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Chiral Duals of Non-Chiral SUSY Gauge Theories: We study $N=1$ SUSY gauge theories in four dimensions with gauge group
$Spin(7)$ and $N_f$ flavors of quarks in the spinorial representation. We find
that in the range $6< N_f < 15$, this theory has a long distance description in
terms of an $SU(N_f-4)$ gauge theory with a symmetric tensor and $N_f$
antifundamentals. As a spin-off, we obtain by deforming along a flat direction
a dual description of the theories based on the exceptional gauge group $G_2$
with $N_f$ fundamental flavors of quarks.
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On Entropy Function for Supersymmetric Black Rings: The entropy function for five-dimensional supersymmetric black rings, which
are solutions of $U(1)^{3}$ minimal supergravity, is calculated via both
on-shell and off-shell formalism. We find that at the tree level, the entropy
function obtained from both perspectives can reproduce the Bekenstein-Hawking
entropy. We also compute the higher order corrections to the entropy arising
form five-dimensional Gauss-Bonnet term as well as supersymmetric $R^{2}$
completion respectively and compare the results with previous microscopic
calculations.
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The phase diagram of an Ising model on a polymerized random surface: We construct a random surface model with a string susceptibility exponent one
quarter by taking an Ising model on a random surface and introducing an
additional degree of freedom which amounts to allowing certain outgrowths on
the surfaces. Fine tuning the Ising temperature and the weight factor for
outgrowths we find a triple point where the susceptibility exponent is one
quarter. At this point magnetized and nonmagnetized gravity phases meet a
branched polymer phase.
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Turbulent meson condensation in quark deconfinement: In a QCD-like strongly coupled gauge theory at large N_c, using the AdS/CFT
correspondence, we find that heavy quark deconfinement is accompanied by a
coherent condensation of higher meson resonances. This is revealed in
non-equilibrium deconfinement transitions triggered by static, as well as,
quenched electric fields even below the Schwinger limit. There, we observe a
"turbulent" energy flow to higher meson modes, which finally results in the
quark deconfinement. Our observation is consistent with seeing deconfinement as
a condensation of long QCD strings.
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Ten Dimensional Black Hole and the D0-brane Threshold Bound State: We discuss the ten dimensional black holes made of D0-branes in the regime
where the effective coupling is large, and yet the 11D geometry is unimportant.
We suggest that these black holes can be interpreted as excitations over the
threshold bound state. Thus, the entropy formula for the former is used to
predict a scaling region of the wave function of the latter. The horizon radius
and the mass gap predicted in this picture agree with the formulas derived from
the classical geometry.
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A New Algorithm for Numerical Calculation of Link Invariants: We propose a new method for numerical calculation of link plynomials for
knots given in 3 dimensions. We calculate derivatives of the Jones polynomial
in a computational time proportional to $N^{\alpha}$ with respect to the system
size $N$ . This method gives a new tool for determining topology of knotted
closed loops in three dimensions using computers.
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The Gelaton Scenario: Equilateral non-Gaussianity from multi-field
dynamics: The distinctive features of single field inflationary models with non-minimal
kinetic terms, like Dirac-Born-Infeld and k-inflation, can be captured by more
familiar multiple field inflationary systems of the type that typically arise
in low energy supergravity models. At least one heavy field, which we call the
gelaton, has an effective potential which depends on the kinetic energy of the
inflaton. Integrating out the gelaton gives rise to an effectively single field
system for which the speed of sound for the adiabatic fluctuations is reduced,
generating potentially observable equilateral non-Gaussianity, while causing
negligible isocurvature fluctuations. This mechanism is only active if there is
a relatively tight coupling between the gelaton and the inflaton, and this puts
an upper limit on the mass of the gelaton for which the inflaton-gelaton system
remains weakly coupled. This approach gives a UV-completable framework for
describing large classes of k-inflationary behavior.
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Singular 7-manifolds with G_2 holonomy and intersecting 6-branes: A 7-manifold with G_2 holonomy can be constructed as a R^3 bundle over a
quaternionic space. We consider a quaternionic base space which is singular and
its metric depends on three parameters, where one of them corresponds to an
interpolation between S^4 and CP^2 or its non-compact analogs. This 4-d
Einstein space has four isometries and the fixed point set of a generic Killing
vector is discussed. When embedded into M-theory the compactification over a
given Killing vector gives intersecting 6-branes as IIA configuration and we
argue that membrane instantons may resolve the curvature singularity.
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On Dijkgraaf-Witten Type Invariants: We explicitly construct a series of lattice models based upon the gauge group
$Z_{p}$ which have the property of subdivision invariance, when the coupling
parameter is quantized and the field configurations are restricted to satisfy a
type of mod-$p$ flatness condition. The simplest model of this type yields the
Dijkgraaf-Witten invariant of a $3$-manifold and is based upon a single link,
or $1$-simplex, field. Depending upon the manifold's dimension, other models
may have more than one species of field variable, and these may be based on
higher dimensional simplices.
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De Rham Cohomology of $CP^{1}$ model with Hopf term: We investigate the $CP^{1}$ model possessing the Hopf term which respects the
second class constraints and admits the well defined the BRST operator $Q$.
Using the operator $Q$, we explicitly construct its de Rham cohomology group by
deriving the ensuing quotient group via both the collections of all $Q$-closed
and $Q$-exact ghost number $p$-forms. Moreover, we study the $CP^{1}$ model
without the Hopf term to evaluate the ensuing effect of the Hopf term on the
cohomology group. We find that the Hopf term effects on the de Rham cohomology
originate from the Hilbert space modified by this Hopf term.
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Comment on "Scaling Hypothesis for the Spectral Densities in the
Nonlinear Sigma Model": We comment on the recent paper by Balog and Niedermaier [hep-th/9701156].
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Reformulation of QCD in the language of general relativity: It is shown that there exists such collection of variables that the standard
QCD Lagrangian can be represented as the sum of usual Palatini Lagrangian for
Einstein general relativity and the Lagrangian of matter and some other fields
where the tetrad fields and the metric are constructed from initial $SU(3)$
Yang - Mills fields.
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Reflections and spinors on manifolds: This paper reviews some recent work on (s)pin structures and the Dirac
operator on hypersurfaces (in particular, on spheres), on real projective
spaces and quadrics. Two approaches to spinor fields on manifolds are compared.
The action of space and time reflections on spinors is discussed, also for
two-component (chiral) spinors.
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Recursion and worldsheet formulae for 6d superamplitudes: Recently two of the authors presented a spinorial extension of the scattering
equations, the `polarized scattering equations' that incorporates spinor
polarization data. These led to new worldsheet amplitude formulae for a variety
of gauge, gravity and brane theories in six dimensions that naturally
incorporate fermions and directly extend to maximal supersymmetry. This paper
provides a number of improvements to the original formulae, together with
extended details of the construction, examples and full proofs of some of the
formulae by BCFW recursion and factorization. We show how our formulae reduce
to corresponding formulae for maximally supersymmetric gauge, gravity and brane
theories in five and four dimensions. In four dimensions our framework
naturally gives the twistorial version of the 4d ambitwistor string, giving new
insights into the nature of the refined and polarized scattering equations they
give rise to, and on the relations between its measure and the CHY measure. Our
formulae exhibit a natural double-copy structure being built from
`half-integrands'. We give further discussion of the matrix of theories and
formulae to which our half-integrands give rise, including controversial
formulae for amplitudes involving Gerbes.
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Scale-invariant cosmological perturbations from Horava-Lifshitz gravity
without inflation: Based on the renormalizable theory of gravitation recently proposed by
Horava, we present a simple scenario to generate almost scale-invariant,
super-horizon curvature perturbations. The anisotropic scaling with dynamical
critical exponent z=3 implies that the amplitude of quantum fluctuations of a
free scalar field generated in the early epoch of the expanding universe is
insensitive to the Hubble expansion rate and, thus, scale-invariant. Those
fluctuations are later converted to curvature perturbations by the curvaton
mechanism or/and the modulated decay of heavy particles/oscillating fields.
This scenario works, for example, for power law expansion a\propto t^p with
p>1/3 and, thus, does not require inflation. Also, this scenario does not rely
on any additional assumptions such as the detailed balance condition.
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General Solution of the WZNW System and 2D Induced Gravity in Curved
Space-time: We find the general solution of the equations of motion for the WZNW system
in curved space-time for arbitrary external gauge fields. Using the connection
between the WZNW system for $SL(2,R)$ group and 2D induced gravity we obtain
the general solution of the equations of motion for 2D induced gravity in
curved space-time from that of the WZNW system. We independently presented the
direct solution of 2D induced gravity equations of motion and obtain the same
result.
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On disc-with-hole and disc-with-handle partition functions in bosonic
string theory: Higher genus partition functions of string world sheets with boundaries are
relevant, e.g. for computation of quantum corrections to Wilson loop
expectation values. As a preparation for a possible study of strings in curved
space like AdS here we consider examples of genus one partition functions of
string world-sheets ending on a circle in the bosonic string theory in flat
space. We begin with the partition function for annular topology, writing it as
an integral over the modulus of the annulus. In the process, we compute the
determinant of the Laplacian on the annulus for Dirichlet-Dirichlet and
Dirichlet-Neumann boundary conditions. We then consider the case of the
disc-with-handle topology using the gluing method. We first write the partition
function using a Schottky parameterisation of the moduli space and then as an
integral over the period matrix.
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Analytical approaches to 2D CDT coupled to matter: We review some recent results by Ambjorn et al. (1202.4435) and the authors
(1202.4322,1203.5034) in which multicritical points of the CDT matrix model
were found and in a particular example identified with a hard dimer model. This
identification requires solving the combinatorial problem of counting
configurations of dimers on CDTs.
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Quantum 3D Tensionless String in Light-cone Gauge: We discuss the quantization of a tensionless closed string in light-cone
gauge. It is known that by using a Hamiltonian BRST scheme the tensionless
p-branes have no Lorentz anomaly in any space-time dimensions and no anomaly of
space-time conformal symmetry in two dimensions. In this paper, we show that
tensionless 3d strings in light-cone gauge also have no anomaly of space-time
conformal symmetry. We also study the spectrum of a tensionless 3d closed
string.
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Decoupling Dark Energy from Matter: We examine the embedding of dark energy in high energy models based upon
supergravity and extend the usual phenomenological setting comprising an
observable sector and a hidden supersymmetry breaking sector by including a
third sector leading to the acceleration of the expansion of the universe. We
find that gravitational constraints on the non-existence of a fifth force
naturally imply that the dark energy sector must possess an approximate shift
symmetry. When exact, the shift symmetry provides an example of a dark energy
sector with a runaway potential and a nearly massless dark energy field whose
coupling to matter is very weak, contrary to the usual lore that dark energy
fields must couple strongly to matter and lead to gravitational
inconsistencies. Moreover, the shape of the potential is stable under one-loop
radiative corrections. When the shift symmetry is slightly broken by higher
order terms in the Kahler potential, the coupling to matter remains small.
However, the cosmological dynamics are largely affected by the shift symmetry
breaking operators leading to the appearance of a minimum of the scalar
potential such that dark energy behaves like an effective cosmological constant
from very early on in the history of the universe.
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Exact Half-BPS Black Hole Entropies in CHL Models from Rademacher Series: The microscopic spectrum of half-BPS excitations in toroidally compactified
heterotic string theory has been computed exactly through the use of results
from analytic number theory. Recently, similar quantities have been understood
macroscopically by evaluating the gravitational path integral on the M-theory
lift of the AdS2 near-horizon geometry of the corresponding black hole. In this
paper, we generalize these results to a subset of the CHL models, which include
the standard compactification of IIA on $K3\times T^2$ as a special case. We
begin by developing a Rademacher-like expansion for the Fourier coefficients of
the partition functions for these theories, which are modular forms for
congruence subgroups. We then interpret these results in a macroscopic setting
by evaluating the path integral for the reduced-rank $\mathcal{N} = 4$
supergravities described by these CFTs.
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Berenstein-Zelevinsky triangles, elementary couplings and fusion rules: We present a general scheme for describing su(N)_k fusion rules in terms of
elementary couplings, using Berenstein-Zelevinsky triangles. A fusion coupling
is characterized by its corresponding tensor product coupling (i.e. its
Berenstein-Zelevinsky triangle) and the threshold level at which it first
appears. We show that a closed expression for this threshold level is encoded
in the Berenstein-Zelevinsky triangle and an explicit method to calculate it is
presented. In this way a complete solution of su(4)_k fusion rules is obtained.
|
Critical gravity in the Chern-Simons modified gravity: We perform the perturbation analysis of the Chern-Simons modified gravity
around the AdS$_4$ spacetimes (its curvature radius $\ell$) to obtain the
critical gravity. In general, we could not obtain an explicit form of perturbed
Einstein equation which shows a massive graviton propagation clearly, but for
the Kerr-Schild perturbation and Chern-Simons coupling $\theta=kx/y$, we find
the AdS wave as a single massive solution to the perturbed Einstein equation.
Its mass squared is given by $M^2=[-9+(2\ell^2/k-1)^2]/4\ell^2$. At the
critical point of $M^2=0(k=\ell^2/2)$, the solution takes the log-form and the
linearized excitation energies vanish.
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Non-relativistic Spinning Particle in a Newton-Cartan Background: We construct the action of a non-relativistic spinning particle moving in a
general torsionless Newton-Cartan background. The particle does not follow the
geodesic equations, instead the motion is governed by the non-relativistic
analog of Papapetrou equation. The spinning particle is described in terms of
Grassmann variables. In the flat case the action is invariant under the
non-relativistic analog of space-time vector supersymmetry.
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Non-geometric Calabi-Yau Backgrounds and K3 automorphisms: We consider compactifications of type IIA superstring theory on mirror-folds
obtained as K3 fibrations over two-tori with non-geometric monodromies
involving mirror symmetries. At special points in the moduli space these are
asymmetric Gepner models. The compactifications are constructed from
non-geometric automorphisms that arise from the diagonal action of an
automorphism of the K3 surface and of an automorphism of the mirror surface. We
identify the corresponding gaugings of N=4 supergravity in four dimensions, and
show that the minima of the potential describe the same four-dimensional
low-energy physics as the worldsheet formulation in terms of asymmetric Gepner
models. In this way, we obtain a class of Minkowski vacua of type II string
theory which preserve N=2 supersymmetry. The massless sector consists of N=2
supergravity coupled to 3 vector multiplets, giving the STU model. In some
cases there are additional massless hypermultiplets.
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Pions as Gluons in Higher Dimensions: We derive the nonlinear sigma model as a peculiar dimensional reduction of
Yang-Mills theory. In this framework, pions are reformulated as
higher-dimensional gluons arranged in a kinematic configuration that only
probes cubic interactions. This procedure yields a purely cubic action for the
nonlinear sigma model which exhibits a symmetry enforcing color-kinematics
duality. Remarkably, the associated kinematic algebra originates directly from
the Poincare algebra in higher dimensions. Applying the same construction to
gravity yields a new quartic action for Born-Infeld theory and, applied once
more, a cubic action for the special Galileon theory. Since the nonlinear sigma
model and special Galileon are subtly encoded in the cubic sectors of
Yang-Mills theory and gravity, respectively, their double copy relationship is
automatic.
