuclei. A previous study of static solitons in the aloof baby
Skyrme model revealed that multi-soliton bound states have a cluster structure,
with constituents that preserve their individual identities due to the
short-range repulsion and long-range attraction between solitons. Furthermore,
there are many different local energy minima that are all well-described by a
simple binary species particle model. In this paper we present the first
results on soliton dynamics in the aloof baby Skyrme model. Numerical field
theory simulations reveal that the lightly bound cluster structure results in a
variety of exotic soliton scattering events that are novel in comparison to
standard Skyrmion scattering. A dynamical version of the binary species point
particle model is shown to provide a good qualitative description of the
dynamics.
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Integrating out the Dirac sea: Effective field theory approach to
exactly solvable four-fermion models: We use 1+1 dimensional large N Gross-Neveu models as a laboratory to derive
microscopically effective Lagrangians for positive energy fermions only. When
applied to baryons, the Euler-Lagrange equation for these effective theories
assumes the form of a non-linear Dirac equation. Its solution reproduces the
full semi-classical results including the Dirac sea to any desired accuracy.
Dynamical effects from the Dirac sea are encoded in higher order derivative
terms and multi-fermion interactions with perturbatively calculable, finite
coefficients. Characteristic differences between models with discrete and
continuous chiral symmetry are observed and clarified.
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Resonances of Kalb-Ramond field on symmetric and asymmetric thick branes: In this paper, we investigate the localization of the Kalb-Ramond field on
symmetric and asymmetric thick branes, which are generated by a background
scalar field. In order to localize the Kalb-Ramond field, we introduce a
coupling with the background scalar field, and find that there exist some
Kaluza-Klein resonant modes. For the case of symmetric brane, we seek the
resonances by using the relative probability method and transfer matrix method,
and obtain the same result for the two methods. For the asymmetric case, we use
the transfer matrix method. We find that the number of resonances will decrease
with the increase of the asymmetry.
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Elliptic Calogero-Moser system from two dimensional current algebra: We show that elliptic Calogero-Moser system and its Lax operator found by
Krichever can be obtained by Hamiltonian reduction from the integrable
Hamiltonian system on the cotangent bundle to the central extension of the
algebra of SL(N,C) currents.Elliptic deformation of Yang-Mills theory is
presented.
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Non-Linear Integral Equations for complex Affine Toda associated to
simply laced Lie algebras: A set of coupled non-linear integral equations is derived for a class of
models connected with the quantum group $U_q(\hat g)$ ($g$ simply laced Lie
algebra), which are solvable using the Bethe Ansatz; these equations describe
arbitrary excited states of a system with finite spatial length $L$. They
generalize the Destri-De Vega equation for the Sine-Gordon/massive Thirring
model to affine Toda field theory with imaginary coupling constant. As an
application, the central charge and all the conformal weights of the UV
conformal field theory are extracted in a straightforward manner. The quantum
group truncation for $q$ at a root of unity is discussed in detail; in the UV
limit we recover through this procedure the RCFTs with extended $W(g)$
conformal symmetry.
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Analysis of the Entanglement with Centers: We begin from the quantization algebras and constraint for analyzing the
choice of centers in the first-order formulation without losing generality.
Then we calculate the entanglement entropy in the non-interacting $p$-form
theory in $2p+2$ dimensional Euclidean flat background with an $S^{2p}$
entangling surface. The universal term of the entanglement entropy in the
non-interacting $p$-form theory is determined in terms of the universal terms
of the non-interacting zero-form theory. We also prove the strong subadditivity
in the non-interacting theory with the non-trivial centers. Finally, we
calculate the mutual information with centers in two-dimensional conformal
field theory. The result shows that the mutual information is independent of
the choice of centers.
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Symmetries of the N=4 SYM S-matrix: Under the assumption of a CSW generalization to loop amplitudes in N=4 SYM,
(1) We prove that, formally the S-matrix is superconformal invariant to any
loop order, and (2) We argue that superconformal symmetry survives
regularization. More precisely, IR safe quantities constructed from the
S-matrix are superconformal covariant. The IR divergences are regularized in a
new holomorphic anomaly friendly regularization. The CSW prescription is known
to be valid for all tree level amplitudes and for one loop MHV amplitudes. In
these cases, our formal results do not rely on any assumptions.
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Duals for SU(N) SUSY gauge theories with an antisymmetric tensor: five
easy flavors: I consider N=1 supersymmetric SU(N_c) gauge theories with matter fields
consisting of one antisymmetric representation, five flavors, and enough
anti-fundamental representations to cancel the gauge anomaly. Previous analyses
are extended to the case of even N_c with no superpotential. Using holomorphy I
show that the theory has an interacting infrared fixed point for sufficiently
large N_c. These theories are interesting due to the fact that in going from
five to four flavors the theory goes from a non-trivial infrared fixed point to
confinement, in contradistinction to SUSY QCD, but in analogy to the behavior
expected in non-SUSY QCD.
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Magnetic Skyrmions coupled to fermions: The index theorem implies that there are fermionic states localized on a
soliton. Presence of these modes may significantly alter the pattern of
interaction between the solitons. As a particular example we investigate the
chiral magnetic Skyrmions coupled to spin-isospin fermions. It is shown that
there are sequences of fermionic modes localized on the Skyrmions. We
investigate the pattern of interaction between the soltions with localized
modes and proved the existence of stable system of magnetic Skyrmions bounded
by the strong attractive dipole interaction mediated by the chargeless
fermionic modes.
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Homotopy algebra of open-closed strings: This paper is a survey of our previous works on open-closed homotopy
algebras, together with geometrical background, especially in terms of
compactifications of configuration spaces (one of Fred's specialities) of
Riemann surfaces, structures on loop spaces, etc. We newly present Merkulov's
geometric A_infty-structure [Internat. Math. Res. Notices (1999) 153--164,
arxiv:math/0001007] as a special example of an OCHA. We also recall the
relation of open-closed homotopy algebras to various aspects of deformation
theory.
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Type I Superstrings without D-branes: Notwithstanding the central role of D-branes in many recently proposed string
dualities, several interesting type I vacua have been found without resorting
directly to D-brane technology. In this talk, we analyze a three-generation
SO(8)xU(12) chiral type I model with N=1 supersymmetry in D=4. It descends from
the type IIB compactification on the Z orbifold and requires only Neumann
boundary conditions, i.e. only the ubiquitous D9-branes (pan-branes). We also
discuss a large class of 6D type I vacua that display rich patterns of
Chan-Paton symmetry breaking/enhancement and various numbers of tensor
multiplets. Finally, we briefly address issues raised by the conjectured
heterotic - type I duality and by the relation between type I vacua and
compactifications of the putative F-theory.
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UV Perturbations in Brane Gas Cosmology: We consider the effect of the ultraviolet (UV) or short wavelength modes on
the background of Brane Gas Cosmology. We find that the string matter sources
are negligible in the UV and that the evolution is given primarily by the
dilaton perturbation. We also find that the linear perturbations are well
behaved and the predictions of Brane Gas Cosmology are robust against the
introduction of linear perturbations. In particular, we find that the
stabilization of the extra dimensions (moduli) remains valid in the presence of
dilaton and string perturbations.
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Interacting holographic dark energy model and generalized second law of
thermodynamics in non-flat universe: In the present paper we consider the interacting holographic model of dark
energy to investigate the validity of the generalized second laws of
thermodynamics in non-flat (closed) universe enclosed by the event horizon
measured from the sphere of the horizon named $L$. We show that for $L$ as the
system's IR cut-off the generalized second law is respected for the special
range of the deceleration parameter.
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Fast Lane for Confinement: Within the Electric Schroedinger Representation of the Yang-Mills theory the
Hamiltonian eigenstate and eigenvalue, as well as the Coulomb and confining
potentials are presented for a special regularization-approximation scheme,
which focuses on the ultra-local behavior of the propagator.
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String Constraints on Discrete Symmetries in MSSM Type II Quivers: We study the presence of discrete gauge symmetries in D-brane semi-realistic
compactifications. After establishing the constraints on the transformation
behaviour of the chiral matter for the presence of a discrete gauge symmetry we
perform a systematic search for discrete gauge symmetries within local
semi-realistic D-brane realizations, based on four D-brane stacks, of the MSSM
and the MSSM with three right-handed neutrinos. The systematic search reveals
that Proton hexality, a discrete symmetry which ensures the absence of R-parity
violating terms as well as the absence of dangerous dimension 5 proton decay
operators, is only rarely realized. Moreover, none of the semi-realistic local
D-brane configurations exhibit any family dependent discrete gauge symmetry.