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Science in a Very Large Universe: As observers of the universe we are quantum physical systems within it. If
the universe is very large in space and/or time, the probability becomes
significant that the data on which we base predictions is replicated at other
locations in spacetime. The physical conditions at these locations that are not
specified by the data may differ. Predictions of our future observations
therefore require an assumed probability distribution (the xerographic
distribution) for our location among the possible ones. It is the combination
of basic theory plus the xerographic distribution that can be predictive and
testable by further observations.
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Parafermions, $W$ Strings and their BRST Charges: We show how to relate the parafermions that occur in the $W_3$ string to the
standard construction of parafermions. This result is then used to show that
one of the screening charges that occurs in parafermionic theories is precisely
the non-trivial part of the $W_3$ string BRST charge. A way of generalizing
this pattern for a $W_N$ string is explained. This enables us to construct the
full BRST charge for a $W_{2,N}$ string and to prove the relation of such a
string to the algebra $W_{N-1}$ for arbitrary $N$, We also show how to
calculate part of the BRST charge for a $W_N$ string, and we explain how our
method might be extended to obtain the full BRST charge for such a string.
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Accelerating cosmologies from non-local higher-derivative gravity: We study accelerating cosmological solutions of a general class of non-linear
gravities which depend on Gauss-Bonnet and other higher derivative invariants.
To achieve this goal a local formulation with auxiliary scalars for arbitrary
higher-derivative non-local gravity is developed. It is demonstrated that
non-local Gauss-Bonnet gravity can be reduced, in the local formulation, to a
model of string-inspired scalar-Gauss-Bonnet gravity. A natural unification, in
the theory here developed, of the early-time inflation epoch with a late-time
acceleration stage can also be realized.
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Holomorphic variables in magnetized brane models with continuous Wilson
lines: We analyze the action of the target-space modular group in toroidal type IIB
orientifold compactifications with magnetized D-branes and continuous Wilson
lines. The transformation of matter fields agree with that of twisted fields in
heterotic compactifications, constituting a check of type I/heterotic duality.
We identify the holomorphic N = 1 variables for these compactifications. Matter
fields and closed string moduli are both redefined by open string moduli. The
redefinition of matter fields can be read directly from the perturbative Yukawa
couplings, whereas closed string moduli redefinitions are obtained from D-brane
instanton superpotential couplings. The resulting expressions reproduce and
generalize, in the presence of internal magnetic fields, previous results in
the literature.
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Introduction to a Non-Commutative Version of the Standard Model: This article provides a basic introduction to some concepts of
non-commutative geometry. The importance of quantum groups and quantum spaces
is stressed. Canonical non-commutativity is understood as an approximation to
the quantum group case. Non-commutative gauge theory and the non-commutative
Standard Model are formulated on a space-time satisfying canonical
non-commutativity relations. We use *-formalism and Seiberg-Witten maps.
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New results on integrable structure of conformal field theory: We explain how to incorporate the action of local integrals of motion into
the fermionic basis for the sine-Gordon model and its UV CFT. The examples up
to the level 4 are presented. Numerical computation support the results.
Possible applications are discussed.
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Konishi Form Factor at Three Loop in ${\cal N}=4$ SYM: We present the first results on the third order corrections to on-shell form
factor (FF) of the Konishi operator in ${\cal N}=4$ supersymmetric Yang-Mills
theory using Feynman diagrammatic approach in modified dimensional reduction
($\overline {DR}$) scheme. We show that it satisfies KG equation in $\overline
{DR}$ scheme while the result obtained in four dimensional helicity (FDH)
scheme needs to be suitably modified not only to satisfy the KG equation but
also to get the correct ultraviolet (UV) anomalous dimensions. We find that the
cusp, soft and collinear anomalous dimensions obtained to third order are same
as those of the FF of the half-BPS operator confirming the universality of the
infrared (IR) structures of on-shell form factors. In addition, the highest
transcendental terms of the FF of Konishi operator are identical to those of
half-BPS operator indicating the probable existence of deeper structure of the
on-shell FF. We also confirm the UV anomalous dimensions of Konishi operator up
to third order providing a consistency check on the both UV and universal IR
structures in ${\cal N}=4$.
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On the large spin limit of twist operators in N=4 SYM: The long range Bethe Ansatz solution of the mixing problem in N=4 SYM allows
to compute in a very efficient way multiloop anomalous dimensions of various
composite operators. In the case of sl(2) twist operators it is important to
obtain closed expressions for the anomalous dimensions in terms of the Lorentz
spin. Conjectures are available altough analytical proofs are missing beyond
one-loop. In this paper, we will present a method to expand at large spin the
solution of the long range Baxter equation in twist 2 and 3. We will also
propose sum rules for special singlet states at higher twist.
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A gauge invariant exact renormalization group I: A manifestly gauge invariant continuous renormalization group flow equation
is constructed for pure SU(N) gauge theory. The formulation makes sense without
gauge fixing and manifestly gauge invariant calculations may thus be carried
out. The flow equation is naturally expressed in terms of fluctuating Wilson
loops, with the effective action appearing as an integral over a `gas' of
Wilson loops. At infinite N, the effective action collapses to a path integral
over the trajectory of a single particle describing one Wilson loop. We show
that further regularization of these flow equations is needed. (This is
introduced in part II.)
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Quarter BPS classified by Brauer algebra: We analyse the one-loop dilatation operator with the help of the Brauer
algebra. We find some BPS operators in N=4 SYM, which are labelled by
irreducible representations of the Brauer algebra. Some of them are quarter BPS
operators. The result includes full non-planar corrections. Our construction
and proof are based on simple algebraic arguments and are carried out for any
number of fields.
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Holographic Entanglement Entropy for the Most General Higher Derivative
Gravity: The holographic entanglement entropy for the most general higher derivative
gravity is investigated. We find a new type of Wald entropy, which appears on
entangling surface without the rotational symmetry and reduces to usual Wald
entropy on Killing horizon. Furthermore, we obtain a formal formula of HEE for
the most general higher derivative gravity and work it out exactly for some
squashed cones. As an important application, we derive HEE for gravitational
action with one derivative of the curvature when the extrinsic curvature
vanishes. We also study some toy models with non-zero extrinsic curvature. We
prove that our formula yields the correct universal term of entanglement
entropy for 4d CFTs. Furthermore, we solve the puzzle raised by Hung, Myers and
Smolkin that the logarithmic term of entanglement entropy derived from Weyl
anomaly of CFTs does not match the holographic result even if the extrinsic
curvature vanishes. We find that such mismatch comes from the `anomaly of
entropy' of the derivative of curvature. After considering such contributions
carefully, we resolve the puzzle successfully. In general, we need to fix the
splitting problem for the conical metrics in order to derive the holographic
entanglement entropy. We find that, at least for Einstein gravity, the
splitting problem can be fixed by using equations of motion. How to derive the
splittings for higher derivative gravity is a non-trivial and open question.
For simplicity, we ignore the splitting problem in this paper and find that it
does not affect our main results.
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Yang-Baxter equation, symmetric functions and Grothendieck polynomials: New development of the theory of Grothendieck polynomials, based on an
exponential solution of the Yang-Baxter equation in the algebra of projectors
are given.
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Spontaneous Conformal Symmetry Breaking and Quantum Quadratic Gravity: We investigate several quantum phenomena related to quadratic gravity after
rewriting the general fourth-order action in a more convenient form that is
second-order in derivatives and produces only first-class constraints in phase
space. We find that a Higgs mechanism may occur in the conformally invariant
subset of the general quadratic action if the theory is conformally coupled to
a scalar field that acquires a non-zero vacuum expectation value and
spontaneously breaks the conformal symmetry. Then, in the broken phase, the
originally massless spin-2 ghost may absorb both the scalar and vector fields
to become massive. We also perform a BRST quantization of second-order
quadratic gravity in the covariant operator formalism and discuss conditions
under which unitarity of the full interacting quantum theory may be
established.
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Point Particle with Extrinsic Curvature as a Boundary of a Nambu-Goto
String: Classical and Quantum Model: It is shown how a string living in a higher dimensional space can be
approximated as a point particle with squared extrinsic curvature. We consider
a generalized Howe-Tucker action for such a "rigid particle" and consider its
classical equations of motion and constraints. We find that the algebra of the
Dirac brackets between the dynamical variables associated with velocity and
acceleration contains the spin tensor. After quantization, the corresponding
operators can be represented by the Dirac matrices, projected onto the
hypersurface that is orthogonal to the direction of momentum. A condition for
the consistency of such a representation is that the states must satisfy the
Dirac equation with a suitable effective mass. The Pauli-Lubanski vector
composed with such projected Dirac matrices is equal to the Pauli-Lubanski
vector composed with the usual, non projected, Dirac matrices, and its
eigenvalues thus correspond to spin one half states.
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The origin of discrete symmetries in F-theory models: While non-abelian groups are undoubtedly the cornerstone of Grand Unified
Theories (GUTs), phenomenology shows that the role of abelian and discrete
symmetries is equally important in model building. The latter are the
appropriate tool to suppress undesired proton decay operators and various
flavour violating interactions, to generate a hierarchical fermion mass
spectrum, etc. In F-theory, GUT symmetries are linked to the singularities of
the elliptically fibred K3 manifolds; they are of ADE type and have been
extensively discussed in recent literature. In this context, abelian and
discrete symmetries usually arise either as a subgroup of the non-abelian
symmetry or from a non-trivial Mordell-Weil group associated to rational
sections of the elliptic fibration. In this note we give a short overview of
the current status and focus in models with rank-one Mordell-Weil group.
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Neutral Multi-Instanton as a Bridge from Weak to Strong Coupling phase
in Two Dimensional QCD: Using a contour integral representation we analyze the multi-instanton sector
in two dimensional $U(N)$ Yang-Mills theory on a sphere and argue the role of
multi-instanton in the large $N$ phase transition. In the strong coupling
region at the large $N$ , we encounter ``singular saddle point''. Because of
this situation, ``neutral'' configurations of the multi-instanton are dominant
in this region. Based on the ``neutral'' multi-instanton approximation we
numerically calculate the multi-instanton amplitude , the free energies and the
Wilson loops for finite $N$ . We also compare our results with the large $N$
exact solution of the free energy and the Wilson loop and argue some problems.
We find the ``neutral'' multi-instanton contribution bridges the gap between
weak and strong coupling phase.
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Radiation reaction for spinning black-hole scattering: Starting from the leading soft term of the 5-point amplitude, involving a
graviton and two Kerr black holes, that factorises into the product of the
elastic amplitude without the graviton and the leading soft factor, we compute
the infrared divergent contribution to the imaginary part of the two-loop
eikonal. Then, using analyticity and crossing symmetry, we determine the
radiative contribution to the real part of the two-loop eikonal and from it the
radiative part of the deflection angle for spins aligned to the orbital angular
momentum, the loss of angular momentum and the zero frequency limit of the
energy spectrum for any spin and for any spin orientation. For spin one we find
perfect agreement with recent results obtained with the supersymmetric
worldline formalism.
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AdS/BCFT correspondence and Horndeski gravity in the presence of gauge
fields: holographic paramagnetism/ferromagnetism phase transition: This paper presents a dual gravity model for a (2+1)-dimensional system with
a limit on finite charge density and temperature, which will be used to study
the properties of the holographic phase transition to
paramagnetism-ferromagnetism in the presence of Horndeski gravity terms. In our
model, the non-zero charge density is supported by a magnetic field. As a
result, the radius $\rho/B$ indicates a localized condensate, as we increase
the Horndeski gravity parameter, that is represented by $\gamma$. Furthermore,
such condensate shows quantum Hall-type behavior. This radius is also inversely
related to the total action coefficients of our model. It was observed that
increasing the Horndeski parameter decreases the critical temperature of the
holographic model and leads to the harder formation of the magnetic moment at
the bottom of the black hole. However, when removing the magnetic field, the
ferromagnetic material presents a disorder of its magnetic moments, which is
observed through the entropy of the system. We also found that at low
temperatures, spontaneous magnetization and ferromagnetic phase transition.
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One Loop Gluon Gluon Scattering in Light Cone Gauge: We calculate the one loop amplitudes for the two gluon scattering process in
light cone gauge with fermions and scalars circulating in the loop. This
extends the earlier works, in which only the gluon circulates the loop. By
putting all fields in the adjoint representation with N_f=2, N_s=6, the
scattering amplitude of gluon by gluon in the special case of N=4 Super
Yang-Mills can be obtained. The massive fermion and scalar with arbitrary
representations are also considered.
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Lagrangian formulation of classical fields within Riemann-Liouville
fractional derivatives: The classical fields with fractional derivatives are investigated by using
the fractional Lagrangian formulation.The fractional Euler-Lagrange equations
were obtained and two examples were studied.
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HS Yang-Mills-like models: a review: We review the attempt to construct massless gauge field theories in Minkowski
spacetime that go under the name of HS-YM. We present their actions and their
symmetries. We motivate their gravitational interpretation. In particular we
show how to recover the local Lorentz invariance, which is absent in the
original formulation of the theories. Then we propose a perturbative
quantization in the so-called frozen momentum frame. We discuss physical and
unphysical modes and show how to deal with them. Finally we uncover the gauge
symmetry hidden under such unphysical modes. This requires a nonlocal
reformulation of the theory, which is, however, characterized by an augmented
degree of symmetry.
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Tubular Solutions of Dirac-Born-Infeld Action on Dp-Brane Background: We use the Dirac-Born-Infeld action on Dp-brane background to find the
tubular bound state of a D2 with $m$ D0-branes and $n$ fundamental strings. The
fundamental strings may be the circular strings along the cross section of tube
or the straight strings along the axial of the tube, and tube solutions are
parallel to the geometry of Dp-brane background. Through the detailed analyses
we show that only on the D6-brane background could we find the stable tubular
solutions. These tubular configurations are prevented form collapse by the
gravitational field on the curved Dp-brane background.
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An Exact Operator That Knows Its Location: We use conformal symmetry to define an AdS$_3$ proto-field $\phi$ as an exact
linear combination of Virasoro descendants of a CFT$_2$ primary operator
$\mathcal{O}$. We find that both symmetry considerations and a gravitational
Wilson line formalism lead to the same results. The operator $\phi$ has many
desirable properties; in particular it has correlators that agree with
gravitational perturbation theory when expanded at large $c$, and that
automatically take the correct form in all vacuum AdS$_3$ geometries, including
BTZ black hole backgrounds. In the future it should be possible to use $\phi$
to probe bulk locality and black hole horizons at a non-perturbative level.
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The Deformed Matrix Model at Finite Radius and a New Duality Symmetry: The $1/x^{2}$ deformed $c=1$ matrix model is studied at finite radius and
non-zero cosmological constant. Calculational techniques are presented and
illustrated in some examples. Furthermore, a new kind of $R \rightarrow 1/R$
duality is discovered which mixes different genus.
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Topological Symmetry, Background Independence, and Matrix Models: We illustrate a physical situation in which topological symmetry, its
breakdown, space-time uncertainty principle, and background independence may
play an important role in constructing and understanding matrix models. First,
we show that the space-time uncertainty principle of string may be understood
as a manifestation of the breakdown of the topological symmetry in the large
$N$ matrix model. Next, we construct a new type of matrix models which is a
matrix model analog of the topological Chern-Simons and BF theories. It is of
interest that these topological matrix models are not only completely
independent of the background metric but also have nontrivial "p-brane"
solutions as well as commuting classical space-time as the classical solutions.
In this paper, we would like to point out some elementary and unsolved problems
associated to the matrix models, whose resolution would lead to the more
satisfying matrix model in future.
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Line defects in conformal field theory: from weak to strong coupling: Conformal field theory finds applications across diverse fields, from
statistical systems at criticality to quantum gravity through the AdS/CFT
correspondence. These theories are subject to strong constraints, enabling a
systematic non-perturbative analysis. Conformal defects provide a controlled
means of breaking the symmetry, introducing new physical phenomena while
preserving crucial benefits of the underlying conformal symmetry. This thesis
investigates conformal line defects in both the weak- and strong-coupling
regimes. Two distinct classes of models are studied. First, we focus on the
supersymmetric Wilson line in $\mathcal{N}=4$ Super Yang--Mills, which serves
as an ideal testing ground for the development of innovative techniques such as
the analytic conformal bootstrap. The second class consists of magnetic lines
in Yukawa models, which have fascinating applications in $3d$ condensed-matter
systems. These systems have the potential to emulate phenomena observed in the
Standard Model in a low-energy setting.
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Positronium collapse and the maximum magnetic field in pure QED: A maximum value for the magnetic field is determined, which provides the full
compensation of the positronium rest mass by the binding energy in the maximum
symmetry state and disappearance of the energy gap separating the
electron-positron system from the vacuum. The compensation becomes possible
owing to the falling to the center phenomenon. The maximum magnetic field may
be related to the vacuum and describe its structure.
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Unifying approaches: derivation of Balitsky hierarchy from the Lipatov
effective action: We consider a derivation of the hierarchy of correlators of ordered
exponentials directly from the Lipatov's effective action~\cite{LipatovEff}
formulated in terms of interacting ordered exponentials~\cite{OurZub}. The
derivation of the Balitsky equation~\cite{Bal} from the hierarchy is discussed
as well as the way the sub-leading eikonal corrections to the Balitsky equation
arise from the transverse field contribution and sub-leading eikonal
corrections to the quark propagator. We outline other possible applications of
the proposed calculation scheme.
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Linear $r$-matrix algebra for classical separable systems: We consider a hierarchy of the natural type Hamiltonian systems of $n$
degrees of freedom with polynomial potentials separable in general ellipsoidal
and general paraboloidal coordinates. We give a Lax representation in terms of
$2\times 2$ matrices for the whole hierarchy and construct the associated
linear $r$-matrix algebra with the $r$-matrix dependent on the dynamical
variables. A Yang-Baxter equation of dynamical type is proposed. Using the
method of variable separation we provide the integration of the systems in
classical mechanics conctructing the separation equations and, hence, the
explicit form of action variables. The quantisation problem is discussed with
the help of the separation variables.
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Gauss-Bonnet Inflation: We consider an Einstein-Scalar-Gauss-Bonnet gravitational theory, and argue
that at early times the Ricci scalar can be safely ignored. We then demonstrate
that the pure scalar-Gauss-Bonnet theory, with a quadratic coupling function,
naturally supports inflationary -- de Sitter -- solutions. During inflation,
the scalar field decays exponentially and its effective potential remains
always bounded. The theory contains also solutions where these de Sitter phases
possess a natural exit mechanism and are replaced by linearly expanding --
Milne -- phases.
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Counting Calabi-Yau Threefolds: We enumerate topologically-inequivalent compact Calabi-Yau threefold
hypersurfaces. By computing arithmetic and algebraic invariants and the
Gopakumar-Vafa invariants of curves, we prove that the number of distinct
simply connected Calabi-Yau threefold hypersurfaces resulting from
triangulations of four-dimensional reflexive polytopes is 4, 27, 183, 1,184 and
8,036 at $h^{1,1}$ = 1, 2, 3, 4, and 5, respectively. We also establish that
there are ten equivalence classes of Wall data of non-simply connected
Calabi-Yau threefolds from the Kreuzer-Skarke list. Finally, we give a
provisional count of threefolds obtained by enumerating non-toric flops at
$h^{1,1} =2$.
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AdS-CFT Correspondence in Noncommutative background, related
thermodynamics and Holographic Superconductor in Magnetic Field: In this work, we formulate a Non-Commutative (NC) extension of AdS-CFT
correspondence that is manifested in the modification of behavior of a
holographic superconductor. The noncommutativity is introduced in the model
through the NC corrected AdS charged black hole metric developed by Nicolini,
Smailagic and Spallucci. First of all we discuss thermodynamic properties of
this black hole in Euclidean formalism. In particular, we compute trace of the
boundary energy-momentum tensor which, as expected, is non-zero due to the NC
scale introduced in the model. Our findings indicate that the non-commutative
effects tend to work against the black hole hair formation. This, in turn, has
an adverse effect on the holographic superconductor by making the
superconducting phase more fragile. This is reflected in the reduced value of
the critical magnetic field and critical temperature. Finally, we comment on a
qualitative agreement between our (holographic superconductor) result and that
obtained for a conventional superconductor in NC space in a purely condensed
matter scenario. In both cases noncommutativity tends to oppose the
superconducting phase.
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M theory Branes : U duality properties and a class of new Static
Solutions: We obtain the most general static intersecting brane solutions by directly
solving the relevant equations of motion analytically and in complete
generality. These solutions reduce to the known ones in special cases, and
contain further a class of new static solutions which are horizonless. We
describe their properties and discuss their physical relevance. Along the way,
we also describe the features of the brane energy momentum tensors, the
equations of motion, and their solutions which arise as consequences of the
intersection rules and the U duality symmetries of M theory.
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Effective field theory of fluctuating wall in open systems: from a kink
in Josephson junction to general domain wall: We investigate macroscopic behaviors of fluctuating domain walls in
nonequilibrium open systems with the help of the effective field theory based
on symmetry. Since the domain wall in open systems breaks the translational
symmetry, there appears a gapless excitation identified as the Nambu-Goldstone
(NG) mode, which shows the non-propagating diffusive behavior in contrast to
those in closed systems. After demonstrating the presence of the diffusive NG
mode in the $(2+1)$-dimensional dissipative Josephson junction, we provide a
symmetry-based general analysis for open systems breaking the one-dimensional
translational symmetry. A general effective Lagrangian is constructed based on
the Schwinger-Keldysh formalism, which supports the presence of the gapless
diffusion mode in the fluctuation spectrum in the thin wall regime. Besides, we
also identify a term peculiar to the open system, which possibly leads to the
instability in the thick-wall regime or the nonlinear Kardar-Parisi-Zhang
coupling in the thin-wall regime although it is absent in the Josephson
junction.
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Strings from geometric tachyon in Rindler space and black hole
thermodynamics: The dynamics of a probe particle or wrapped brane moving in the
two-dimensional Rindler space can be described by a time-dependent tachyon
field theory. Using knowledge of tachyon condensation, we learn that the
infalling brane gets thermalised and produces open string pairs at the Hagedorn
temperature when entering into the near-horizon Rindler wedge. It is shown that
the Hagedorn temperature of the infalling brane is equal to the Hawking
temperature of the host black hole detected in the same time coordinate. The
infalling brane will decay completely into closed strings, mainly massive
modes, when it reaches the horizon in infinitely long time as observed by
observers at spatial infinity. Preliminary estimates indicate that the
degeneracy of states of the closed strings emitted from the infalling brane
should be responsible for the increased entropy in the host black hole due to
absorption of the brane.
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Massless fermions and superconductivity of string-wall composites: An axion cosmic string is known to be a chiral superconductor when the axion
couples to an electrically charged fermion. After the QCD phase transition, a
QCD axion string is attached by $N$ domain walls. We would like to elucidate
the fate of massless fermions on a global string after domain walls attached
not only in the axion model but also in general models having string-wall
composites. We investigate the Dirac equation under various string-wall
composite backgrounds both in the axion(-like) models and in the ${\cal N}=2$
supersymmetry inspired Abelian-Higgs models. We give an answer to the
elementary question of whether massless fermions exist, and if so, where they
are localized. The answer depends on fermion/boson masses in the models, and
the massless fermion can be localized either on the string, on one of the
domain walls, or in one of the vacua. We find analytic solutions for the
fermion zero mode function by which we prove the existence of the massless
fermion on the string-wall composites. We also show supercurrents flowing along
the string-wall composites and anomalous electric currents flowing in from
outside.
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Gauge Coupling Field, Currents, Anomalies and N=1 Super-Yang-Mills
Effective Actions: Working with a gauge coupling field in a linear superfield, we construct
effective Lagrangians for N=1 super-Yang-Mills theory fully compatible with the
expected all-order behaviour or physical quantities. Using the one-loop
dependence on its ultraviolet cutoff and anomaly matching or cancellation of R
and dilatation anomalies, we obtain the Wilsonian effective Lagrangian. With
similar anomaly matching or cancellation methods, we derive the effective
action for gaugino condensates, as a function of the real coupling field. Both
effective actions lead to a derivation of the NSVZ beta function from algebraic
arguments only. The extension of results to N=2 theories or to matter systems
is briefly considered. The main tool for the discussion of anomalies is a
generic supercurrent structure with 16_B+16_F operators (the S multiplet),
which we derive using superspace identities and field equations for a fully
general gauge theory Lagrangian with the linear gauge coupling superfield, and
with various U(1)_R currents. As a byproduct, we show under which conditions
the S multiplet can be improved to contain the Callan-Coleman-Jackiw
energy-momentum tensor whose trace measures the breaking of scale invariance.
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On the equivalence between topologically and non-topologically massive
abelian gauge theories: We analyse the equivalence between topologically massive gauge theory (TMGT)
and different formulations of non-topologically massive gauge theories (NTMGTs)
in the canonical approach. The different NTMGTs studied are St\"uckelberg
formulation of (A) a first order formulation involving one and two form fields,
(B) Proca theory, and (C) massive Kalb-Ramond theory. We first quantise these
reducible gauge systems by using the phase space extension procedure and using
it, identify the phase space variables of NTMGTs which are equivalent to the
canonical variables of TMGT and show that under this the Hamiltonian also get
mapped. Interestingly it is found that the different NTMGTs are equivalent to
different formulations of TMGTs which differ only by a total divergence term.
We also provide covariant mappings between the fields in TMGT to NTMGTs at the
level of correlation function.
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Comment on Shadow and Non-Shadow Extensions of the Standard Model: The models in the two papers hep-ph/0608068 and hep-ph/0701254 by Chang et
al. with the so-called shadow gauge and scalar fields are nothing but
convenient tailored versions of our model in hep-th/0403039. The same remarks
applies to the work in hep-th/0612165 by Meissner and Nicolai.
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On polynomial solutions of differential equations: A general method of obtaining linear differential equations having polynomial
solutions is proposed. The method is based on an equivalence of the spectral
problem for an element of the universal enveloping algebra of some Lie algebra
in the "projectivized" representation possessing an invariant subspace and the
spectral problem for a certain linear differential operator with variable
coefficients. It is shown in general that polynomial solutions of partial
differential equations occur; in the case of Lie superalgebras there are
polynomial solutions of some matrix differential equations, quantum algebras
give rise to polynomial solutions of finite--difference equations.
Particularly, known classical orthogonal polynomials will appear when
considering $SL(2,{\bf R})$ acting on ${\bf RP_1}$. As examples, some
polynomials connected to projectivized representations of $sl_2 ({\bf R})$,
$sl_2 ({\bf R})_q$, $osp(2,2)$ and $so_3$ are briefly discussed.
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Gravity from a fermionic condensate of a gauge theory: The most prominent realization of gravity as a gauge theory similar to the
gauge theories of the standard model comes from enlarging the gauge group from
the Lorentz group to the de Sitter group. To regain ordinary Einstein-Cartan
gravity the symmetry must be broken, which can be accomplished by known
quasi-dynamic mechanisms. Motivated by symmetry breaking models in particle
physics and condensed matter systems, we propose that the symmetry can
naturally be broken by a homogenous and isotropic fermionic condensate of
ordinary spinors. We demonstrate that the condensate is compatible with the
Einstein-Cartan equations and can be imposed in a fully de Sitter invariant
manner. This lends support, and provides a physically realistic mechanism for
understanding gravity as a gauge theory with a spontaneously broken local de
Sitter symmetry.
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Noncommutativity vs. Transversality in QED in a strong magnetic field: Quantum electrodynamics (QED) in a strong constant magnetic field is
investigated from the viewpoint of its connection with noncommutative QED. It
turns out that within the lowest Landau level (LLL) approximation the 1-loop
contribution of fermions provides an effective action with the noncommutative
U(1)_{NC} gauge symmetry. As a result, the Ward-Takahashi identities connected
with the initial U(1) gauge symmetry are broken down in the LLL approximation.
On the other hand, it is shown that the sum over the infinite number of the
higher Landau levels (HLL's) is relevant despite the fact that each
contribution of the HLL is suppressed. Owing to this nondecoupling phenomenon
the transversality is restored in the whole effective action. The kinematic
region where the LLL contribution is dominant is also discussed.
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Low-energy Chern-Simons-Proca theory: Some time ago, the infrared limit of the Abelian Chern-Simons-Proca theory
was investigated. In this letter, we show how the Chern-Simons-Proca theory can
emerge as an effective low energy theory. Our result is obtained by means of a
procedure that takes into account the proliferation, or dilution, of
topological defects presented in the system.
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$T^3$-Invariant Heterotic Hull-Strominger Solutions: We consider the heterotic string on Calabi-Yau manifolds admitting a
Strominger-Yau-Zaslow fibration. Upon reducing the system in the
$T^3$-directions, the Hermitian Yang-Mills conditions can then be reinterpreted
as a complex flat connection on $\mathbb{R}^3$ satisfying a certain co-closure
condition. We give a number of abelian and non-abelian examples, and also
compute the back-reaction on the geometry through the non-trivial
$\alpha'$-corrected heterotic Bianchi identity, which includes an important
correction to the equations for the complex flat connection. These are all new
local solutions to the Hull-Strominger system on $T^3\times\mathbb{R}^3$. We
also propose a method for computing the spectrum of certain non-abelian models,
in close analogy with the Morse-Witten complex of the abelian models.
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A Chern-Simons approach to self-dual gravity in (2+1)-dimensions and
quantisation of Poisson structure: The (2+1)-dimensional analog self-dual gravity which is obtained via
dimension reduction of the (3+1)-dimensional Holst action without reducing the
internal gauge group is studied. A Chern-Simons formulation for this theory is
constructed based on the gauge group $SL(2,\CC)_\RR\rcross \Rsix$ and maps the
3d complex self-dual dynamical variable and connection to $6d$ real variables
which combines into a $12d$ Cartan connection. Quantization is given by the
application of the combinatorial quantisation program of Chern-Simons theory.
The Poisson structure for the moduli space of flat connections on
$(SL(2,\CC)_\RR\rcross \Rsix)^{n+2g}$ which emerges in the combinatorial
description of the phase space on $\RR \times \Sigma_{g,n},$ where
$\Sigma_{g,n}$ is a genus $g$ surface with $n$ punctures is given in terms of
the classical $r$-matrix for the quantum double $D(SL(2,\CC)_\RR)$ viewed as
the double of a double $ D(SU(2)\dcross AN(2))$. This quantum double provides a
feature for quantum symmetries of the quantum theory for the model.
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Supersymmetric, fermionic solutions in three-dimensional supergravity: Building upon known supersymmetric backgrounds, we derive novel half-BPS
fermionic solutions in three-dimensional supergravity. By virtue of an
essential dependence on fermionic degrees of freedom, they possess no purely
bosonic analogue. In the Anti de Sitter case this notably includes nonsingular
solutions for which the corresponding Chern-Simons gauge field
$\mathcal{A}=\omega\pm e/L$ vanishes, providing access to configurations which
are ordinarily singular in pure gravity.