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Relativistic quantum dynamics of a charged particle in cosmic string
spacetime in the presence of magnetic field and scalar potential: In this paper we analyze the relativistic quantum motion of charged spin-0
and spin-1/2 particles in the presence of a uniform magnetic field and scalar
potentials in the cosmic string spacetime. In order to develop this analysis,
we assume that the magnetic field is parallel to the string and the scalar
potentials present a cylindrical symmetry with their center on the string. Two
distinct configurations for the scalar potential, $S(r)$, are considered: $(i)$
the potential proportional to the inverse of the polar distance, i.e.,
$S\propto1/r$, and $(ii)$ the potential proportional to this distance, i.e.,
$S\propto r$. The energy spectra are explicitly computed for different physical
situations and presented their dependences on the magnetic field strength and
scalar coupling constants.
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Topological gravity and transgression holography: We show that Poincare-invariant topological gravity in even dimensions can be
formulated as a transgression field theory in one higher dimension whose gauge
connections are associated to linear and nonlinear realizations of the Poincare
group ISO(d-1,1). The resulting theory is a gauged WZW model whereby the
transition functions relating gauge fields live in the coset
ISO(d-1,1)/SO(d-1,1). The coordinate parametrizing the coset space is
identified with the scalar field in the adjoint representation of the gauge
group of the even-dimensional topological gravity theory. The supersymmetric
extension leads to topological supergravity in two dimensions starting from a
transgression field theory which is invariant under the supersymmetric
extension of the Poincare group in three dimensions. We also apply this
construction to a three-dimensional Chern-Simons theory of gravity which is
invariant under the Maxwell algebra and obtain the corresponding WZW model.
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Action for (Free) Open String Modes in AdS Space Using the Loop Variable
Approach: The loop variable technique (for open strings in flat space) is a gauge
invariant generalization of the renormalization group method for obtaining
equations of motion. Unlike the beta functions, which are only proportional to
the equations of motion, here it gives the full equation of motion. In an
earlier paper, a technique was described for adapting this method to open
strings in gravitational backgrounds. However unlike the flat space case, these
equations cannot be derived from an action and are therefore not complete. This
is because there are ambiguities in the method that involve curvature couplings
that cannot be fixed by appealing to gauge invariance alone but need a more
complete treatment of the closed string background. An indirect method to
resolve these ambiguities is to require symmetricity of the second derivatives
of the action. In general this will involve modifying the equations by terms
with arbitrarily high powers of curvature tensors. This is illustrated for the
massive spin 2 field. It is shown that in the special case of an AdS or dS
background, the exact action can easily be determined in this way.
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Integrable Field Theories derived from 4D Self-dual Gravity: We reformulate the self-dual Einstein equation as a trio of differential form
equations for simple two-forms. Using them, we can quickly show the equivalence
of the theory and 2D sigma models valued in an infinite-dimensional group,
which was shown by Park and Husain earlier. We also derive other field theories
including the 2D Higgs bundle equation. This formulation elucidates the
relation among those field theories.
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AdS$_2$ near-horizons, defects and string dualities: We construct a new family of $\text{AdS}_2\times S^3\times S^2$ solutions to
Type IIB supergravity arising as near-horizon geometries of D1-F1-D3-D5-NS5-D7
brane intersections preserving 4 supersymmetries. We show that a subclass of
these solutions asymptotes locally to the $\text{AdS}_6\times S^2\times
\Sigma_2$ solution to Type IIB supergravity holographically dual to the five
dimensional Sp(N) fixed point theory. This suggests that these solutions can be
interpreted as D1-F1-D3 line defects within this CFT. Switching off the
D7-branes, we act with $\text{SL}(2, \mathbb{R})$ to construct a second family
of solutions that can be related to an $\text{AdS}_3\times S^3\times S^3$ class
of M-theory backgrounds describing surface defects within the six dimensional
(1,0) SCFT dual to $\text{AdS}_7/\mathbb{Z}_k\times S^4$. Finally, using
non-Abelian T-duality we construct new classes of $\text{AdS}_2\times S^2\times
S^2$ solutions to Type IIA supergravity with 4 supercharges and elaborate on
their M-theory origin.
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Unfolded Dynamics Approach and Quantum Field Theory: We study quantization of a self-interacting scalar field within the unfolded
dynamics approach. To this end we find and analyze a classical unfolded system
describing 4d off-shell scalar field with a general self-interaction potential.
Then we systematically construct three different but related unfolded
formulations of the corresponding quantum field theory, supporting them with
illustrative calculations: an unfolded functional Schwinger-Dyson system, an
unfolded system for correlation functions and an unfolded effective system for
vertex functions. The most curious feature we reveal is that an unfolded
quantum commutator gets naturally regularized: a standard delta-function is
replaced with a heat kernel, parameterized by the unfolded proper time. We also
identify an auxiliary 5d system, having this proper time as a physical time,
which generates 4d scalar action as its on-shell action.
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TASI Lectures on Solitons: These lectures cover aspects of solitons with focus on applications to the
quantum dynamics of supersymmetric gauge theories and string theory. The
lectures consist of four sections, each dealing with a different soliton. We
start with instantons and work down in co-dimension to monopoles, vortices and,
eventually, domain walls. Emphasis is placed on the moduli space of solitons
and, in particular, on the web of connections that links solitons of different
types. The D-brane realization of the ADHM and Nahm construction for instantons
and monopoles is reviewed, together with related constructions for vortices and
domain walls. Each lecture ends with a series of vignettes detailing the roles
solitons play in the quantum dynamics of supersymmetric gauge theories in
various dimensions. This includes applications to the AdS/CFT correspondence,
little string theory, S-duality, cosmic strings, and the quantitative
correspondence between 2d sigma models and 4d gauge theories.
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Scrambling and Entangling Spinning Particles: In this paper we revisit the gravitational eikonal amplitudes of two
scattering spinning particles and inspect their scrambling power in the spin
spaces that is quantified through the tripartite information. We found that in
the non-relativistic limit and a special high-energy limit the leading
contribution is a quantity that is universal and theory independent. The
minimal coupling is singled out with minimal scrambling in a different high
momenta limit. We also inspected the initial state dependence of entanglement
generation and found that the spin coherent state with vanishing spin may not
necessarily be the hardest to entangle. Interestingly, among a family of mixed
states, the only P-rep state there known to be the best approximation of
classical mixed states was singled out as one with minimal entanglement
generated.
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Finite $N$ indices and the giant graviton expansion: The superconformal index of $\mathcal N=4$ super-Yang Mills theory with
$U(N)$ gauge group can be written as a matrix integral over the gauge group.
Recently, Murthy demonstrated that this integral can be reexpressed as a sum of
terms corresponding to a giant graviton expansion of the index, and provided an
explicit formula for the case of a single giant graviton. Here we give similar
explicit formulae for an arbitrary number, $m\ge1$, of giant gravitons. We
provide 1/2 and 1/16 BPS index examples up to the order where three giant
gravitons contribute and demonstrate that the expansion of the matrix integral
differs from the giant graviton expansion computed in the supergravity dual.
This shows that the giant graviton expansion is not necessarily unique once two
or more giant gravitons start appearing.
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Geometric Bounds on the 1-Form Gauge Sector: We classify the allowed structures of the discrete 1-form gauge sector in
six-dimensional supergravity theories realized as F-theory compactifications.
This provides upper bounds on the 1-form gauge factors $\mathbb{Z}_m$ and in
particular demands each cyclic factor to obey $m\leq 6$. Our bounds correspond
to the universal geometric constraints on the torsion subgroup of the
Mordell-Weil group of elliptic Calabi-Yau three-folds. For any F-theory vacua
with at least one tensor multiplet, we derive the constraints from the
$\mathbb{P}^1$ fibration structure of the base two-fold and identify their
physical origin in terms of the worldsheet symmetry of the associated effective
heterotic string. The bounds are also extended to the F-theory vacua with no
tensor multiplets via a specific deformation of the theory followed by a small
instanton transition, along which the 1-form gauge sector is not reduced. We
envision that our geometric bounds can be promoted to a swampland constraint on
any six-dimensional gravitational theories with minimal supersymmetry and also
extend them to four-dimensional F-theory vacua.
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Topological defects for the free boson CFT: Two different conformal field theories can be joined together along a defect
line. We study such defects for the case where the conformal field theories on
either side are single free bosons compactified on a circle. We concentrate on
topological defects for which the left- and right-moving Virasoro algebras are
separately preserved, but not necessarily any additional symmetries. For the
case where both radii are rational multiples of the self-dual radius we
classify these topological defects. We also show that the isomorphism between
two T-dual free boson conformal field theories can be described by the action
of a topological defect, and hence that T-duality can be understood as a
special type of order-disorder duality.