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The integral representation of solutions of KZ equation and a
modification by $\mathcal{K}$ operator insertion: A root of unity limit of the $q$-deformed Virasoro algebra is considered. The
$\widehat{sl}(2)_k$ current algebra and the integral formulas of the solutions
of the KZ equations can be realized by the $q$-deformed boson at the limit and
an additional boson. We explicitly construct the integral representation of the
four-point blocks with a $\mathcal{K}$-operator insertion.
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An effective gauge theory of fractons: perturbative and non-local
aspects: We construct, from first principles, a covariant local model for scalar
fractonic matter coupled to a symmetric tensor gauge field. The free gauge
field action is just the one of Blasi-Maggiore model. The scalar sector is a
non-trivial covariant generalization of Pretko's quartic model. Because the
model has no quadratic term in the scalar field, a direct perturbative
treatment fails. Remarkably, we demonstrate that the action can be driven to a
perturbative effective action. However, with the price of carrying non-local
interacting terms. We study the perturbative regime of the model and show that
there are at least four distinct phases in the model: One with massive
fractonic modes; one with massless fractons; a mixed phase with massive and
massless fractons; and another one where fractons cannot occur at all in the
physical spectrum.
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Integrable degenerate $\mathcal E$-models from 4d Chern-Simons theory: We present a general construction of integrable degenerate $\mathcal
E$-models on a 2d manifold $\Sigma$ using the formalism of Costello and
Yamazaki based on 4d Chern-Simons theory on $\Sigma \times \mathbb{C}P^1$. We
begin with a physically motivated review of the mathematical results of
[arXiv:2008.01829] where a unifying 2d action was obtained from 4d Chern-Simons
theory which depends on a pair of 2d fields $h$ and $\mathcal L$ on $\Sigma$
subject to a constraint and with $\mathcal L$ depending rationally on the
complex coordinate on $\mathbb{C}P^1$. When the meromorphic 1-form $\omega$
entering the action of 4d Chern-Simons theory is required to have a double pole
at infinity, the constraint between $h$ and $\mathcal L$ was solved in
[arXiv:2011.13809] to obtain integrable non-degenerate $\mathcal E$-models. We
extend the latter approach to the most general setting of an arbitrary 1-form
$\omega$ and obtain integrable degenerate $\mathcal E$-models. To illustrate
the procedure we reproduce two well known examples of integrable degenerate
$\mathcal E$-models: the pseudo dual of the principal chiral model and the
bi-Yang-Baxter $\sigma$-model.
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BRST quantization of the pure spinor superstring: We present a derivation of the scattering amplitude prescription for the pure
spinor superstring from first principles, both in the minimal and non-minimal
formulations, and show that they are equivalent. This is achieved by first
coupling the worldsheet action to topological gravity and then proceeding to
BRST quantize this system. Our analysis includes the introduction of constant
ghosts and associated auxiliary fields needed to gauge fix symmetries
associated with zero modes. All fields introduced in the process of
quantization can be integrated out explicitly, resulting in the prescriptions
for computing scattering amplitudes that have appeared previously in the
literature. The zero mode insertions in the path integral follow from the
integration over the constant auxiliary fields.
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Quantized bulk scalar fields in the Randall-Sundrum brane-model: We examine the lowest order quantum corrections to the effective action
arising from a quantized real scalar field in the Randall-Sundrum background
spacetime. The leading term is the familiar vacuum, or Casimir, energy density.
The next term represents an induced gravity term that can renormalize the
4-dimensional Newtonian gravitational constant. The calculations are performed
for an arbitrary spacetime dimension. Two inequivalent boundary conditions,
corresponding to twisted and untwisted field configurations, are considered. A
careful discussion of the regularization and renormalization of the effective
action is given, with the relevant counterterms found. It is shown that the
requirement of self-consistency of the Randall-Sundrum solution is not simply a
matter of minimizing the Casimir energy density. The massless, conformally
coupled scalar field results are obtained as a special limiting case of our
results. We clarify a number of differences with previous work.
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Who changes the string coupling ?: In general bosonic closed string backgrounds the ghost-dilaton is not the
only state in the semi-relative BRST cohomology that can change the
dimensionless string coupling. This fact is used to establish complete dilaton
theorems in closed string field theory. The ghost-dilaton, however, is the
crucial state: for backgrounds where it becomes BRST trivial we prove that the
string coupling becomes an unobservable parameter of the string action. For
backgrounds where the matter CFT includes free uncompactified bosons we
introduce a refined BRST problem by including the zero-modes "x" of the bosons
as legal operators on the complex. We argue that string field theory can be
defined on this enlarged complex and that its BRST cohomology captures
accurately the notion of a string background. In this complex the ghost-dilaton
appears to be the only BRST-physical state changing the string coupling.
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Modular interpolating functions for N=4 SYM: We construct interpolating functions fully compatible with S-duality. We then
consider the problem of resumming perturbative expansions for anomalous
dimensions of low twist non-protected operators in N=4 super Yang-Mills theory.
When the rank of the gauge group is small, the interpolations suggest that
anomalous dimensions of leading twist operators take their maximum value at the
point $\tau =\exp(i\pi/3)$. For fixed spin and large enough rank, there is a
level-crossing region, where the anomalous dimension of the leading twist
operator reaches its maximum and then bounces back.
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Late time Wilson lines: In the AdS$_3$/CFT$_2$ correspondence, physical interest attaches to
understanding Virasoro conformal blocks at large central charge and in a
kinematical regime of large Lorentzian time separation, $t\sim c$. However,
almost no analytical information about this regime is presently available. By
employing the Wilson line representation we derive new results on conformal
blocks at late times, effectively resumming all dependence on $t/c$. This is
achieved in the context of "light-light" blocks, as opposed to the richer, but
much less tractable, "heavy-light" blocks. The results exhibit an initial
decay, followed by erratic behavior and recurrences. We also connect this
result to gravitational contributions to anomalous dimensions of double trace
operators by using the Lorentzian inversion formula to extract the latter.
Inverting the stress tensor block provides a pedagogical example of inversion
formula machinery.
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Transition Amplitude in 2+1 dimensional Chern-Simons Gravity on a Torus: The discussions on the modular invariance in section 5 are refined.
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Thermofield Double States in Group Field Theory: Group field theories are higher-rank generalizations of matrix/tensor models,
and encode the simplicial geometries of quantum gravity. In this paper, we
study the thermofield double states in group field theories. The starting point
is the equilibrium Gibbs states in group field theory recently found by Kotecha
and Oriti, based on which we construct the thermofield double state as a
"thermal" vacuum respecting the Kubo-Martin-Schwinger condition. We work with
the Weyl $C^*$-algebra of group fields, and a particular type of thermofield
double states with single type of symmetry are obtained from the squeezed
states on this Weyl algebra. The thermofield double states, when viewed as
states on the group field theory Fock vacuum, are condensate states at finite
flow parameter $\beta$. We suggest that the equilibrium flow parameters $\beta$
of this type of thermofield double states in the group field theory condensate
pictures of black hole horizon and quantum cosmology are related to the inverse
temperatures in gravitational thermodynamics.
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$R^2\log R$ quantum corrections and the inflationary observables: We study a model of inflation with terms quadratic and logarithmic in the
Ricci scalar, where the gravitational action is $f(R)=R+\alpha R^2+\beta R^2
\ln R$. These terms are expected to arise from one loop corrections involving
matter fields in curved space-time. The spectral index $n_s$ and the tensor to
scalar ratio yield $10^{-4}\lesssim r\lesssim0.03$ and $0.94\lesssim n_s
\lesssim 0.99$. i.e. $r$ is an order of magnitude bigger or smaller than the
original Starobinsky model which predicted $r\sim 10^{-3}$. Further enhancement
of $r$ gives a scale invariant $n_s\sim 1$ or higher. Other inflationary
observables are $d n_s/d\ln k \gtrsim -5.2 \times 10^{-4},\, \mu \lesssim 2.1
\times 10^{-8} ,\, y \lesssim 2.6 \times 10^{-9}$. Despite the enhancement in
$r$, if the recent BICEP2 measurement stands, this model is disfavoured.
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An Action for the Infrared Regime of Gauge Theories and the Problem of
Color Transformations: It has been known for a while that there is spontaneous breaking of Lorentz
symmetry in the nonzero charged sectors of quantum electrodynamics due to the
infrared problem of soft photons. More recently, it has also been suggested
that similar results hold for color transformations in a nonabelian gauge
theory. Here we show that an action where a diffeomorphism has been carried out
for the part describing hard gauge particles and matter fields can be used to
analyze these issues. In addition to rederiving old results in this formalism,
we also show that color transformations cannot be unitarily implemented on
perturbative gluon states if gluon fields of arbitrarily low energy are
allowed. Implications for confinement and mass gap are briefly commented upon.
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Supereigenvalue Models and Topological Recursion: We show that the Eynard-Orantin topological recursion, in conjunction with
simple auxiliary equations, can be used to calculate all correlation functions
of supereigenvalue models.
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Renormalized Poincaré algebra for effective particles in quantum field
theory: Using an expansion in powers of an infinitesimally small coupling constant
$g$, all generators of the Poincar\'e group in local scalar quantum field
theory with interaction term $g \phi^3$ are expressed in terms of annihilation
and creation operators $a_\lambda$ and $a^\dagger_\lambda$ that result from a
boost-invariant renormalization group procedure for effective particles. The
group parameter $\lambda$ is equal to the momentum-space width of form factors
that appear in vertices of the effective-particle Hamiltonians, $H_\lambda$. It
is verified for terms order 1, $g$, and $g^2$, that the calculated generators
satisfy required commutation relations for arbitrary values of $\lambda$.
One-particle eigenstates of $H_\lambda$ are shown to properly transform under
all Poincar\'e transformations. The transformations are obtained by
exponentiating the calculated algebra. From a phenomenological point of view,
this study is a prerequisite to construction of observables such as spin and
angular momentum of hadrons in quantum chromodynamics.
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Magnon Bound-state Scattering in Gauge and String Theory: It has been shown that, in the infinite length limit, the magnons of the
gauge theory spin chain can form bound states carrying one finite and one
strictly infinite R-charge. These bound states have been argued to be
associated to simple poles of the multi-particle scattering matrix and to world
sheet solitons carrying the same charges. Classically, they can be mapped to
the solitons of the complex sine-Gordon theory.
Under relatively general assumptions we derive the condition that simple
poles of the two-particle scattering matrix correspond to physical bound states
and construct higher bound states ``one magnon at a time''. We construct the
scattering matrix of the bound states of the BDS and the AFS S-matrices. The
bound state S-matrix exhibits simple and double poles and thus its analytic
structure is much richer than that of the elementary magnon S-matrix. We also
discuss the bound states appearing in larger sectors and their S-matrices. The
large 't Hooft coupling limit of the scattering phase of the bound states in
the SU(2) sector is found to agree with the semiclassical scattering of world
sheet solitons. Intriguingly, the contribution of the dressing phase has an
independent world sheet interpretation as the soliton-antisoliton scattering
phase shift. The small momentum limit provides independent tests of these
identifications.
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Operator algebra of the SL(2) conformal field theories: Structure constants of Operator Algebras for the SL(2) degenerate conformal
field theories are calculated.
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The SAGEX Review on Scattering Amplitudes, Chapter 1: Modern
Fundamentals of Amplitudes: This chapter introduces the foundational elements of scattering amplitudes.
It is meant to be accessible to readers with only a basic understanding of
quantum field theory. Topics covered include: the four-dimensional
spinor-helicity formalism and the colour decomposition of Yang-Mills scattering
amplitudes; the study of soft and collinear limits of Yang-Mills and gravity
amplitudes; the BCFW recursion relation and generalised unitarity, also in the
superamplitudes formalism of $\mathcal{N}{=}4$ supersymmetric Yang-Mills; an
overview of standard and hidden symmetries of the $S$-matrix of
$\mathcal{N}{=}4$ supersymmetric Yang-Mills, such as the conformal, dual
conformal and Yangian symmetries; and a brief excursus on form factors of
protected and non-protected operators in Yang-Mills theory. Several examples
and explicit calculations are also provided.
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One-parameter family of additive energies and momenta in 1+1 dimensional
STR: The velocity dependence of energy and momentum is studied. It is shown that
in the case of STR in the space-time of only one spatial dimension the standard
energy and momentum definition can be naturally modified without lost of local
Lorenz invariance, conservation rules and additivity for multiparticle system.
One parameter family of energies and momenta is constructed and it is shown
that within natural conditions there is no further freedom. Choosing proper
family parameter one can obtain energy and momentum increasing with velocity
faster or slower in comparison with the standard case, but almost coinciding
with them in the wide velocity region.
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A Matrix Model for QCD: Gribov's observation that global gauge fixing is impossible has led to
suggestions that there may be a deep connection between gauge-fixing and
confinement. We find an unexpected relation between the topological
non-triviality of the gauge bundle and coloured states in $SU(N)$ Yang-Mills
theory, and show that such states are necessarily impure. We approximate QCD by
a rectangular matrix model that captures the essential topological features of
the gauge bundle, and demonstrate the impure nature of coloured states
explicitly. Our matrix model also allows the inclusion of the QCD
$\theta$-term, as well as to perform explicit computations of low-lying
glueball masses. This mass spectrum is gapped.
Since an impure state cannot evolve to a pure one by a unitary
transformation, our result shows that the solution to the confinement problem
in pure QCD is fundamentally quantum information-theoretic.
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Giant Gravitons from Holomorphic Surfaces: We introduce a class of supersymmetric cycles in spacetimes of the form AdS
times a sphere or $T^{1,1}$ which can be considered as generalizations of the
giant gravitons. Branes wrapped on these cycles preserve $1\over 2$, $1\over 4$
or $1\over 8$ of the supersymmetry. On the CFT side these configurations
correspond to superpositions of the large number of BPS states.
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On Consistent Equations for Massive Spin-2 Field Coupled to Gravity in
String Theory: We investigate the problem of derivation of consistent equations of motion
for the massive spin 2 field interacting with gravity within both field theory
and string theory. In field theory we derive the most general classical action
with non-minimal couplings in arbitrary spacetime dimension, find the most
general gravitational background on which this action describes a consistent
theory and generalize the analysis for the coupling with background scalar
dilaton field. We show also that massive spin 2 field allows in principle
consistent description in arbitrary background if one builds its action in the
form of an infinite series in the inverse mass square. Using sigma-model
description of string theory in background fields we obtain in the lowest order
in $\alpha'$ the explicit form of effective equations of motion for the massive
spin 2 field interacting with gravity from the requirement of quantum Weyl
invariance and demonstrate that they coincide with the general form of
consistent equations derived in field theory.
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On Decomposing N=2 Line Bundles as Tensor Products of N=1 Line Bundles: We obtain the existence of a cohomological obstruction to expressing N=2 line
bundles as tensor products of N=1 bundles. The motivation behind this paper is
an attempt at understanding the N=2 super KP equation via Baker functions,
which are special sections of line bundles on supercurves.
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Confining Properties of the Homogeneous Self-Dual Field and the
Effective Potential in SU(2) Yang-Mills Theory: We examine in non-Abelian gauge theory the heavy quark limit in the presence
of the (anti-)self-dual homogeneous background field and see that a confining
potential emerges, consistent with the Wilson criterion, although the potential
is quadratic and not linear in the quark separation. This builds upon the
well-known feature that propagators in such a background field are entire
functions. The way in which deconfinement can occur at finite temperature is
then studied in the static temporal gauge by calculation of the effective
potential at high temperature. Finally we discuss the problems to be surmounted
in setting up the calculation of the effective potential nonperturbatively on
the lattice.
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Dimensional reduction as a method to obtain dual theories for massive
spin two in arbitray dimensions: Using the parent Lagrangian method together with a dimensional reduction from
$D$ to $(D-1)$ dimensions we construct dual theories for massive spin two
fields in arbitrary dimensions in terms of a mixed symmetry tensor
$T_{A[A_{1}A_{2}... A_{D-2}]}$. Our starting point is the well studied massless
parent action in dimension $D$. The resulting massive Stueckelberg-like parent
actions in $(D-1)$ dimensions inherits all the gauge symmetries of the original
massless action and can be gauge fixed in two alternative ways, yielding the
possibility of having either a parent action with a symmetric or a
non-symmetric Fierz-Pauli field $e_{AB}$. Even though the dual sector in terms
of the standard spin two field includes only the symmetrical part $e_{\{AB\}}$
in both cases, these two possibilities yield different results in terms of the
alternative dual field $T_{A[A_{1}A_{2}... A_{D-2}]}$. In particular, the
non-symmetric case reproduces the Freund-Curtright action as the dual to the
massive spin two field action in four dimensions.
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All gaugings and stable de Sitter in D=7 half-maximal supergravity: We study the general formulation of gauged supergravity in seven dimensions
with sixteen supercharges keeping duality covariance by means of the embedding
tensor formalism. We first classify all inequivalent duality orbits of
consistent deformations. Secondly, we analyse the complete set of critical
points in a systematic way. Interestingly, we find the first examples of stable
de Sitter solutions within a theory with such a large amount of supersymmetry.
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A Picture of D-branes at Strong Coupling: We use a phase space description to (re)derive a first order form of the
Born-Infeld action for D-branes. This derivation also makes it possible to
consider the limit where the tension of the D-brane goes to zero. We find that
in this limit, which can be considered to be the strong coupling limit of the
fundamental string theory, the world-volume of the D-brane generically splits
into a collection of tensile strings.
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Real or Imaginary? (On pair creation in de Sitter space): Using properly defined Feynman propagator we obtain non--zero imaginary
contribution to the scalar field effective action in even dimensional de Sitter
space. Such a propagator follows from the path integral in de Sitter space and
obeys composition principle proposed in arXiv:0709.2899. The obtained
expression for the effective action shows particle production with the
Gibbons--Hawking rate.
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Dual Actions for Born-Infeld and Dp-Brane Theories: Dual actions with respect to U(1) gauge fields for Born-Infeld and $Dp$-brane
theories are reexamined. Taking into account an additional condition, i.e. a
corollary to the field equation of the auxiliary metric, one obtains an
alternative dual action that does not involve the infinite power series in the
auxiliary metric given by ref. \cite{s14}, but just picks out the first term
from the series formally. New effective interactions of the theories are
revealed. That is, the new dual action gives rise to an effective interaction
in terms of one interaction term rather than infinite terms of different
(higher) orders of interactions physically. However, the price paid for
eliminating the infinite power series is that the new action is not quadratic
but highly nonlinear in the Hodge dual of a $(p-1)$-form field strength. This
non-linearity is inevitable to the requirement the two dual actions are
equivalent.
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Gravity in the 3+1-Split Formalism II: Self-Duality and the Emergence of
the Gravitational Chern-Simons in the Boundary: We study self-duality in the context of the 3+1-split formalism of gravity
with non-zero cosmological constant. Lorentzian self-dual configurations are
conformally flat spacetimes and have boundary data determined by classical
solutions of the three-dimensional gravitational Chern-Simons. For Euclidean
self-dual configurations, the relationship between their boundary initial
positions and initial velocity is also determined by the three-dimensional
gravitational Chern-Simons. Our results imply that bulk self-dual
configurations are holographically described by the gravitational Chern-Simons
theory which can either viewed as a boundary generating functional or as a
boundary effective action.
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Integrable sigma models and perturbed coset models: Sigma models arise frequently in particle physics and condensed-matter
physics as low-energy effective theories. In this paper I compute the exact
free energy at any temperature in two hierarchies of integrable sigma models in
two dimensions. These theories, the SU(N)/SO(N) and O(2P)/O(P) x O(P) models,
are asymptotically free and exhibit charge fractionalization. When the
instanton coupling theta=pi, they flow to the SU(N)_1 and O(2P)_1 conformal
field theories, respectively. I also generalize the free energy computation to
massive and massless perturbations of the coset conformal field theories
SU(N)_k/SO(N)_{2k} and O(2P)_k/O(P)_k x O(P)_k.
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The Layer Phase in the Non-isotropic SU(3) Gauge Model at Finite
Temperature: The phase structure of a non-isotropic non-Abelian SU(3) lattice gauge model
at finite temperature is investigated to the third order in the
variational-cumulant expansion (VCE) approach. The layer phase exists in this
model in the cases of dimensions D=4, D=5 (d=D-1).
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Boulware-Deser ghost in extended quasidilaton massive gravity: In the extended quasidilaton massive gravity we perform a nonlinear
transformation of the shift vector and then calculate the second derivatives of
the Hamiltonian density with respect to the lapse function and the (nonlinearly
transformed) shift vector. It is then shown that the $4\times 4$ Hessian matrix
is invertible, meaning that the equations of motion for the lapse function and
the shift vector simply determine themselves. Therefore, there is no primary
constraint that removes the Boulware-Deser ghost.
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Quasilocalized gravity without asymptotic flatness: We present a toy model of a generic five-dimensional warped geometry in which
the 4D graviton is not fully localized on the brane. Studying the tensor sector
of metric perturbation around this background, we find that its contribution to
the effective gravitational potential is of 4D type (1/r) at the intermediate
scales and that at the large scales it becomes 1/r^{1+alpha}, 0<alpha=< 1 being
a function of the parameters of the model (alpha=1 corresponds to the
asymptotically flat geometry). Large-distance behavior of the potential is
therefore not necessarily five-dimensional. Our analysis applies also to the
case of quasilocalized massless particles other than graviton.
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Gauged Floreanini-Jackiw type chiral boson and its BRST quantization: The gauged model of Siegel type chiral boson is considered. It has been shown
that the action of gauged model of Floreanini-Jackiw (FJ) type chiral boson is
contained in it in an interesting manner. A BRST invariant action corresponding
to the action of gauged FJ type chiral boson has been formulated using Batalin,
Fradkin and Vilkovisky based improved Fujiwara, Igarishi and Kubo (FIK)
formalism. An alternative quantization of the gauge symmetric action has been
made with a Lorentz gauge and an attempt has been made to establish the
equivalence between the gauge symmetric version of the extended phase space and
original gauge non-invariant version of the usual phase space.
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Wick rotation and the positivity of energy in quantum field theory: We propose a new axiom system for unitary quantum field theories on curved
space-time backgrounds, by postulating that the partition function and the
correlators extend analytically to a certain domain of complex-valued metrics.
Ordinary Riemannian metrics are contained in the allowable domain, while
Lorentzian metrics lie on its boundary.
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Quantum Field Theories Coupled to Supergravity: AdS/CFT and Local
Couplings: This article is based on my PhD thesis and covers the following topics:
Holographic meson spectra in a dilaton flow background, the mixed Coulomb-Higgs
branch in terms of instantons on D7 branes, and a dual description of
heavy-light mesons. Moreover, in a second part the conformal anomaly of four
dimensional supersymmetric quantum field theories coupled to classical N=1
supergravity is explored in a superfield formulation. The complete basis for
the anomaly and consistency conditions, which arise from cohomological
considerations, are given. Possible implications for an extension of
Zamolodchikov's c-theorem to four dimensional supersymmetric quantum field
theories are discussed.
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Renormalization Group Approach to Scalar Theory: Effective potential for scalar $\lambda\phi^4$ theory is obtained using the
exact renormalization group method which includes both the usual one-loop
contribution as well as the dominant higher loop effects. Our numerical
calculation indicates a breakdown of naive one-loop result for sufficiently
large renormalized coupling constant.
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Nonperturbative calculation of the anomalous magnetic moment in the
Yukawa model within truncated Fock space: Within the covariant formulation of light-front dynamics, we calculate the
state vector of a physical fermion in the Yukawa model. The state vector is
decomposed in Fock sectors and we consider the first three ones: the single
constituent fermion, the constituent fermion coupled to one scalar boson, and
the constituent fermion coupled to two scalar bosons. This last three-body
sector generates nontrivial and nonperturbative contributions to the state
vector, which are calculated numerically. Field-theoretical divergences are
regularized using Pauli-Villars fermion and boson fields. Physical observables
can be unambiguously deduced using a systematic renormalization scheme we have
developed previously. As a first application, we consider the anomalous
magnetic moment of the physical fermion.
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EFT Beyond the Horizon: Stochastic Inflation and How Primordial Quantum
Fluctuations Go Classical: We identify the effective theory describing inflationary super-Hubble scales
and show it to be a special case of effective field theories appropriate to
open systems. Open systems allow information to be exchanged between the
degrees of freedom of interest and those that are integrated out, such as for
particles moving through a fluid. Strictly speaking they cannot in general be
described by an effective lagrangian; rather the appropriate `low-energy' limit
is instead a Lindblad equation describing the evolution of the density matrix
of the slow degrees of freedom. We derive the equation relevant to super-Hubble
modes of quantum fields in near-de Sitter spacetimes and derive two
implications. We show the evolution of the diagonal density-matrix elements
quickly approaches the Fokker-Planck equation of Starobinsky's stochastic
inflationary picture. This provides an alternative first-principles derivation
of this picture's stochastic noise and drift, as well as its leading
corrections. (An application computes the noise for systems with a sub-luminal
sound speed.) We argue that the presence of interactions drives the
off-diagonal density-matrix elements to zero in the field basis. This shows why
the field basis is the `pointer basis' for the decoherence of primordial
quantum fluctuations while they are outside the horizon, thus allowing them to
re-enter as classical fluctuations, as assumed when analyzing CMB data. The
decoherence process is efficient, occurring after several Hubble times even for
interactions as weak as gravitational-strength. Crucially, the details of the
interactions largely control only the decoherence time and not the nature of
the final late-time stochastic state, much as interactions can control the
equilibration time for thermal systems but are largely irrelevant to the
properties of the resulting equilibrium state.
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N=2 supersymmetric dynamics for pedestrians: We give a pedagogical introduction to the dynamics of N=2 supersymmetric
systems in four dimensions. The topic ranges from the Lagrangian and the
Seiberg-Witten solutions of SU(2) gauge theories to Argyres-Douglas CFTs and
Gaiotto dualities.
This is a write-up of the author's lectures at Tohoku University, Nagoya
University and Rikkyo University. Comments will be appreciated.
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Gauge dependence of vacuum expectation values of gauge invariant
operators from soft breaking of BRST symmetry. Example of Gribov-Zwanziger
action: We review the study of influence of the so-called soft BRST symmetry breaking
within the Batalin-Vilkovisky (BV) formalism introduced in our papers [JHEP
1110 (2011) 043, arXiv:1108.4820 [hep-th], MPLA 27 (2012) 1250067,
arXiv:1201.4720 [hep-th]] on gauge dependence of the effective action and
vacuum expectation values of gauge invariant operators. We derive the Ward
identities for generating functionals of Green's functions for a given theory
with soft BRST symmetry breaking term being added to the quantum action and
investigate theirs gauge dependence. It is strongly argued that gauge theories
with a soft breaking of BRST symmetry are inconsistent within the BV formalism
because of the gauge-dependence of $S$-matrix. The application to the
Gribov-Zwanziger action (enlarging SU(N) Yang-Mills gauge theory by means of
not gauge-invariant horizon function) for the one-parameter family of $R_\xi$
gauges with use of the new form of the Hermitian augmented Faddeev-Popov
operator (being by Faddeev-Popov operator for transverse components of
Yang--Mills fields) is considered.
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The Universality of Penrose Limits near Space-Time Singularities: We prove that Penrose limits of metrics with arbitrary singularities of
power-law type show a universal leading u^{-2}-behaviour near the singularity
provided that the dominant energy condition is satisfied and not saturated. For
generic power-law singularities of this type the oscillator frequencies of the
resulting homogeneous singular plane wave turn out to lie in a range which is
known to allow for an analytic extension of string modes through the
singularity. The discussion is phrased in terms of the recently obtained
covariant characterisation of the Penrose limit; the relation with null
geodesic deviation is explained in detail.
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Boundary conditions at spatial infinity for fields in Casimir
calculations: The importance of imposing proper boundary conditions for fields at spatial
infinity in the Casimir calculations is elucidated.
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Weyl semimetal/insulator transition from holography: We study a holographic model which exhibits a quantum phase transition from
the strongly interacting Weyl semimetal phase to an insulating phase. In the
holographic insulating phase there is a hard gap in the real part of frequency
dependent diagonal conductivities. However, the anomalous Hall conductivity is
nonzero at zero frequency, indicting that it is a Chern insulator. This
holographic quantum phase transition is always of first order, signified by a
discontinuous anomalous Hall conductivity at the phase transition, in contrast
to the very continuous holographic Weyl semimetal/trivial semimetal phase
transition. Our work reveals the novel phase structure of strongly interacting
Weyl semimetal.
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N=2 Supersymmetric RG Flows and the IIB Dilaton: We show that there is a non-trivial relationship between the dilaton of IIB
supergravity, and the coset of scalar fields in five-dimensional, gauged N=8
supergravity. This has important consequences for the running of the gauge
coupling in massive perturbations of the AdS/CFT correspondence. We conjecture
an exact analytic expression for the ten-dimensional dilaton in terms of
five-dimensional quantities, and we test this conjecture. Specifically, we
construct a family of solutions to IIB supergravity that preserve half of the
supersymmetries, and are lifts of supersymmetric flows in five-dimensional,
gauged N=8 supergravity. Via the AdS/CFT correspondence these flows correspond
to softly broken N=4, large N Yang-Mills theory on part of the Coulomb branch
of N=2 supersymmetric Yang-Mills. Our solutions involve non-trivial backgrounds
for all the tensor gauge fields as well as for the dilaton and axion.
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Non-BPS Branes of Supersymmetric Brane Worlds: We consider five-dimensional brane worlds with N=2 gauged supergravity in the
bulk coupled supersymmetrically to two boundary branes at the fixed points of a
Z_2 symmetry. We analyse two mechanisms that break supersymmetry either by
choosing flipped fermionic boundary conditions on the boundary branes or by
modifying the gravitino variation to include both Z_2-odd and Z_2-even
operators. In all cases we find the corresponding background. Including an even
part in the gravitino variation leads to tilted branes. Choosing the flipped
boundary conditions leads to AdS_4 branes and stabilized radion in the detuned
case, when the expectation value of the even variation is nonzero. Another
solution has the interpretation of moving AdS_4 branes separated by a horizon.
The solution with moving branes separated by a horizon can be extended to the
tuned case. In the presence of a horizon, temperature mediation communicates
supersymmetry breakdown to the branes.