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Bootstrapping the long-range Ising model in three dimensions: The 3D Ising model and the generalized free scalar of dimension at least 0.75
belong to a continuous line of nonlocal fixed points, each referred to as a
long-range Ising model. They can be distinguished by the dimension of the
lightest spin-2 operator, which interpolates between 3 and 3.5 if we focus on
the non-trivial part of the fixed line. A property common to all such theories
is the presence of three relevant conformal primaries, two of which form a
shadow pair. This pair is analogous to a superconformal multiplet in that it
enforces relations between certain conformal blocks. By demanding that crossing
symmetry and unitarity hold for a set of correlators involving the relevant
operators, we compute numerical bounds on their scaling dimensions and OPE
coefficients. Specifically, we raise the minimal spin-2 operator dimension to
find successively smaller regions which eventually form a kink. Whenever a kink
appears, its co-ordinates show good agreement with the epsilon expansion
predictions for the critical exponents in the corresponding statistical model.
As a byproduct, our results reveal an infinite tower of protected operators
with odd spin.
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Unified Split Octonion Formulation of Dyons: Demonstrating the split octonion formalism for unified fields of dyons
(electromagnetic fields) and gravito-dyons (gravito-Heavisidian fields of
linear gravity), relevant field equations are derived in compact, simpler and
manifestly covariant forms. It has been shown that this unified model
reproduces the dynamics of structure of fields associated with individual
charges (masses) in the absence of others.
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On the Geometry of Metastable Supersymmetry Breaking: We give a concise geometric recipe for constructing D-brane gauge theories
that exhibit metastable SUSY breaking. We present two simple examples in terms
of branes at deformed CY singularities.
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Realize Emergent Gravity to Generic Situations: We clarify the problem in which occasions can gravitational force be regarded
emergent from thermodynamics, by proposing an entropic mechanism that can
extract the entropic gradient existing in spacetime, due to the variation of
the Casini-Bekenstein bound in specific quasi-static processes with the heat
flux $\delta Q$ into the whole casual wedge. We explicitly formulate the
derivation of inertial force as the emergent gravitational attraction from the
Entanglement First Law. We find the saturation of the bound along with the
vanishing relative entropy corresponds to the variation of minimal surface. To
covariant meaning, it is the Bousso bound. Besides, this understanding is
connected to recent Pennington's work on Black Hole Information Paradox,
suggesting a Page-Curve function origins from removing attraction by the
external heat bath. Our theory from entanglement now overcomes several
criticism towards Verlinde's original entropic force proposal, and is able to
co-exist with Susskind's Complexity Tendency. This entropic mechanism
reproduces the Newton's Second Law in Rindler space and the gravitational force
(together with derivation of the Einstein equation) beyond the near-horizon
region, and can be adapted into AdS/CFT and other generic situations.
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ABJM Theory with mass and FI deformations and Quantum Phase Transitions: The phase structure of ABJM theory with mass $m$ deformation and
non-vanishing Fayet-Iliopoulos (FI) parameter, $\zeta$, is studied through the
use of localisation on ${\mathbb S}^3$. The partition function of the theory
then reduces to a matrix integral, which, in the large $N$ limit and at large
sphere radius, is exactly computed by a saddle-point approximation. When the
couplings are analytically continued to real values, the phase diagram of the
model becomes immensely rich, with an infinite series of third-order phase
transitions at vanishing FI-parameter. As the FI term is introduced, new
effects appear. For any given $0 < \zeta < m/2$, the number of phases is finite
and for $\zeta\geq m/2$ the theory does not have any phase transitions at all.
Finally, we argue that ABJM theory with physical couplings does not undergo
phase transitions and investigate the case of $U(2)\times U(2)$ gauge group in
detail by an explicit calculation of the partition function.
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String Theory: A Theory of Unification: These notes on string theory are based on a series of talks I gave during my
graduate studies. As the talks, this introductory essay is intended for young
students and non-string theory physicists.
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Vibrating giant spikes and the large-winding sector: The single spike is a rigidly rotating classical string configuration closely
related to the giant magnon. We calculate bosonic and fermionic modes of this
solution, from which we see that it is not supersymmetric. It can be viewed as
an excitation above a hoop of string wound around the equator, in the same
sense that the magnon is an excitation above an orbiting point particle. We
find the operator which plays the role of the Hamiltonian for this sector,
which compared to the magnon's E-J has the angular momentum replaced by a
winding charge. The single spike solution is unstable, and we use the modes to
attempt a semi-classical computation of its lifetime.
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Three-point Green function of massless QED in position space to lowest
order: The transverse part of the three-point Green function of massless QED is
determined to the lowest order in position space. Taken together with the
evaluation of the longitudinal part in arXiv:0803.2630, this gives a relation
for QED which is analogous to the star-triangle relation. We relate our result
to conformal-invariant three-point functions.
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A Note on Gauss-Bonnet Black Holes at Criticality: With in the extended thermodynamics, we give a comparative study of critical
heat engines for Gauss-Bonnet and charged black holes in AdS in five
dimensions, in the limit of large Gauss-Bonnet parameter $\alpha$ and charge
$q$, respectively. We show that the approach of efficiency of heat engines to
Carnot limit in Gauss-Bonnet black holes is higher(lower) than charged black
holes when corresponding parameters are small(large).
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Finite-cutoff JT gravity and self-avoiding loops: We study quantum JT gravity at finite cutoff using a mapping to the
statistical mechanics of a self-avoiding loop in hyperbolic space, with
positive pressure and fixed length. The semiclassical limit (small $G_N$)
corresponds to large pressure, and we solve the problem in that limit in three
overlapping regimes that apply for different loop sizes. For intermediate loop
sizes, a semiclassical effective description is valid, but for very large or
very small loops, fluctuations dominate. For large loops, this quantum regime
is controlled by the Schwarzian theory. For small loops, the effective
description fails altogether, but the problem is controlled using a conjecture
from the theory of self-avoiding walks.
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Non-topological solitons in field theories with kinetic self-coupling: We investigate some fundamental features of a class of non-linear
relativistic lagrangian field theories with kinetic self-coupling. We focus our
attention upon theories admitting static, spherically symmetric solutions in
three space dimensions which are finite-energy and stable. We determine general
conditions for the existence and stability of these non-topological soliton
solutions. In particular, we perform a linear stability analysis that goes
beyond the usual Derrick-like criteria. On the basis of these considerations we
obtain a complete characterization of the soliton-supporting members of the
aforementioned class of non-linear field theories. We then classify the family
of soliton-supporting theories according to the central and asymptotic
behaviors of the soliton field, and provide illustrative explicit examples of
models belonging to each of the corresponding sub-families. In the present work
we restrict most of our considerations to one and many-components scalar
models. We show that in these cases the finite-energy static spherically
symmetric solutions are stable against charge-preserving perturbations,
provided that the vacuum energy of the model vanishes and the energy density is
positive definite. We also discuss briefly the extension of the present
approach to models involving other types of fields, but a detailed study of
this more general scenario will be addressed in a separate publication.
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The minimal entanglement wedge cross section in the GMMG/GCFT flat
holography: We focus on a proper candidate for the entanglement wedge in asymptotically
flat bulk geometries that are described by the generalized minimal massive
gravity (GMMG) in the context of the flat holography. To this end, we describe
the boundary by two dimensional Galilean conformal field theory (GCFT) at the
bipartite mixed state of the two disjoint intervals. We make a conjecture on
the minimal entanglement wedge cross section (EWCS) and we find that the
results are consistent with the previous computations on the holographic
entanglement negativity.
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Higher Derivative Corrections to Shear Viscosity from Graviton's
Effective Coupling: The shear viscosity coefficient of strongly coupled boundary gauge theory
plasma depends on the horizon value of the effective coupling of transverse
graviton moving in black hole background. The proof for the above statement is
based on the canonical form of graviton's action. But in presence of generic
higher derivative terms in the bulk Lagrangian the action is no longer
canonical. We give a procedure to find an effective action for graviton (to
first order in coefficient of higher derivative term) in canonical form in
presence of any arbitrary higher derivative terms in the bulk. From that
effective action we find the effective coupling constant for transverse
graviton which in general depends on the radial coordinate $r$. We also argue
that horizon value of this effective coupling is related to the shear viscosity
coefficient of the boundary fluid in higher derivative gravity. We explicitly
check this procedure for two specific examples: (1) four derivative action and
(2) eight derivative action ($Weyl^4$ term). For both cases we show that our
results for shear viscosity coefficient (up to first order in coefficient of
higher derivative term) completely agree with the existing results in the
literature.
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Quantum effects in classical systems having complex energy: On the basis of extensive numerical studies it is argued that there are
strong analogies between the probabilistic behavior of quantum systems defined
by Hermitian Hamiltonians and the deterministic behavior of classical
mechanical systems extended into the complex domain. Three models are examined:
the quartic double-well potential $V(x)=x^4-5x^2$, the cubic potential
$V(x)=frac{1}{2}x^2-gx^3$, and the periodic potential $V(x)=-\cos x$. For the
quartic potential a wave packet that is initially localized in one side of the
double-well can tunnel to the other side. Complex solutions to the classical
equations of motion exhibit a remarkably analogous behavior. Furthermore,
classical solutions come in two varieties, which resemble the even-parity and
odd-parity quantum-mechanical bound states. For the cubic potential, a quantum
wave packet that is initially in the quadratic portion of the potential near
the origin will tunnel through the barrier and give rise to a probability
current that flows out to infinity. The complex solutions to the corresponding
classical equations of motion exhibit strongly analogous behavior. For the
periodic potential a quantum particle whose energy lies between -1 and 1 can
tunnel repeatedly between adjacent classically allowed regions and thus execute
a localized random walk as it hops from region to region. Furthermore, if the
energy of the quantum particle lies in a conduction band, then the particle
delocalizes and drifts freely through the periodic potential. A classical
particle having complex energy executes a qualitatively analogous local random
walk, and there exists a narrow energy band for which the classical particle
becomes delocalized and moves freely through the potential.
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Remarks on the Aharonov-Bohm Green function: Some elementary algebraic points regarding the Green function for a localised
flux tube are developed. A calculation of the effective action density is
included.
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Gravitational chiral anomaly for spin 3/2 field interacting with spin
1/2 field: The gravitational chiral quantum anomaly is calculated in the framework of
the extended Rarita-Schwinger-Adler (RSA) field theory, which includes the
interaction with an additional spin 1/2 field. It is shown that the factor in
the gravitational chiral anomaly, normalized to the Dirac field anomaly, is
equal to -19. The resulting value distinguishes the RSA theory from the other
theories of spin 3/2. A direct verification of the conformality of the RSA
theory in the strong interaction limit at the level of one-loop three-point
graphs was made.
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Multistring Vertices and Hyperbolic Kac Moody Algebras: Multistring vertices and the overlap identities which they satisfy are
exploited to understand properties of hyperbolic Kac Moody algebras, and
$E_{10}$ in particular. Since any such algebra can be embedded in the larger
Lie algebra of physical states of an associated completely compactified
subcritical bosonic string, one can in principle determine the root spaces by
analyzing which (positive norm) physical states decouple from the $N$-string
vertex. Consequently, the Lie algebra of physical states decomposes into a
direct sum of the hyperbolic algebra and the space of decoupled states. Both
these spaces contain transversal and longitudinal states. Longitudinal
decoupling holds generally, and may also be valid for uncompactified strings,
with possible consequences for Liouville theory; the identification of the
decoupled states simply amounts to finding the zeroes of certain ``decoupling
polynomials''. This is not the case for transversal decoupling, which crucially
depends on special properties of the root lattice, as we explicitly demonstrate
for a non-trivial root space of $E_{10}$. Because the $N$-vertices of the
compactified string contain the complete information about decoupling, all the
properties of the hyperbolic algebra are encoded into them. In view of the
integer grading of hyperbolic algebras such as $E_{10}$ by the level, these
algebras can be interpreted as interacting strings moving on the respective
group manifolds associated with the underlying finite-dimensional Lie algebras.
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On moduli spaces of flat connections with non-simply connected structure
group: We consider the moduli space of flat G-bundles over the twodimensional torus,
where G is a real, compact, simple Lie group which is not simply connected. We
show that the connected components that describe topologically non-trivial
bundles are isomorphic as symplectic spaces to moduli spaces of topologically
trivial bundles with a different structure group. Some physical applications of
this isomorphism which allows to trade topological non-triviality for a change
of the gauge group are sketched.
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Uniqueness of the Jackiw non-Noetherian conformal scalar field: Jackiw was undoubtedly the first to exhibit an example of a scalar field
action which is not conformally invariant whereas its equation of motion is.
This feature has recently been dubbed as a non-Noetherian conformal scalar
field. The paradigmatic example of Jackiw was the generalization to curved
spacetime of the two-dimensional Liouville action. Here, we prove that, up to
second order, this is the unique example of a non-Noetherian conformal scalar
field in two dimensions. We establish this result using an old and somewhat
forgotten theorem which is none other than the solution to the inverse problem
of the calculus of variations.
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Swampland Variations on a Theme by KKLT: The KKLT scenario in a warped throat, if consistent, provides a concrete
counterexample to both the AdS scale separation and the dS swampland
conjectures. First, we define and analyze the relevant effective field theory
for the conifold modulus and the overall Kaehler modulus that both have
exponentially small masses. The scalar potential still admits KKLT-like AdS and
dS minima. Second, we critically analyze the reliability of the employed
Wilsonian effective action by evaluating the masses of light modes localized in
the warped throat. The resulting mass spectrum is discussed with respect to the
swampland distance conjecture. We find the recently observed emergent nature of
the latter not only at large distance points but also at the conifold point
motivating a general extension of it. In this respect, KKLT and trans-Planckian
field distance are on equal footing. It is pointed out that the reliability of
the KKLT minimum will depend on how this emergent behavior is interpreted.
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Sequences of dipole black rings and Kaluza-Klein bubbles: We construct new exact solutions to 5D Einstein-Maxwell equations describing
sequences of Kaluza-Klein bubbles and dipole black rings. The solutions are
generated by 2-soliton transformations from vacuum black ring - bubble
sequences. The properties of the solutions are investigated. We also derive the
Smarr-like relations and the mass and tension first laws in the general case
for such configurations of Kaluza-Klein bubbles and dipole black rings. The
novel moment is the appearance of the magnetic flux in the Smarr-like relations
and the first laws.
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Open string pair creation from worldsheet instantons: Worldline instantons provide a particularly elegant way to derive Schwinger's
well-known formula for the pair creation rate due to a constant electric field
in quantum electrodynamics. In this note, we show how to extend this method to
the corresponding problem of open string pair creation.
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Deconstruction of Gauge Symmetry Breaking by Discrete Symmetry and $G^N$
Unification: We deconstruct the non-supersymmetric SU(5) breaking by discrete symmetry on
the space-time $M^4\times S^1$ and $M^4\times S^1/(Z_2\times Z_2')$ in the
Higgs mechanism deconstruction scenario. And we explain the subtle point on how
to exactly match the continuum results with the latticized results on the
quotient space $S^1/Z_2$ and $S^1/(Z_2\times Z_2')$. We also propose an
effective deconstruction scenario and discuss the gauge symmetry breaking by
the discrete symmetry on theory space in this approach. As an application, we
suggest the $G^N$ unification where $G^N$ is broken down to $SU(3)\times
SU(2)\times U(1)^{n-3}$ by the bifundamental link fields and the
doublet-triplet splitting can be achieved.
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The classical dynamics of gauge theories in the deep infrared: Gauge and gravitational theories in asymptotically flat settings possess
infinitely many conserved charges associated with large gauge transformations
or diffeomorphisms that are nontrivial at infinity. To what extent do these
charges constrain the scattering in these theories? It has been claimed in the
literature that the constraints are trivial, due to a decoupling of hard and
soft sectors for which the conserved charges constrain only the dynamics in the
soft sector. We show that the argument for this decoupling fails due to the
failure in infinite dimensions of a property of symplectic geometry which holds
in finite dimensions. Specializing to electromagnetism coupled to a massless
charged scalar field in four dimensional Minkowski spacetime, we show
explicitly that the two sectors are always coupled using a perturbative
classical computation of the scattering map. Specifically, while the two
sectors are uncoupled at low orders, they are coupled at quartic order via the
electromagnetic memory effect. This coupling cannot be removed by adjusting the
definitions of the hard and soft sectors (which includes the classical analog
of dressing the hard degrees of freedom). We conclude that the conserved
charges yield nontrivial constraints on the scattering of hard degrees of
freedom. This conclusion should also apply to gravitational scattering and to
black hole formation and evaporation.
In developing the classical scattering theory, we show that generic Lorenz
gauge solutions fail to satisfy the matching condition on the vector potential
at spatial infinity proposed by Strominger to define the field configuration
space, and we suggest a way to remedy this. We also show that when soft degrees
of freedom are present, the order at which nonlinearities first arise in the
scattering map is second order in Lorenz gauge, but can be third order in other
gauges.