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Black Rings in U(1)^3 Supergravity and their dual 2d CFT: We study the near horizon geometry of black ring solutions in
five-dimensional U(1)^3 supergravity with three electric dipole charges and one
angular momentum. We consider the extremal vanishing horizon (EVH) limit of
these solutions and show that the near horizon geometries develop locally AdS_3
throats which at the near-EVH near horizon limit the AdS_3 factor turns to a
BTZ black hole. By analysing the first law of thermodynamics for black rings we
show that at EVH limit it reduces to the first law of thermodynamics for BTZ
black holes. Using the AdS3/CFT2 duality, we propose a dual CFT to describe the
near-horizon low energy dynamics of near-EVH black rings. We also discuss the
connection between our CFT proposal and the Kerr/CFT correspondence in the
cases where these two overlap.
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Anomalies and Symmetry Fractionalization: We study ordinary, zero-form symmetry $G$ and its anomalies in a system with
a one-form symmetry $\Gamma$. In a theory with one-form symmetry, the action of
$G$ on charged line operators is not completely determined, and additional
data, a fractionalization class, needs to be specified. Distinct choices of a
fractionalization class can result in different values for the anomalies of $G$
if the theory has an anomaly involving $\Gamma$. Therefore, the computation of
the 't Hooft anomaly for an ordinary symmetry $G$ generally requires first
discovering the one-form symmetry $\Gamma$ of the physical system. We show that
the multiple values of the anomaly for $G$ can be realized by twisted gauge
transformations, since twisted gauge transformations shift fractionalization
classes. We illustrate these ideas in QCD theories in diverse dimensions. We
successfully match the anomalies of time-reversal symmetries in $2+1d$ gauge
theories, across the different fractionalization classes, with previous
conjectures for the infrared phases of such strongly coupled theories, and also
provide new checks of these proposals. We perform consistency checks of recent
proposals about two-dimensional adjoint QCD and present new results about the
anomaly of the axial $\mathbb{Z}_{2N}$ symmetry in $3+1d$ ${\cal N}=1$
super-Yang-Mills. Finally, we study fractionalization classes that lead to
2-group symmetry, both in QCD-like theories, and in $2+1d$ $\mathbb{Z}_2$ gauge
theory.
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Numerical solution of gravitational dynamics in asymptotically anti-de
Sitter spacetimes: A variety of gravitational dynamics problems in asymptotically anti-de Sitter
(AdS) spacetime are amenable to efficient numerical solution using a common
approach involving a null slicing of spacetime based on infalling geodesics,
convenient exploitation of the residual diffeomorphism freedom, and use of
spectral methods for discretizing and solving the resulting differential
equations. Relevant issues and choices leading to this approach are discussed
in detail. Three examples, motivated by applications to non-equilibrium
dynamics in strongly coupled gauge theories, are discussed as instructive test
cases. These are gravitational descriptions of homogeneous isotropization,
collisions of planar shocks, and turbulent fluid flows in two spatial
dimensions.
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Gaudin Model, Bethe Ansatz and Critical Level: We propose a new method of diagonalization of hamiltonians of the Gaudin
model associated to an arbitrary simple Lie algebra, which is based on Wakimoto
modules over affine algebras at the critical level. We construct eigenvectors
of these hamiltonians by restricting certain invariant functionals on tensor
products of Wakimoto modules. In conformal field theory language, the
eigenvectors are given by certain bosonic correlation functions. Analogues of
Bethe ansatz equations naturally appear as Kac-Kazhdan type equations on the
existence of certain singular vectors in Wakimoto modules. We use this
construction to expalain a connection between Gaudin's model and correlation
functions of WZNW models.
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Perturbations in Bouncing Cosmological Models: I describe the features and general properties of bouncing models and the
evolution of cosmological perturbations on such backgrounds. I will outline
possible observational consequences of the existence of a bounce in the
primordial Universe and I will make a comparison of these models with standard
long inflationary scenarios.
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Cosmological Decoherence from Thermal Gravitons: We study the effects of gravitationally-driven decoherence on tunneling
processes associated with false vacuum decays, such as the Coleman--De~Luccia
instanton. We compute the thermal graviton-induced decoherence rate for a wave
function describing a perfect fluid of nonzero energy density in a finite
region. When the effective cosmological constant is positive, the thermal
graviton background sourced by a de Sitter horizon provides an unavoidable
decoherence effect, which may have important consequences for tunneling
processes in cosmological history. We discuss generalizations and consequences
of this effect and comment on its observability and applications to black hole
physics.
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Continuum Limit of Spin-1 Chain (the only change is added references): We study the continuum limit of the spin-1 chain in the non-Abelian
bosonization approach of Affleck and show that the Hamiltonian of integrable
spin-1 chain yields the Lagrangian of supersymmetric sine-Gordon model in the
zero lattice spacing limit. We also show that the quantum group generators of
the spin-1 chain give non-local charges of the supersymmetric sine-Gordon
theory.
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AdS (In)stability: Lessons From The Scalar Field: We argued in arXiv:1408.0624 that the quartic scalar field in AdS has
features that could be instructive for answering the gravitational stability
question of AdS. Indeed, the conserved charges identified there have recently
been observed in the full gravity theory as well. In this paper, we continue
our investigation of the scalar field in AdS and provide evidence that in the
Two-Time Formalism (TTF), even for initial conditions that are far from
quasi-periodicity, the energy in the higher modes at late times is
exponentially suppressed in the mode number. Based on this and some related
observations, we argue that there is no thermalization in the scalar TTF model
within time-scales that go as $\sim 1/\epsilon^2$, where $\epsilon$ measures
the initial amplitude (with only low-lying modes excited). It is tempting to
speculate that the result holds also for AdS collapse.
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Quantum corrections to the mass and central charge of solitons in 1+1
dimensions: We first discuss how the longstanding confusion in the literature concerning
one-loop quantum corrections to 1+1 dimensional solitons has finally been
resolved. Then we use 't Hooft and Veltman's dimensional regularization to
compute the kink mass, and find that chiral domain wall fermions, induced by
fermionic zero modes, lead to spontaneous parity violation and an anomalous
contribution to the central charge such that the BPS bound becomes saturated.
On the other hand, Siegel's dimensional reduction shifts this anomaly to the
counter terms in the renormalized current multiplet. The superconformal anomaly
is located in an evanescent counter term, and imposing supersymmetry, this
counter term induces the same anomalous contribution to the central charge.
Next we discuss a new regularization scheme: local mode regularization. The
local energy density computed in this scheme satisfies the BPS equality (it is
equal to the local central charge density). In an appendix we give a very
detailed account of the DHN method to compute soliton masses applied to the
supersymmetric kink.
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Scattering on the Moduli Space of N=4 Super Yang-Mills: We calculate one-loop scattering amplitudes in N=4 super Yang-Mills theory
away from the origin of the moduli space and demonstrate that the results are
extremely simple, in much the same way as in the conformally invariant theory.
Specifically, we consider the model where an SU(2) gauge group is spontaneously
broken down to U(1). The complete component Lagrange density of the model is
given in a form useful for perturbative calculations. We argue that the
scattering amplitudes with massive external states deserve further study.
Finally, our work shows that loop corrections can be readily computed in a
mass-regulated N=4 theory, which may be relevant in trying to connect
weak-coupling results with those at strong coupling, as discussed recently by
Alday and Maldacena.
|
Relativistic Hydrodynamics under Rotation: Prospects & Limitations from
a Holographic Perspective: The AdS/CFT correspondence, or holography, has provided numerous important
insights into the behavior of strongly-coupled many-body systems. Crucially, it
has provided a testing ground for the construction of new effective field
theories, especially those in the low frequency, long wavelength limit known as
hydrodynamics. In this article we continue the study of strongly-coupled
rotating fluids using holography and hydrodynamics. We provide an overview of
recent developments arising from the study of simply spinning Myers-Perry black
holes. We review techniques to obtain hydrodynamic and non-hydrodynamic modes,
describe how branch point singularities in the complex frequency and momentum
space limit the radius of convergence of the hydrodynamic gradient expansion,
and outline the relation of pole-skipping in the linear response functions to
early time chaotic behavior.
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Mini-Instantons in SU(2) Gauge Theory: The effects of instantons close to the cut-off is studied in four dimensional
SU(2) gauge theory with higher order derivative terms in the action. It is
found in the framework of the dilute instanton gas approximation that the
convergence of the topological observables requires non-universal beta
function.
|
Entanglement entropy of excited states in conformal perturbation theory
and the Einstein equation: For a conformal field theory (CFT) deformed by a relevant operator, the
entanglement entropy of a ball-shaped region may be computed as a perturbative
expansion in the coupling. A similar perturbative expansion exists for excited
states near the vacuum. Using these expansions, this work investigates the
behavior of excited state entanglement entropies of small, ball-shaped regions.
The motivation for these calculations is Jacobson's recent work on the
equivalence of the Einstein equation and the hypothesis of maximal vacuum
entropy [arXiv:1505.04753], which relies on a conjecture stating that the
behavior of these entropies is sufficiently similar to a CFT. In addition to
the expected type of terms which scale with the ball radius as $R^d$, the
entanglement entropy calculation gives rise to terms scaling as $R^{2\Delta}$,
where $\Delta$ is the dimension of the deforming operator. When
$\Delta\leq\frac{d}{2}$, the latter terms dominate the former, and suggest that
a modification to the conjecture is needed.
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$~N=2$~ Superstring Theory Generates Supersymmetric Chern-Simons
Theories: Abstrct: We show that the action of self-dual supersymmetric Yang-Mills
theory in four-dimensions, which describes the consistent massless background
fields for $~N=2$~ superstring, generates the actions for $~N=1$~ and $~N=2$~
supersymmetric non-Abelian Chern-Simons theories in three-dimensions after
appropriate dimensional reductions. Since the latters play important roles for
supersymmetric integrable models, this result indicates the fundamental
significance of the $~N=2$~ superstring theory controlling (possibly all)
supersymmetric integrable models in lower-dimensions.
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Two-Sheeted Universe, Analyticity and the Arrow of Time: Our universe seems to be radiation dominated at early times, and vacuum
energy dominated at late times. When we consider the maximal analytic extension
of this spacetime, its symmetries and complex analytic properties suggest a
picture in which spacetime has two sheets, exchanged by an isometry which, in
turn, picks a preferred (CPT-symmetric) vacuum state for quantum fields on the
spacetime. Previously (arXiv:1803.08928, arXiv:1803.08930), we showed how this
line of thought provides new explanations for dark matter, the
matter-antimatter asymmetry, the absence of primordial vector and tensor
perturbations, and the {\it phase} of the primordial scalar perturbations; and
additional testable predictions. In this paper, we develop this picture in
several respects and, in particular, point out that it also provides a new
explanation for why the thermodynamic arrow of time points away from the bang.
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General String Cosmologies at Order $α'{}^{\,3}$: We compute the cosmological reduction of general string theories, including
bosonic, heterotic and type II string theory to order $\alpha'^{3}$, i.e., with
up to eight derivatives. To this end we refine recently introduced methods that
allow one to bring the reduced theory in one dimension to a canonical form with
only first-order time derivatives. The resulting theories are compatible with a
continuous $O(d,d,\mathbb{R})$ invariance, which in turn fixes the B-field
couplings.
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The decoupling limit of Multi-Gravity: Multi-Galileons, Dualities and
More: In this paper we investigate the decoupling limit of a particular class of
multi-gravity theories, i.e. of theories of interacting spin-2 fields. We
explicitly compute the interactions of helicity-0 modes in this limit, showing
that they take on the form of multi-Galileons and dual forms. In the process we
extend the recently discovered Galileon dualities, deriving a set of new
multi-Galileon dualities. These are also intrinsically connected to healthy,
but higher-derivative, multi-scalar field theories akin to `beyond Horndeski'
models.
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Thermofield Quantum Electrodynamics in 1 + 1 Dimensions at Finite
Chemical Potential: A Bosonization Approach: The recent generalization of the Lowenstein-Swieca operator solution of
Quantum Electrodynamics in 1+1 dimensions to finite temperature in Thermofield
Dynamics is further generalized to include a non-vanishing chemical potential.
The operator solution to the Euler-Lagrange equations respecting the
Kubo-Martin-Schwinger condition is constructed. Two forms of this condition and
their associated solutions are discussed. The correlation functions of an
arbitrary number of chiral densities are computed in the thermal theta-vacuum.
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Glueballs in the Klebanov-Strassler Theory: Pseudoscalars vs Scalars: We discuss the $0^{+-}$ singlet sector of glueballs in the Klebanov-Strassler
theory. We report the results of a numerical study of the linearized equations
in the Klebanov-Strasller background and make a comparison with the spectrum of
the scalar sector. While for four towers of the total six towers of massive
pseudoscalar states our results match the spectrum of the corresponding towers
of scalars, the values for the remaining two towers diverge with those of the
scalars. We discuss possible interpretations of this divergence.
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Chiral Gravitational Waves and Baryon Superfluid Dark Matter: We develop a unified model of darkgenesis and baryogenesis involving strongly
interacting dark quarks, utilizing the gravitational anomaly of chiral gauge
theories. In these models, both the visible and dark baryon asymmetries are
generated by the gravitational anomaly induced by the presence of chiral
primordial gravitational waves. We provide a concrete model of an SU(2) gauge
theory with two massless quarks. In this model, the dark quarks condense and
form a dark baryon charge superfluid (DBS), in which the Higgs-mode acts as
cold dark matter. We elucidate the essential features of this dark matter
scenario and discuss its phenomenological prospects.
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Expanding and contracting universes in third quantized string cosmology: We discuss the possibility of quantum transitions from the string
perturbative vacuum to cosmological configurations characterized by isotropic
contraction and decreasing dilaton. When the dilaton potential preserves the
sign of the Hubble factor throughout the evolution, such transitions can be
represented as an anti-tunnelling of the Wheeler--De Witt wave function in
minisuperspace or, in a third-quantization language, as the production of pairs
of universes out of the vacuum.
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Boundary Terms in Generalized Geometry and doubled field theory: We propose a boundary action to complement the recently developed duality
manifest actions in string and M-theory using generalized geometry. This
boundary action combines the Gibbons-Hawking term with boundary pieces that
were previously neglected in the construction of these actions. The combination
may be written in terms of the metric of generalized geometry. The result is to
produce an action that is duality invariant including boundary terms.
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Comments on Mesonic Correlators in the Worldline Formalism: We elaborate on how to incorporate mesonic correlators into the worldline
formalism. We consider possible applications to QCD-like theories in various
dimensions. We focus on large-N_c two dimensional QCD (the 't Hooft model) and
relate it to a single harmonic oscillator. We also discuss the dependence of
the Peskin S-parameter on the number of massless flavors and their
representation and compare our expression to the corresponding expression
obtained at weak coupling. Finally, we use the worldline formalism to discuss
how the Veneziano limit of QCD is realized in holography in the limit of small
N_f/N_c.
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Approaching the BFKL pomeron via integrable classical solutions: We identify classical string solutions which directly give the classical part
of the strong coupling pomeron intercept. The relevant solution is a close
cousin of the GKP folded string, which is not surprising given the known
relation with twist-2 operators. Our methods are applicable, however, also for
nonzero conformal spin where we do not have a clear link with anomalous
dimensions of a concrete class of operators. We analyze the BFKL folded string
from the algebraic curve perspective and investigate its possible particle
content.
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Covariant Action for the Super-Five-Brane of M-Theory: We propose a complete, d=6 covariant and kappa-symmetric, action for an
M-theory five-brane propagating in D=11 supergravity background.