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Quantization of the Relativistic Particle: We revise the problem of the quantization of relativistic particle,
presenting a modified consistent canonical scheme, which allows one not only to
include arbitrary backgrounds in the consideration but to get in course of the
quantization a consistent relativistic quantum mechanics, which reproduces
literally the behavior of the one-particle sector of the corresponding quantum
field. At the same time this construction presents a possible solution of the
well-known old problem how to construct a consistent quantum mechanics on the
base of a relativistic wave equation.
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Scale Transformations on the Noncommutative Plane and the Seiberg-Witten
Map: We write down three kinds of scale transformations {\tt i-iii)} on the
noncommutative plane. {\tt i)} is the analogue of standard dilations on the
plane, {\tt ii)} is a re-scaling of the noncommutative parameter $\theta$, and
{\tt iii)} is a combination of the previous two, whereby the defining relations
for the noncommutative plane are preserved. The action of the three
transformations is defined on gauge fields evaluated at fixed coordinates and
$\theta$.
The transformations are obtained only up to terms which transform covariantly
under gauge transformations. We give possible constraints on these terms. We
show how the transformations {\tt i)} and {\tt ii)} depend on the choice of
star product, and show the relation of {\tt ii)} to Seiberg-Witten
transformations. Because {\tt iii)} preserves the fundamental commutation
relations it is a symmetry of the algebra. One has the possibility of
implementing it as a symmetry of the dynamics, as well, in noncommutative field
theories where $\theta$ is not fixed.
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Gauged Supergravities in Three Dimensions: A Panoramic Overview: Maximal and non-maximal supergravities in three spacetime dimensions allow
for a large variety of semisimple and non-semisimple gauge groups, as well as
complex gauge groups that have no analog in higher dimensions. In this
contribution we review the recent progress in constructing these theories and
discuss some of their possible applications.
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Probing strongly coupled anisotropic plasmas from higher curvature
gravity: We consider five-dimensional AdS-axion-dilaton gravity with a Gauss-Bonnet
term and use a black brane solution displaying spatial anisotropy as the
gravity dual of a strongly coupled anisotropic plasma. We compute several
observables relevant to the study of the plasma, namely, the drag force, the
jet quenching parameter, the quarkonium potential and the thermal photon
production. The effects of higher derivative corrections and of the anisotropy
are discussed and compared with previous results.
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New Kähler invariant Fayet-Iliopoulos terms in supergravity and
cosmological applications: Recently, a new type of constant Fayet-Iliopoulos (FI) terms was introduced
in $\mathcal{N}=1$ supergravity, which do not require the gauging of the
$R$-symmetry. We revisit and generalise these constructions, building a new
class of K\"ahler invariant FI terms parametrised by a function of the
gravitino mass as functional of the chiral superfields, which is then used to
describe new models of inflation. They are based on a no-scale supergravity
model of the inflaton chiral multiplet, supplemented by an abelian vector
multiplet with the new FI-term. We show that the inflaton potential is
compatible with the CMB observational data, with a vacuum energy at the minimum
that can be tuned to a tiny positive value. Finally, the axionic shift symmetry
can be gauged by the $U(1)$ which becomes massive. These models offer a
mechanism for fixing the gravitino mass in no-scale supergravities, that
corresponds to a flat direction of the scalar potential in the absence of the
new FI-term; its origin in string theory is an interesting open problem.
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Counting Higher Genus Curves with Crosscaps in Calabi-Yau Orientifolds: We compute all loop topological string amplitudes on orientifolds of local
Calabi-Yau manifolds, by using geometric transitions involving SO/Sp
Chern-Simons theory, localization on the moduli space of holomorphic maps with
involution, and the topological vertex. In particular we count Klein bottles
and projective planes with any number of handles in some Calabi-Yau
orientifolds.
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T-duality and $α'$-corrections: We construct an $O(d,d)$ invariant universal formulation of the first-order
$\alpha'$-corrections of the string effective actions involving the dilaton,
metric and two-form fields. Two free parameters interpolate between
four-derivative terms that are even and odd with respect to a $Z_2$-parity
transformation that changes the sign of the two-form field. The $Z_2$-symmetric
model reproduces the closed bosonic string, and the heterotic string effective
action is obtained through a $Z_2$-parity-breaking choice of parameters. The
theory is an extension of the generalized frame formulation of Double Field
Theory, in which the gauge transformations are deformed by a first-order
generalized Green-Schwarz transformation. This deformation defines a duality
covariant gauge principle that requires and fixes the four-derivative terms. We
discuss the $O(d,d)$ structure of the theory and the (non-)covariance of the
required field redefinitions.
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String Threshold corrections in models with spontaneously broken
supersymmetry: We analyse a class of four-dimensional heterotic ground states with N=2
space-time supersymmetry. From the ten-dimensional perspective, such models can
be viewed as compactifications on a six-dimensional manifold with SU(2)
holonomy, which is locally but not globally K3 x T^2. The maximal N=4
supersymmetry is spontaneously broken to N=2. The masses of the two massive
gravitinos depend on the (T,U) moduli of T^2. We evaluate the one-loop
threshold corrections of gauge and R^2 couplings and we show that they fall in
several universality classes, in contrast to what happens in usual K3 x T^2
compactifications, where the N=4 supersymmetry is explicitly broken to N=2, and
where a single universality class appears. These universality properties follow
from the structure of the elliptic genus. The behaviour of the threshold
corrections as functions of the moduli is analysed in detail: it is singular
across several rational lines of the T^2 moduli because of the appearance of
extra massless states, and suffers only from logarithmic singularities at large
radii. These features differ substantially from the ordinary K3 x T^2
compactifications, thereby reflecting the existence of spontaneously-broken N=4
supersymmetry. Although our results are valid in the general framework defined
above, we also point out several properties, specific to orbifold
constructions, which might be of phenomenological relevance.
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Generalized symmetries and 2-groups via electromagnetic duality in
AdS/CFT: We discuss how electromagnetically dualizing a 1-form to a 2-form in AdS$_5$
exchanges regular and alternate boundary conditions, and thus gauges the
originally global $U(1)$ symmetry in the dual field theory. The generalized
symmetry current dual to the 2-form in the bulk is identified as the dual field
strength of the gauged $U(1)$, and the associated double-trace operator with a
logarithmically running coupling is just the gauged $U(1)$ Maxwell action.
Applying this dualization to an AdS Maxwell-Chern-Simons theory dual to a
global $U(1) \times U(1)$ model with an 't Hooft anomaly results in a theory
with a modified field strength that holographically realizes a 2-group
symmetry. We explicitly carry out the holographic renormalization to verify
this, and discuss the generalization to other rank fields in other dimensions.
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3D gauged supergravity from SU(2) reduction of $N=1$ 6D supergravity: We obtain Yang-Mills $SU(2)\times G$ gauged supergravity in three dimensions
from $SU(2)$ group manifold reduction of (1,0) six dimensional supergravity
coupled to an anti-symmetric tensor multiplet and gauge vector multiplets in
the adjoint of $G$. The reduced theory is consistently truncated to $N=4$ 3D
supergravity coupled to $4(1+\textrm{dim}\, G)$ bosonic and $4(1+\textrm{dim}\,
G)$ fermionic propagating degrees of freedom. This is in contrast to the
reduction in which there are also massive vector fields. The scalar manifold is
$\mathbf{R}\times \frac{SO(3,\, \textrm{dim}\, G)}{SO(3)\times
SO(\textrm{dim}\, G)}$, and there is a $SU(2)\times G$ gauge group. We then
construct $N=4$ Chern-Simons $(SO(3)\ltimes \mathbf{R}^3)\times (G\ltimes
\mathbf{R}^{\textrm{dim}G})$ three dimensional gauged supergravity with scalar
manifold $\frac{SO(4,\,1+\textrm{dim}G)}{SO(4)\times SO(1+\textrm{dim}G)}$ and
explicitly show that this theory is on-shell equivalent to the Yang-Mills
$SO(3)\times G$ gauged supergravity theory obtained from the $SU(2)$ reduction,
after integrating out the scalars and gauge fields corresponding to the
translational symmetries $\mathbf{R}^3\times \mathbf{R}^{\textrm{dim}\, G}$.
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Boundary states in the SU(2)$_k$ WZW model from open string field theory: We analyze boundary states in the SU(2)$_k$ WZW model using open string field
theory in the level truncation approximation. We develop algorithms that allow
effective calculation of action in this model and we search for classical
solutions of the equations of motion, which are conjectured to describe
boundary states. We find three types of solutions. First, there are real
solutions that represent maximally symmetric Cardy boundary states and we show
that they satisfy certain selection rules regarding their SU(2) parameters.