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Correlation function with the insertion of zero modes of modular
Hamiltonians: Zero modes of modular Hamiltonian of one interval are found in momentum space
for two dimensional massless free scalar theory. Finite correlators are
extracted from separate region connected correlation functions with the
insertion of zero modes. Correlators of $(n,1)$-type are claimed to be
conformal block up to a set of theory dependent constants. We fix the
correlators of $(2,1)$-type with the coefficients of three point function in 2d
CFTs.
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Supersymmetry Breaking and Composite Extra Dimensions: We study supergravity models in four dimensions where the hidden sector is
superconformal and strongly-coupled over several decades of energy below the
Planck scale, before undergoing spontaneous breakdown of scale invariance and
supersymmetry. We show that large anomalous dimensions can suppress Kahler
contact terms between the hidden and visible sectors, leading to models in
which the hidden sector is "sequestered" and anomaly-mediated supersymmetry
breaking can naturally dominate, thus solving the supersymmetric flavor
problem. We construct simple, explicit models of the hidden sector based on
supersymmetric QCD in the conformal window. The present approach can be
usefully interpreted as having an extra dimension responsible for sequestering
replaced by the many states of a (spontaneously-broken) strongly-coupled
superconformal hidden sector, as dictated by the AdS/CFT correspondence.
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Holographic thermodynamics of rotating black holes: We provide mass/energy formulas for the extended thermodynamics, mixed
thermodynamics, and holographic conformal field theory (CFT) thermodynamics for
the charged and rotating Kerr-Newman Anti-de Sitter black holes. Then for the
CFT thermal states dual to the black hole, we find the first-order phase
transitions and criticality phenomena in the canonical ensemble with fixed
angular momentum, volume, and central charge. We observe that the CFT states
cannot be analogous to the Van der Waals fluids, despite the critical exponents
falling into the universality class predicted by the mean field theory.
Additionally, we examine the (de)confinement phase transitions within the grand
canonical ensemble with fixed angular velocity, volume, and central charge of
the CFT. Our findings suggest that the near zero temperature (de)confinement
phase transitions can occur with the angular velocity of the CFT that solely
depends on the CFT volume.
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A Bound on Thermal Relativistic Correlators at Large Spacelike Momenta: We consider thermal Wightman correlators in a relativistic quantum field
theory in the limit where the spatial momenta of the insertions become large
while their frequencies stay fixed. We show that, in this limit, the size of
these correlators is bounded by $e^{-\beta R}$, where $R$ is the radius of the
smallest sphere that contains the polygon formed by the momenta. We show that
perturbative quantum field theories can saturate this bound through suitably
high-order loop diagrams. We also consider holographic theories in
$d$-spacetime dimensions, where we show that the leading two-point function of
generalized free-fields saturates the bound in $d = 2$ and is below the bound
for $d > 2$. We briefly discuss interactions in holographic theories and
conclude with a discussion of several open problems.
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Spin foams, causal links and geometry-induced interactions: Current theories of particle physics, including the standard model, are
dominated by the paradigm that nature is basically translation invariant.
Deviations from translation invariance are described by the action of forces.
General relativity is based on a different paradigm: There is no translation
invariance in general. Interaction is a consequence of the geometry of
spacetime, formed by the presence of matter, rather than of forces.
In recent years the formation of spacetime on a quantum mechanical level, has
been intensively studied within the framework of spin foams, following an old
idea from R. Penrose. In this connection it would be appropriate to reconsider
the meaning of those paradigms and attempt to apply the paradigm of general
relativity to particle physics.
A spin foam model with underlying SO(3,2) symmetry is well-suited for this
purpose. It represents a purely geometric model in the sense of the second
paradigm. By applying perturbative methods, starting from a translation
invariant first approximation, this model is reformulated in the sense of the
first paradigm. It will be shown that the model then defines a spacetime
manifold equipped with a particle theory in the form of locally interacting
quantized fields. This includes all four types of interaction: electromagnetic,
weak, chromodynamics and gravitation together with realistic numerical values
of the corresponding coupling constants.
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Chern-Simons Gauge Theory on Orbifolds: Open Strings from Three
Dimensions: Chern-Simons gauge theory is formulated on three dimensional $Z_2$ orbifolds.
The locus of singular points on a given orbifold is equivalent to a link of
Wilson lines. This allows one to reduce any correlation function on orbifolds
to a sum of more complicated correlation functions in the simpler theory on
manifolds. Chern-Simons theory on manifolds is known to be related to 2D CFT on
closed string surfaces; here I show that the theory on orbifolds is related to
2D CFT of unoriented closed and open string models, i.e. to worldsheet orbifold
models. In particular, the boundary components of the worldsheet correspond to
the components of the singular locus in the 3D orbifold. This correspondence
leads to a simple identification of the open string spectra, including their
Chan-Paton degeneration, in terms of fusing Wilson lines in the corresponding
Chern-Simons theory. The correspondence is studied in detail, and some exactly
solvable examples are presented. Some of these examples indicate that it is
natural to think of the orbifold group $Z_2$ as a part of the gauge group of
the Chern-Simons theory, thus generalizing the standard definition of gauge
theories.
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Topological Defect Lines in Two Dimensional Fermionic CFTs: We consider topological defect lines (TDLs) in two-dimensional fermionic
conformal field theories (CFTs). Besides inheriting all the properties of TDLs
in bosonic CFTs, TDLs in fermionic CFTs could host fermionic defect operators
at their endpoints and junctions. Furthermore, there is a new type of TDLs,
called q-type TDLs, that have no analog in bosonic CFTs. Their distinguishing
feature is an extra one-dimensional Majorana fermion living on the worldline of
the TDLs. The properties of TDLs in fermionic CFTs are captured in the
mathematical language of the super fusion category. We propose a classification
of the rank-2 super fusion categories generalizing the $\mathbb Z_8$
classification for the anomalies of $\mathbb Z_2$ symmetry. We explicitly solve
the F-moves for all the nontrivial categories, and derive the corresponding
spin selection rules that constrain the spectrum of the defect operators. We
find the full set of TDLs in the standard fermionic minimal models and a
partial set of TDLs in the two exceptional models, which give CFT realizations
to the rank-2 super fusion categories. Finally, we discuss a constraint on the
renormalization group flow that preserves a q-type TDL.
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Probing Five-Dimensional Black Holes with D-Branes: We consider a one-brane probe in the presence of a five-dimensional black
hole in the classical limit. The velocity-dependent force on a slowly-moving
probe is characterized by a metric on the probe moduli space. This metric is
computed for large black holes using low-energy supergravity, and for small
black holes using D-brane gauge theory. The results are compared.
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Microscopic wormholes and the geometry of entanglement: It has recently been suggested that Einstein-Rosen (ER) bridges can be
interpreted as maximally entangled states of two black holes that form a
complex Einstein-Podolsky-Rosen (EPR) pair. This relationship has been dubbed
as the ER = EPR correlation. In this work, we consider the latter conjecture in
the context of quadratic Palatini theory. An important result, which stems from
the underlying assumptions about the geometry on which the theory is
constructed, is the fact that all the charged solutions of the quadratic
Palatini theory possess a wormhole structure. Our results show that spacetime
may have a foam-like microstructure with wormholes generated by fluctuations of
the quantum vacuum. This involves the spontaneous creation/annihilation of
entangled particle-antiparticle pairs, existing in a maximally entangled state
connected by a non-traversable wormhole. Since the particles are produced from
the vacuum and therefore exist in a singlet state, they are necessarily
entangled with one another. This gives further support to the ER=EPR claim.
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Schrödinger Spacetimes with Screen and Reduced Entanglement: We study a particular class of type II string vacua which become
Schr\"odinger like spacetime in the IR region but are conformally AdS in
asymptotic UV region. These solutions are found to possess some unique
properties such as the presence of a spacetime `screen'. This Schr\"odinger
(spacetime) screen is however very different from a black-hole horizon. It
requires the presence of finite chemical potential and a negative charge
density in the Schr\"odinger CFT. We find that these vacua give rise to reduced
entanglement entropy as compared to Lifshitz-AdS counterpart, perhaps due to
the screening effects.
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New modes from higher curvature corrections in holography: In gravitational theories involving higher curvature corrections the metric
describes additional degrees of freedom beyond the graviton. Holographic
duality maps these to operators in the dual CFT. We identify infinite families
of theories for which these new modes cannot be truncated and the usual
Fefferman-Graham expansion needs to be modified. New massive gravity in three
dimensions and critical gravity in four dimensions are particular
representatives of these families. We propose modified expansion, study the
near-boundary behaviour of the metric and derive fall-off properties of the
additional modes in theories involving higher derivative corrections.
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String creation in D6-brane background: The production of string charge during a crossing of certain oriented
D-branes is studied. We compute the string charge in the system of a probe
D2-brane and a background D6-brane by use of the equations of motion in the
ten-dimensions. We confirm the creation of string charge as inflow from the
background D6-brane.
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Off-shell Amplitudes in Superstring Theory: Computing the renormalized masses and S-matrix elements in string theory,
involving states whose masses are not protected from quantum corrections,
requires defining off-shell amplitude with certain factorization properties.
While in the bosonic string theory one can in principle construct such an
amplitude from string field theory, there is no fully consistent field theory
for type II and heterotic string theory. In this paper we give a practical
construction of off-shell amplitudes satisfying the desired factorization
property using the formalism of picture changing operators. We describe a
systematic procedure for dealing with the spurious singularities of the
integration measure that we encounter in superstring perturbation theory. This
procedure is also useful for computing on-shell amplitudes, as we demonstrate
by computing the effect of Fayet-Iliopoulos D-terms in four dimensional
heterotic string theory compactifications using this formalism.
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Determinantal Calabi-Yau varieties in Grassmannians and the Givental
$I$-functions: We examine a class of Calabi-Yau varieties of the determinantal type in
Grassmannians and clarify what kind of examples can be constructed explicitly.
We also demonstrate how to compute their genus-0 Gromov-Witten invariants from
the analysis of the Givental $I$-functions. By constructing $I$-functions from
the supersymmetric localization formula for the two dimensional gauged linear
sigma models, we describe an algorithm to evaluate the genus-0 A-model
correlation functions appropriately. We also check that our results for the
Gromov-Witten invariants are consistent with previous results for known
examples included in our construction.
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One-loop effective action around de Sitter space: The non-local one-loop contribution to the gravitational effective action
around de Sitter space is computed using the background field method with pure
trace external gravitational fields and it is shown to vanish. The calculation
is performed in a generic covariant gauge and the result is verified to be
gauge invariant.
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Quantum Spacetimes and Finite N Effects in 4D Super Yang-Mills Theories: The truncation in the number of single-trace chiral primary operators of
$\N=4$ SYM and its conjectured connection with gravity on quantum spacetimes
are elaborated. The model of quantum spacetime we use is $AdS^5_q \times S^5_q$
for $q$ a root of unity. The quantum sphere is defined as a homogeneous space
with manifest $SU_q(3)$ symmetry, but as anticipated from the field theory
correspondence, we show that there is a hidden $SO_q(6)$ symmetry in the
constrution. We also study some properties of quantum space quotients as
candidate models for the quantum spacetime relevant for some $Z_n$ quiver
quotients of the $\N=4$ theory which break SUSY to $\N=2$. We find various
qualitative agreements between the proposed models and the properties of the
corresponding finite $N$ gauge theories.
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On N=1 Mirror Symmetry for Open Type II Strings: We study the open string extension of the mirror map for N=1 supersymmetric
type II vacua with D-branes on non-compact Calabi-Yau manifolds. Its definition
is given in terms of a system of differential equations that annihilate certain
period and chain integrals. The solutions describe the flat coordinates on the
N=1 parameter space, and the exact disc instanton corrected superpotential on
the D-brane world-volume. A gauged linear sigma model for the combined
open-closed string system is also given. It allows to use methods of toric
geometry to describe D-brane phase transitions and the N=1 K\"ahler cone.
Applications to a variety of D-brane geometries are described in some detail.
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Conformally Soft Photons and Gravitons: The four-dimensional $S$-matrix is reconsidered as a correlator on the
celestial sphere at null infinity. Asymptotic particle states can be
characterized by the point at which they enter or exit the celestial sphere as
well as their $SL(2,\mathbb C)$ Lorentz quantum numbers: namely their conformal
scaling dimension and spin $h\pm \bar h$ instead of the energy and momentum.
This characterization precludes the notion of a soft particle whose energy is
taken to zero. We propose it should be replaced by the notion of a conformally
soft particle with $h=0$ or $\bar h=0$. For photons we explicitly construct
conformally soft $SL(2,\mathbb C)$ currents with dimensions $(1,0)$ and
identify them with the generator of a $U(1)$ Kac-Moody symmetry on the
celestial sphere. For gravity the generator of celestial conformal symmetry is
constructed from a $(2,0)$ $SL(2,\mathbb C)$ primary wavefunction.
Interestingly, BMS supertranslations are generated by a spin-one weight
$(\frac{3}{2},\frac{1}{2})$ operator, which nevertheless shares holomorphic
characteristics of a conformally soft operator. This is because the right hand
side of its OPE with a weight $(h,\bar h)$ operator ${\cal O}_{h,\bar h}$
involves the shifted operator ${\cal O}_{h+\frac{1}{2},\bar h+ \frac{1}{2}}$.
This OPE relation looks quite unusual from the celestial CFT$_2$ perspective
but is equivalent to the leading soft graviton theorem and may usefully
constrain celestial correlators in quantum gravity.
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Easy bootstrap for the 3D Ising model: As a simple lattice model that exhibits a phase transition, the Ising model
plays a fundamental role in statistical and condensed matter physics. Its
continuum limit also furnishes a basic example of interacting quantum field
theories and universality classes. Motivated by a recent bootstrap study of the
quantum quartic oscillator, we revisit the conformal bootstrap approach to the
3D Ising model at criticality. Surprisingly, the low-lying properties are
determined to good accuracy by simple asymptotic formulae and a few
nonperturbative crossing constraints. For instance, the two relevant scaling
dimensions $(\Delta_\sigma,\Delta_\epsilon)\approx (0.51810,1.4123)$ are close
to the precise results from the bootstrap bounds.
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Supersymmetric BCS: Effects of an external magnetic field and spatial
fluctuations of the gap: Recently an N=1 supersymmetric model of BCS superconductivity was proposed
realizing spontaneous symmetry breaking of a U(1)_R symmetry. Due to scalar
contributions the superconducting phase transition turned out to be first order
rather than second order as in standard BCS theory. Here we consider the
effects of an external magnetic field and spatial fluctuations of the gap in
that model. This allows us to compute the magnetic penetration length and the
coherence length, and also to distinguish between type I and type II
superconductors. We compare the supersymmetric and standard relativistic BCS
results, where the main differences come from the different orders of the phase
transition.
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Warped Wilson Line DBI Inflation: We propose a novel inflationary scenario in string theory in which the
inflaton field is a 'Wilson line' degree of freedom in the worldvolume of a
probe Dp-brane, in a warped flux compactification. Kinetic terms for Wilson
line fields on the world volume of a D-brane take a nonstandard
Dirac-Born-Infeld (DBI) form. Thus, we work in the framework of DBI inflation.
This extends the original slow roll Wilson line inflationary scenario, where
only the quadratic piece was considered. Warped DBI Wilson line inflation
offers an attractive alternative to ordinary (position field) DBI inflation,
inasmuch as observational and theoretical constraints get considerably relaxed.