Next, we find complex solutions that go beyond the SU(2) model and describe
maximally symmetric SL(2,$\mathbb C$) boundary conditions. Finally, we find
exotic solutions that correspond to symmetry-breaking boundary states. Most of
real exotic solutions describe the so-called B-brane boundary states, but some
may represent yet unknown boundary states.
|
Integrable Boundary Conditions for the O(N) Nonlinear $σ$ Model: We discuss the new integrable boundary conditions for the O(N) nonlinear
$\sigma$ model and related solutions of the boundary Yang-Baxter equation,
which were presented in our previous paper hep-th/0108039.
|
Diffusion constant of slowly rotating black three-brane: In this paper, we take the slowly rotating black three-brane background and
perturb it by introducing a vector gauge field. We find the components of the
gauge field through Maxwell equations and Bianchi identities. Using currents
and some ansatz we find Fick's first law at long wavelength regime. An
interesting result for this non-trivial supergravity background is that the
diffusion constant on the stretched horizon which emerges from Fick's first law
is a complex constant. The pure imaginary part of the diffusion constant
appears because the black three-brane has angular momentum. By taking the
static limit of the corresponding black brane the well known diffusion constant
will be recovered. On the other hand, from the point of view of the Fick's
second law, we have the dispersion relation $\omega=-iDq^{2}$ and we found a
damping of hydrodynamical flow in the holographically dual theory. Existence of
imaginary term in the diffusion constant introduces an oscillating propagation
of the gauge field in the dual field theory.
|
Geometric aspects of the AdS/CFT correspondence: We discuss classical gravitational aspects of the AdS/CFT correspondence,
with the aim of obtaining a rigorous (mathematical) understanding of the
semi-classical limit of the gravitational partition function. The paper surveys
recent progress in the area, together with a selection of new results and open
problems.
|
Compactifications of F-Theory on Calabi--Yau Threefolds -- I: We study compactifications of F-theory on certain Calabi--Yau threefolds. We
find that $N=2$ dualities of type II/heterotic strings in 4 dimensions get
promoted to $N=1$ dualities between heterotic string and F-theory in 6
dimensions. The six dimensional heterotic/heterotic duality becomes a classical
geometric symmetry of the Calabi--Yau in the F-theory setup. Moreover the
F-theory compactification sheds light on the nature of the strong coupling
transition and what lies beyond the transition at finite values of heterotic
string coupling constant.
|
M theory as a matrix extension of Chern-Simons theory: We study a new class of matrix models, the simplest of which is based on an
Sp(2) symmetry and has a compactification which is equivalent to Chern-Simons
theory on the three-torus. By replacing Sp(2) with the super-algebra Osp(1|32),
which has been conjectured to be the full symmetry group of M theory, we arrive
at a supercovariant matrix model which appears to contain within it the
previously proposed M theory matrix models. There is no background spacetime so
that time and dynamics are introduced via compactifications which break the
full covariance of the model. Three compactifications are studied corresponding
to a hamiltonian quantization in D=10+1, a Lorentz invariant quantization in
D=9+1 and a light cone gauge quantization in D=11=9+1+1. In all cases
constraints arise which eliminate certain higher spin fields in terms of lower
spin dynamical fields. In the SO(9,1) invariant compactification we argue that
the one loop effective action reduces to the IKKT covariant matrix model. In
the light cone gauge compactification the theory contains the standard M theory
light cone gauge matrix model, but there appears an additional transverse five
form field.
|
A Non-Riemannian Metric on Space-Time Emergent From Scalar Quantum Field
Theory: We show that the two-point function
\sigma(x,x')=\sqrt{<[\phi(x)-\phi(x')]^{2}>} of a scalar quantum field theory
is a metric (i.e., a symmetric positive function satisfying the triangle
inequality) on space-time (with imaginary time). It is very different from the
Euclidean metric |x-x'| at large distances, yet agrees with it at short
distances. For example, space-time has finite diameter which is not universal.
The Lipschitz equivalence class of the metric is independent of the cutoff.
\sigma(x,x') is not the length of the geodesic in any Riemannian metric.
Nevertheless, it is possible to embed space-time in a higher dimensional space
so that \sigma(x,x') is the length of the geodesic in the ambient space.
\sigma(x,x') should be useful in constructing the continuum limit of quantum
field theory with fundamental scalar particles.
|
Exploring soft constraints on effective actions: We study effective actions for simultaneous breaking of space-time and
internal symmetries. Novel features arise due to the mixing of Goldstone modes
under the broken symmetries which, in contrast to the usual Adler's zero, leads
to non-vanishing soft limits. Such scenarios are common for spontaneously
broken SCFT's. We explicitly test these soft theorems for $\mathcal{N}=4$ sYM
in the Coulomb branch both perturbatively and non-perturbatively. We explore
the soft constraints systematically utilizing recursion relations. In the pure
dilaton sector of a general CFT, we show that all amplitudes up to order $s^{n}
\sim \partial^{2n}$ are completely determined in terms of the $k$-point
amplitudes at order $s^k$ with $k \leq n$. Terms with at most one derivative
acting on each dilaton insertion are completely fixed and coincide with those
appearing in the conformal DBI, i.e. DBI in AdS. With maximal supersymmetry,
the effective actions are further constrained, leading to new
non-renormalization theorems. In particular, the effective action is fixed up
to eight derivatives in terms of just one unknown four-point coefficient and
one more coefficient for ten-derivative terms. Finally, we also study the
interplay between scale and conformal invariance in this context.
|
Higher Spin Entanglement Entropy: In this paper, we develop a perturbation formulation to calculate the single
interval higher spin R$\acute{e}$nyi and entanglement entropy for two
dimensional conformal field theory with $\mathcal{W}_{\infty}(\lambda)$
symmetry. The system is at finite temperature and is deformed by higher spin
chemical potential. We manage to compute higher spin R$\acute{e}$nyi entropy
with various spin deformations up to order $\mathcal{O}(\mu^2)$. For spin 3
deformation, we calculate exact higher spin R$\acute{e}$nyi entropy up to
$\mathcal{O}(\mu^4)$. When $\lambda=3$, in the large $c$ limit, we find perfect
match with tree level holographic higher spin entanglement entropy up to order
$\mu^4$ obtained by the Wilson line prescription. We also find quantum
corrections to higher spin entanglement entropy which is beyond tree level
holographic results. The quantum correction is universal at order $\mu^4$ in
the sense that it is independent of $\lambda$. Our computation relies on a
multi-valued conformal map from $n$-sheeted Riemann surface $\mathcal{R}_n$ to
complex plane and correlation functions of primary fields on complex plane. The
method can be applied to general conformal field theories with $\mathcal{W}$
symmetry.
|
Gauge-Invariant Double-Copies via Recursion: We prove that all tree-level amplitudes in pure (super-)gravity can be
expressed as term-wise, gauge-invariant double-copies of those of pure
(super-)Yang-Mills obtained via BCFW recursion. These representations are far
from unique: varying the recursive scheme leads to a wide variety of distinct,
but equally valid representations of gravitational amplitudes, all realized as
double-copies.
|
Comments on Noncommutative Sigma Models: We review the derivation of a noncommutative version of the nonlinear sigma
model on $\CPn$ and it's soliton solutions for finite $\theta$ emphasizing the
similarities it bears to the GMS scalar field theory. It is also shown that
unlike the scalar theory, some care needs to be taken in defining the
topological charge of BPS solitons of the theory due to nonvanishing surface
terms in the energy functional. Finally it is shown that, like its commutative
analogue, the noncommutative $\CPn$-model also exhibits a non-BPS sector.
Unlike the commutative case however, there are some surprises in the
noncommutative case that merit further study.
|
Symmetry and Observables in Induced QCD: We review some of the basic features of the Kazakov-Migdal model of induced
QCD. We emphasize the role of $Z_N$ symmetry in determining the observable
properties of the model and also argue that it can be broken explicitly without
ruining the solvability of induced QCD in the infinite $N$ limit. We outline
the sort of critical behavior which the master field must have in order that
the model is still solvable. We also review some aspects of the $D=1$ version
of the model where the partition function can be obtained analytically. To be
published in the Proceedings of "Mathematical Physics, String Theory and
Quantum Gravity", Rhakov, Ukraine. October, 1992
|
A Topological Study of Induced Representation: From the point of view of topology we study the induced representation
technique which E. Wigner proposed in 1939. We comment on the gauge structure
in the induced representation technique and construc the explicit form of the
gauge fields. The topological results ofour study are applied to quantum
mechanics on a d-dimensional sphere and its path integral is formulated.
|
Self-gravitating darkon fluid with anisotropic scaling: The fluid model for the dark sector of the universe (darkon fluid) introduced
previously in \cite{PRD} is reformulated as a modified model involving only
variables from physical phase space. The Lagrangian of the model does not
possess a free particle limit and hence the particles it describes, darkons,
exist only as a self-gravitating fluid. This darkon fluid presents a dynamical
realisation of the zero-mass Galilean algebra extended by anisotropic
dilational symmetry with dynamical exponent $z=5/3$. The model possesses
cosmologically relevant solutions which are identical to those of \cite{PRD}.
We derive also the equations for the cosmological perturbations at early times
and determine their solutions. In addition, we discuss also some implications
of adding higher spatial-derivative terms.
|
Single-particle digitization strategy for quantum computation of a
$φ^4$ scalar field theory: Motivated by the parton picture of high energy quantum chromodynamics, we
develop a single-particle digitization strategy for the efficient quantum
simulation of relativistic scattering processes in a $d+1$ dimensional scalar
$\phi^4$ field theory. We work out quantum algorithms for initial state
preparation, time evolution and final state measurements. We outline a
non-perturbative renormalization strategy in this single-particle framework.
|
Renormalization of Gauge Theories and Gravity: We study the perturbative quantization of gauge theories and gravity. Our
investigations start with the geometry of spacetimes and particle fields. Then
we discuss the various Lagrange densities of (effective) Quantum General
Relativity coupled to the Standard Model. In addition, we study the
corresponding BRST double complex of diffeomorphisms and gauge transformations.
Next we apply Connes--Kreimer renormalization theory to the perturbative
Feynman graph expansion: In this framework, subdivergences are organized via
the coproduct of a Hopf algebra and the renormalization operation is described
as an algebraic Birkhoff decomposition. To this end, we generalize and improve
known coproduct identities and a theorem of van Suijlekom (2007) that relates
(generalized) gauge symmetries to Hopf ideals. In particular, our
generalization applies to gravity, as was suggested by Kreimer (2008). In
addition, our results are applicable to theories with multiple vertex residues,
coupling constants and such with a transversal structure. Additionally, we also
provide criteria for the compatibility of these Hopf ideals with Feynman rules
and the chosen renormalization scheme. We proceed by calculating the
corresponding gravity-matter Feynman rules for any valence and with a general
gauge parameter. Then we display all propagator and three-valent vertex Feynman
rules and calculate the respective cancellation identities. Finally, we propose
planned follow-up projects: This includes a generalization of Wigner's
classification of elementary particles to linearized gravity, the
representation of cancellation identities via Feynman graph cohomology and an
investigation on the equivalence of different definitions for the graviton
field. In particular, we argue that the appropriate setup to study perturbative
BRST cohomology is a differential-graded Hopf algebra.
|
Weyl gauge symmetry and its spontaneous breaking in Standard Model and
inflation: We discuss the local (gauged) Weyl symmetry and its spontaneous breaking and
apply it to model building beyond the Standard Model (SM) and inflation. In
models with non-minimal couplings of the scalar fields to the Ricci scalar,
that are conformal invariant, the spontaneous generation by a scalar field(s)
vev of a positive Newton constant demands a negative kinetic term for the
scalar field, or vice-versa. This is naturally avoided in models with
additional Weyl gauge symmetry. The Weyl gauge field $\omega_\mu$ couples to
the scalar sector but not to the fermionic sector of a SM-like Lagrangian. The
field $\omega_\mu$ undergoes a Stueckelberg mechanism and becomes massive after
"eating" the (radial mode) would-be-Goldstone field (dilaton $\rho$) in the
scalar sector. Before the decoupling of $\omega_\mu$, the dilaton can act as UV
regulator and maintain the Weyl symmetry at the {\it quantum} level, with
relevance for solving the hierarchy problem. After the decoupling of
$\omega_\mu$, the scalar potential depends only on the remaining (angular
variables) scalar fields, that can be the Higgs field, inflaton, etc. We show
that successful inflation is then possible with one of these scalar fields
identified as the inflaton. While our approach is derived in the Riemannian
geometry with $\omega_\mu$ introduced to avoid ghosts, the natural framework is
that of Weyl geometry which for the same matter spectrum is shown to generate
the same Lagrangian, up to a total derivative.
|
Scalar and Tensor Inhomogeneities from Dimensional Decoupling: We discuss some perturbative techniques suitable for the gauge-invariant
treatment of the scalar and tensor inhomogeneities of an anisotropic and
homogeneous background geometry whose spatial section naturally decomposes into
the direct product of two maximally symmetric Eucledian manifolds, describing a
general situation of dimensional decoupling in which $d$ external dimensions
evolve (in conformal time) with scale factor $a(\eta)$ and $n$ internal
dimensions evolve with scale factor $b(\eta)$. We analyze the growing mode
problem which typically arises in contracting backgrounds and we focus our
attention on the situation where the amplitude of the fluctuations not only
depends on the external space-time but also on the internal spatial
coordinates. In order to illustrate the possible relevance of this analysis we
compute the gravity waves spectrum produced in some highly simplified model of
cosmological evolution and we find that the spectral amplitude, whose magnitude
can be constrained by the usual bounds applied to the stochastic gravity waves
backgrounds, depends on the curvature scale at which the compactification
occurs and also on the typical frequency of the internal excitations.
|
IIB matrix model, bosonic master field, and emergent spacetime: The IIB matrix model has been suggested as a particular formulation of
nonperturbative superstring theory (M-theory). It has now been realized that an
emerging classical spacetime may reside in its large-$N$ master field. This
bosonic master field can, in principle, give rise to Minkowski and
Robertson-Walker spacetimes. The outstanding task is to solve the bosonic
master-field equation, which is essentially an algebraic equation. In this
article, we present new results for the $(D,\,N)=(10,\,4)$ bosonic master-field
equation of the IIB matrix model, where $D$ is the number of bosonic matrices
and $N$ the matrix size. We also give, in a self-contained appendix, explicit
results for critical points of the effective bosonic action. The main physics
application of the (dimensionless) IIB matrix model may be in providing a
(conformal) phase that replaces the Friedmann big bang singularity.
|
Generalized Dirichlet Branes and Zero-modes: We investigate the effective dynamics of an arbitrary Dirichlet p-brane, in a
path-integral formalism, by incorporating the massless excitations of closed
string modes in open bosonic string theory. It is shown that the closed string
background fields in the bosonic sector of type II theories induce invariant
extrinsic curvature on the world-volume. In addition, the curvature can be seen
to be associated with a divergence at the boundary of string world-sheet. The
re-normalization of the collective coordinates, next to leading order in its
derivative expansion, is performed to handle the divergence and the effective
dynamics is encoded in Dirac-Born-Infeld action. Furthermore, the collective
dynamics is generalized to include appropriate fermionic partners in type I
super-string theory. The role of string modes is reviewed in terms of the
collective coordinates and the gauge theory on the world-volume is argued to be
non-local in presence of the U(1) invariant field strength.
|
On supersymmetric $D6$-$\bar D 6$ systems with magnetic fields: We study systems of $D6$ and $\bar D 6$ branes with non zero world-volume
magnetic fields in the weak coupling limit. We find two configurations for
which the conditions for absence of tachyons in the spectra coincide exactly
with those found in the low energy effective theory approach, for the systems
to preserve 1/8 of the supersymmetries of the Type $IIA$ string theory vacuum.
These conditions give rise to a four-parameter family of solutions in each
case. We present further evidence of the stability of these systems by
computing the lowest order interaction amplitude, verifying the no force
condition as well as the supersymmetric character of the spectrum.
|
Wave Function Evolution of a Dissipative System: For a dissipative system with Ohmic friction, we obtain a simple and exact
solution for the wave function of the system plus the bath. It is described by
the direct product in two independent Hilbert space. One of them is described
by an effective Hamiltonian, the other represents the effect of the bath, i.e.,
the Brownian motion, thus clarifying the structure of the wave function of the
system whose energy is dissipated by its interaction with the bath. No path
integral technology is needed in this treatment. The derivation of the
Weisskopf-Wigner line width theory follows easily.
|
Higher categorical symmetries and gauging in two-dimensional spin
systems: We present a framework to systematically investigate higher categorical
symmetries in two-dimensional spin systems. Though exotic, such generalised
symmetries have been shown to naturally arise as dual symmetries upon gauging
invertible symmetries. Our framework relies on an approach to dualities whereby
dual quantum lattice models only differ in a choice of module 2-category over
some input fusion 2-category. Given an arbitrary two-dimensional spin system
with an ordinary symmetry, we explain how to perform the (twisted) gauging of
any of its sub-symmetries. We then demonstrate that the resulting model has a
symmetry structure encoded into the Morita dual of the input fusion 2-category
with respect to the corresponding module 2-category. We exemplify this approach
by specialising to certain finite group generalisations of the transverse-field
Ising model, for which we explicitly define lattice symmetry operators
organised into fusion 2-categories of higher representations of higher groups.
|
Static Black Hole and Vacuum Energy: Thin Shell and Incompressible Fluid: With the back reaction of the vacuum energy-momentum tensor consistently
taken into account, we study static spherically symmetric black-hole-like
solutions to the semi-classical Einstein equation. The vacuum energy is assumed
to be given by that of 2-dimensional massless scalar fields, as a widely used
model in the literature for black holes. The solutions have no horizon.
Instead, there is a local minimum in the radius. We consider thin shells as
well as incompressible fluid as the matter content of the black-hole-like
geometry. The geometry has several interesting features due to the back
reaction of vacuum energy. In particular, Buchdahl's inequality can be violated
without divergence in pressure, even if the surface is below the Schwarzschild
radius. At the same time, the surface of the star can not be far below the
Schwarzschild radius for a density not much higher than the Planck scale, and
the proper distance from its surface to the origin can be very short even for
very large Schwarzschild radius. The results also imply that, contrary to the
folklore, in principle the Boulware vacuum can be physical for black holes.
|
Quantum Field Theories With Compact Noncommutative Extra Dimensions: We study field theories on spaces with additional compact noncommutative
dimensions. As an example, we study \phi^3 on R^{1,3}\times T^{2}_\theta using
perturbation theory. The infrared divergences in the noncompact theory give
rise to unusual dynamics for the mode of \phi which is constant along the
torus. Correlation functions involving this mode vanish. Moreover, we show that
the spectrum of Kaluza-Klein excitations can be very different from the
analogous commuting theory. There is an additional contribution to the
Kaluza-Klein mass formula that resembles the contribution of winding states in
string theory. We also consider the effect of noncommutativity on the four
dimensional Kaluza-Klein excitations of a six dimensional gauge field.
|
A Course on Noncommutative Geometry in String Theory: In this pedagogical mini course the basics of the derivation of the
noncommutative structures appearing in string theory are reviewed. First we
discuss the well established appearance of the noncommutative Moyal-Weyl
star-product in the correlation functions of open string vertex operators on a
magnetized D-brane. Second, we will review the most recent attempts to
generalize these concepts to the closed string moving in a nongeometric flux
background.
|
Conformal inflation with chameleon coupling: We investigate the possibility that the inflaton, in particular in conformal
inflation models, is also a chameleon, i.e. that it couples to the energy
density of some heavy non-relativistic matter present during inflation. We find
new and interesting attractor behaviours, either prolonging inflation, or
changing the observables $n_s,r$, depending on the sign of the chameleon
coupling exponent. We also check that the chameleon coupling with the heavy
matter field strongly suppress entropy modes during inflation.
|
Minimal Affinizations of Representations of quantum groups: the
U_q(g)--module structure: We describe the underlying U_q(g)--module structure of representations of
quantum affine algebras.
|
Vacuum energy and relativistic invariance: It is argued that the zero-point energies of free quantum fields diverge at
most quadratically and not quartically, as is generally believed. This is a
consequence of the relativistic invariance which requires that the energy
density of the vacuum $\rho$ and its pressure $p$ satisfy $\rho=-p$. The
usually obtained quartic divergence is an artifact of the use of a noninvariant
regularization which violates this relation. One consequence of our results is
that the zero-point energies of free massless fields vanish. Implications for
the cosmological constant problem are briefly discussed.
|
2-simplexes and superconformal central charges: The superconformal central charge is an important quantity for theories
emerging from string theory geometrical implementation of Quantum Field Theory
since it is linked, for example, to the scaling dimension of fields. Butti and
Zaffaroni construction of the central charge for toric Calabi-Yau threefold
geometries is a powerful tool but its implementation could be quite tricky.
Here we present an equivalent new construction based on a 2-simplexes
decomposition of the toric diagram.
|
Exact conserved quantities on the cylinder I: conformal case: The nonlinear integral equations describing the spectra of the left and right
(continuous) quantum KdV equations on the cylinder are derived from integrable
lattice field theories, which turn out to allow the Bethe Ansatz equations of a
twisted ``spin -1/2'' chain. A very useful mapping to the more common nonlinear
integral equation of the twisted continuous spin $+1/2$ chain is found. The
diagonalization of the transfer matrix is performed. The vacua sector is
analysed in detail detecting the primary states of the minimal conformal models
and giving integral expressions for the eigenvalues of the transfer matrix.
Contact with the seminal papers \cite{BLZ, BLZ2} by Bazhanov, Lukyanov and
Zamolodchikov is realised. General expressions for the eigenvalues of the
infinite-dimensional abelian algebra of local integrals of motion are given and
explicitly calculated at the free fermion point.
|
Spin-3/2 and spin-2 charged massive states in a constant electromagnetic
background: We develop in components the superspace action obtained in arXiv:2110.07623
describing the first massive level of the open charged superstring in a flat
four-dimensional spacetime. In the absence of an electromagnetic background, we
show how the Rarita-Schwinger and Fierz-Pauli Lagrangians are retrieved for
spin-3/2 and 2, respectively. We then write different forms of the action in
the presence of the electromagnetic background. The resulting equations of
motion describe the propagation of fields of charged spin-3/2 and spin-1/2 on
the one hand, and spin-2, 1 and 0 on the other.
|
An analytic Lifshitz black hole: A Lifshitz point is described by a quantum field theory with anisotropic
scale invariance (but not Galilean invariance). In arXiv:0808.1725, gravity
duals were conjectured for such theories. We construct analytically a black
hole which asymptotes to a vacuum Lifshitz solution; this black hole solves the
equations of motion of some simple (but somewhat strange) extensions of the
models of arXiv:0808.1725. We study its thermodynamics and scalar response
functions. The scalar wave equation turns out to be exactly solvable.
Interestingly, the Green's functions do not exhibit the ultralocal behavior
seen previously in the free Lifshitz scalar theory.
|
Quantum Gravitational Corrections to Particle Creation by Black Holes: We calculate quantum gravitational corrections to the amplitude for the
emission of a Hawking particle by a black hole. We show explicitly how the
amplitudes depend on quantum corrections to the exterior metric (quantum hair).
This reveals the mechanism by which information escapes the black hole. The
quantum state of the black hole is reflected in the quantum state of the
exterior metric, which in turn influences the emission of Hawking quanta.
|
Phases of N=2 Necklace Quivers: We classify the phases of N=2 elliptic models in terms of their global
properties i.e. the spectrum of line operators. We show the agreement between
the field theory and the M-theory analysis and how the phases form orbits under
the action of the S-duality group which corresponds to the mapping class group
of the Riemann surface in M-theory.
|
An étude of momentum space scalar amplitudes in AdS: In this paper, we explore momentum space approach to computing scalar
amplitudes in Anti-de Sitter space. We show that the algorithm derived by
Arkani-Hamed, Benincasa, and Postnikov for cosmological wavefunctions can be
straightforwardly adopted for AdS transition amplitudes in momentum space,
allowing one to bypass bulk point integrations. We demonstrate the utility of
this approach in AdS by presenting several explicit results both at tree and
loop level.
|
N=1/2 Global SUSY: R-Matrix Approach: R-matrix method is used to construct supersymmetric extensions of theta -
Euclidean group preserving N = 1/2 supersymmetry and its three- parameter
generalization. These quantum symmetry supergroups can be considered as global
counterparts of appropriately twisted Euclidean superalgebras. The
corresponding generalized global symmetry transformations act on deformed
superspaces as the usual ones do on undeformed spaces. However, they depend on
non(anti)commuting parameters satisfying (anti)commutation relations defined by
relevant R matrix.
|
Derivation of the Konishi anomaly relation from Dijkgraaf-Vafa with
(Bi-)fundamental matters: We explicitly write down the Feynman rules following the work of Dijkfraaf,
Vafa and collaborators for N=1 super Yang-Mills having products of SU groups as
the gauge group and matter chiral superfields in adjoint, fundamental, and
bi-fundamental representations without baryonic perturbations. As an
application of this, we show expectation values calculated by these methods
satisfy the Konishi anomaly relation.
|
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