Besides the standard large non-Gaussianities in DBI scenarios, it is also
possible to achieve an observable amount of gravitational waves.
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Confinement/deconfinement transition in the D0-brane matrix model -- A
signature of M-theory?: We study the confinement/deconfinement transition in the D0-brane matrix
model (often called the BFSS matrix model) and its one-parameter deformation
(the BMN matrix model) numerically by lattice Monte Carlo simulations. Our
results confirm general expectations from the dual string/M-theory picture for
strong coupling. In particular, we observe the confined phase in the BFSS
matrix model, which is a nontrivial consequence of the M-theory picture. We
suggest that these models provide us with an ideal framework to study the
Schwarzschild black hole, M-theory, and furthermore, the parameter region of
the phase transition between type IIA superstring theory and M-theory. A
detailed study of M-theory via lattice Monte Carlo simulations of the D0-brane
matrix model might be doable with much smaller computational resources than
previously expected.
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Closed Strings in Misner Space: Cosmological Production of Winding
Strings: Misner space, also known as the Lorentzian orbifold $R^{1,1}/boost$, is one
of the simplest examples of a cosmological singularity in string theory. In
this work, the study of weakly coupled closed strings on this space is pursued
in several directions: (i) physical states in the twisted sectors are found to
come in two kinds: short strings, which wind along the compact space-like
direction in the cosmological (Milne) regions, and long strings, which wind
along the compact time-like direction in the (Rindler) whiskers. The latter can
be viewed as infinitely long static open strings, stretching from Rindler
infinity to a finite radius and folding back onto themselves. (ii) As in the
Schwinger effect, tunneling between these states corresponds to local pair
production of winding strings. The tunneling rate approaches unity as the
winding number $w$ gets large, as a consequence of the singular geometry. (iii)
The one-loop string amplitude has singularities on the moduli space, associated
to periodic closed string trajectories in Euclidean time. In the untwisted
sector, they can be traced to the combined existence of CTCs and Regge
trajectories in the spectrum. In the twisted sectors, they indicate pair
production of winding strings. (iv) At a classical level and in sufficiently
low dimension, the condensation of winding strings can indeed lead to a bounce,
although the required initial conditions are not compatible with Misner
geometry at early times. (v) The semi-classical analysis of winding string pair
creation can be generalized to more general (off-shell) geometries. We show
that a regular geometry regularizes the divergence at large winding number.
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Charged Particles in a 2+1 Curved Background: The coupling to a 2+1 background geometry of a quantized charged test
particle in a strong magnetic field is analyzed. Canonical operators adapting
to the fast and slow freedoms produce a natural expansion in the inverse square
root of the magnetic field strength. The fast freedom is solved to the second
order.
At any given time, space is parameterized by a couple of conjugate operators
and effectively behaves as the `phase space' of the slow freedom. The slow
Hamiltonian depends on the magnetic field norm, its covariant derivatives, the
scalar curvature and presents a peculiar coupling with the spin-connection.
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Gravity duals of N=2 SCFTs and asymptotic emergence of the electrostatic
description: We built the first eleven-dimensional supergravity solutions with
SO(2,4)xSO(3)xU(1)_R symmetry that exhibit the asymptotic emergence of an extra
U(1) isometry. This enables us to make the connection with the usual
electrostatics-quiver description. The solution is obtained via the Toda frame
of Kahler surfaces with vanishing scalar curvature and SU(2) action.
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More on Screening and Confinement in 2D QCD: We provide further evidence for the screening behavior of massless SU(N_c)
bosonized QCD by (i) computing the potential between external quarks, (ii)
bosonizing also the external sources and analyzing the states of the combined
system and (iii) using an expansion in N_f- the number of flavors. We write
down novel "non-abelian Schwinger like" solutions of the equations of motion,
compute their masses and argue that an exchange of massive modes of this type
is associated with the screening mechanism. Confinement for massive dynamical
fermions is shown using (ii) and (iii). We show the screening behavior of the
N=1 super Yang Mills theory, by applying a point splitting method to the scalar
current.
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Symmetric energy-momentum tensor in Maxwell, Yang-Mills, and Proca
theories obtained using only Noether's theorem: The symmetric and gauge-invariant energy-momentum tensors for source-free
Maxwell and Yang-Mills theories are obtained by means of translations in
spacetime via a systematic implementation of Noether's theorem. For the
source-free neutral Proca field, the same procedure yields also the symmetric
energy-momentum tensor. In all cases, the key point to get the right
expressions for the energy-momentum tensors is the appropriate handling of
their equations of motion and the Bianchi identities. It must be stressed that
these results are obtained without using Belinfante's symmetrization techniques
which are usually employed to this end.
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Quantum dispersion relations for the $AdS_4 \times CP^3$ GKP string: We compute the one-loop correction to the dispersion relations of the
excitations of the $AdS_4 \times CP^3$ sigma model dual to ABJM theory,
expanded around the cusp background. The results parallel those of N = 4 SYM.
As in that case, the dispersion relations are compatible with the predictions
from the Bethe ansatz for the GKP string, though showing some known
discrepancies on which we comment.
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On the complex structure of Yang-Mills theory: We consider the coupled set of spectral Dyson-Schwinger equations in
Yang-Mills theory for ghost and gluon propagators, which gives us access to the
ghost and gluon spectral functions. The set-up is used for a systematic
analytic evaluation of the constraints on generalised spectral representations
in Yang-Mills theory that are most relevant for informed spectral
reconstructions. We also provide numerical results for the coupled set of
spectral functions for a large range of potential mass gaps of the gluon, and
discuss the limitations and extensions of the present work.
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Anharmonic Waves in Field Theory: This work starts from the premise that sinusoidal plane waves cease to be
solutions of field theories when turning on an interaction. A nonlinear
interaction term generates harmonics analogous to those observed in nonlinear
optical media. This calls for a generalization to anharmonic waves in both
classical and quantum field theory. Three simple requirements make anharmonic
waves compatible with relativistic field theory and quantum physics. Some
non-essential concepts have to be abandoned, such as orthogonality, the
superposition principle, and the existence of single-particle energy
eigenstates. The most general class of anharmonic waves allows for a zero
frequency term in the Fourier series, which corresponds to a quantum field with
a non-zero vacuum expectation value. Anharmonic quantum fields are defined by
generalizing the expansion of a field operator into creation and annihilation
operators. This method provides a framework for handling exact quantum fields,
which define exact single particle states.
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Exact string solutions and duality: We review known exact classical solutions in (bosonic) string theory. The
main classes of solutions are `cosets' (gauged WZW models), `plane wave'-type
backgrounds (admitting a covariantly constant null Killing vector) and
`$F$-models' (backgrounds with two null Killing vectors generalising the
`fundamental string' solution). The recently constructed $D=4$ solutions with
Minkowski signature are given explicitly. We consider various relations between
these solutions and, in particular, discuss some aspects of the duality
symmetry. [To appear in the Proceedings of the 2nd Journe'e Cosmologie,
Observatoire de Paris, June 2-4, 1994.]
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BRST Invariant Theory Of A Generalized 1+1 Dimensional Nonlinear Sigma
Model With Topological Term: We give a generalized Lagrangian density of 1+1 Dimensional O(3) nonlinear
sigma model with subsidiary constraints, different Lagrange multiplier fields
and topological term, find a lost intrinsic constraint condition, convert the
subsidiary constraints into inner constraints in the nonlinear sigma model,
give the example of not introducing the lost constraint, by comparing the
example with the case of introducing the lost constraint, we obtain that when
not introducing the lost constraint, one has to obtain a lot of various
non-intrinsic constraints. We further deduce the gauge generator, give general
BRST transformation of the model under the general conditions. It is discovered
that there exists a gauge parameter originating from the freedom degree of BRST
transformation in a general O(3) nonlinear sigma model, and we gain the general
commutation relations of ghost field.
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Comparing models for a unitary black hole S-matrix: This paper compares features, challenges, and puzzles of different models for
a unitary black hole S-matrix, focussing on both recent nonisometric models, as
well as "nonviolent unitarization," which is based on new quantum interactions
of a black hole. As a foundation for comparison, the description of real-time
Hawking evolution is first overviewed, including leading effects of
gravitational dressing and backreaction. Connection is then made to qubit
models for evolution, and some technology is outlined to facilitate their
description. Important features of both nonisometric models and nonviolent
unitarization are investigated in qubit models, which illustrate essential
differences between the respective approaches. The nonisometric models present
puzzles for understanding evolution of internal outgoing excitations, which can
be excited by interactions such as particle decay. Qubit models for nonviolent
unitarization are further developed, and nicely illustrate aspects of that
approach. Some remaining questions in generalizing to more complete models for
evolution are discussed.
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The QCD theta-parameter in canonical quantization: The role of the QCD theta-parameter is investigated in pure Yang-Mills theory
in the spacetime given by the four-dimensional Euclidean torus. While in this
setting the introduction of possibly unphysical boundary conditions is avoided,
it must be specified how the sum over the topological sectors is to be carried
out. To connect with observables in real time, we perceive the partition
function as the trace over the canonical density matrix. The system then
corresponds to one of a finite temperature on a spatial three-torus. Carrying
out the trace operation requires canonical quantization and gauge fixing.
Fixing the gauge and demanding that the Hermiticity of the Hamiltonian is
maintained leads to a restriction of the Hilbert space of physical wave
functionals that generalizes the constraints derived from imposing Gauss' law.
Consequently, we find that the states in the Hilbert space are properly
normalizable under an inner product that integrates over each physical
configuration represented by the gauge potential one time and one time only.
The observables derived from the constrained Hilbert space do not violate
charge-parity symmetry. We note that an exact hidden symmetry of the theory
that is present for arbitrary values of theta in the Hamiltonian is effectively
promoted to parity conservation in this constrained space. These results,
derived on a torus in order to avoid the introduction of boundary conditions,
also carry over to Minkowski spacetime when taking account of all possible
gauge transformations.
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Ward Identity for Membranes: Ward identities in the case of scattering of antisymmetric three form RR
gauge fields off a D2-brane target has been studied in type-IIA theory.
|
T-Duality and Time development of a (2+1)-Dimensional String Universe: The time development of a model of (2+1)-dimensional torus universe is
studied based on background field equations which follow from a string theory.
The metrics in various cases are characterized by a real parameter which
specifies a ratio of the lengths of two independent cycles. When the parameter
is a rational number, the space is asymptotically stretched along a cycle while
the other cycle kept finite. When the parameter is an irrational number, the
lengths of two cycles, as well as the space volume (area), grow in proportion
to the proper time $t$ for an observer sitting at rest in this universe in the
asymptotic region.
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Asymptotic structure of Carrollian limits of Einstein-Yang-Mills theory
in four spacetime dimensions: In this paper, three things are done. First, we study from an algebraic point
of view the infinite-dimensional BMS-like extensions of the Carroll algebra
relevant to the asymptotic structure of the electric and magnetic Carrollian
limits of Einstein gravity. In the course of this study we exhibit by
"Carroll-Galileo duality" a new infinite-dimensional BMS-like extension of the
Galilean algebra and of its centrally extended Bargmann algebra. Second, we
consider the electric Carrollian limit of the pure Einstein theory and indicate
that more flexible boundary conditions than the ones that follow from just
taking the limit of the Einsteinian boundary conditions are actually
consistent. These boundary conditions lead to a bigger asymptotic symmetry
algebra that involves spatial supertranslations depending on three functions of
the angles (instead of one). Third, we turn to the Carrollian limit of the
coupled Einstein-Yang-Mills system. An infinite-dimensional color enhancement
of the gauge algebra is found in the electric Carrollian limit of the
Yang-Mills field, which allows angle-dependent Yang-Mills transformations at
spatial infinity, not available in the Einstein-Yang-Mills case prior to taking
the Carrollian electric limit. This enhancement does not occur in the magnetic
limit.
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Type IIA embeddings of $D=5$ minimal gauged supergravity via Non-Abelian
T-duality: In this note, we construct explicit Type IIA uplifts of $D=5$ minimal gauged
supergravity, by T-dualising known Type IIB uplifts on $N_5 = S^5$, $T^{1,1}$
and $Y^{p,q}$ along their $SU(2)$ isometries. When the $D=5$ gauge field is set
to zero, our uplifts recover precisely the known non-Abelian T-duals of the
$AdS_5\times N_5$ solutions. As an application, we obtain new supersymmetric
$AdS_3\times\Sigma\times M_5$ solutions in Type IIA, where $\Sigma =
\mathbb{WCP}^1_{[n_-,n_+]}$ is a weighted projective space. Existing
holographic results of T-dualised AdS solutions suggest that our solutions
capture features of $d = 2$ SCFTs with $\mathcal{N}=(0, 2)$ supersymmetry.
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Nambu-Sigma model and effective membrane actions: We propose an effective action for a p'-brane with open p-branes ending on
it. The action has dual descriptions similar to the commutative and
non-commutative ones of the DBI action for D-branes and open strings. The
Poisson structure governing the non-commutativity of the D-brane is replaced by
a Nambu structure and the open-closed string relations are generalized to the
case of p'-branes utilizing a novel Nambu sigma model description of p-branes.
In the case of an M5-brane our action interpolates between M5-actions already
proposed in the literature and matrix model like actions involving Nambu
structures.
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Feynman rules for higher-spin gauge fields on AdS$_{d+1}$: We determine the Feynman rules for the minimal type A higher-spin gauge
theory on AdS$_{d+1}$ at cubic order. In particular, we establish the quantum
action at cubic order in de Donder gauge, including ghosts. We also give the
full de Donder gauge propagators of higher-spin gauge fields and their ghosts.
This provides all ingredients needed to quantise the theory at cubic order.
|
The statistical mechanics of near-extremal black holes: An important open question in black hole thermodynamics is about the
existence of a "mass gap" between an extremal black hole and the lightest
near-extremal state within a sector of fixed charge. In this paper, we reliably
compute the partition function of Reissner-Nordstr\"{o}m near-extremal black
holes at temperature scales comparable to the conjectured gap. We find that the
density of states at fixed charge does not exhibit a gap; rather, at the
expected gap energy scale, we see a continuum of states. We compute the
partition function in the canonical and grand canonical ensembles, keeping
track of all the fields appearing through a dimensional reduction on $S^2$ in
the near-horizon region. Our calculation shows that the relevant degrees of
freedom at low temperatures are those of $2d$ Jackiw-Teitelboim gravity coupled
to the electromagnetic $U(1)$ gauge field and to an $SO(3)$ gauge field
generated by the dimensional reduction.
|
Viscosity Bound Violation in Higher Derivative Gravity: Motivated by the vast string landscape, we consider the shear viscosity to
entropy density ratio in conformal field theories dual to Einstein gravity with
curvature square corrections. After field redefinitions these theories reduce
to Gauss-Bonnet gravity, which has special properties that allow us to compute
the shear viscosity nonperturbatively in the Gauss-Bonnet coupling. By tuning
of the coupling, the value of the shear viscosity to entropy density ratio can
be adjusted to any positive value from infinity down to zero, thus violating
the conjectured viscosity bound. At linear order in the coupling, we also check
consistency of four different methods to calculate the shear viscosity, and we
find that all of them agree. We search for possible pathologies associated with
this class of theories violating the viscosity bound.
|
Generalized Born-Infeld-like models for kinks and branes: In this work we deal with a non-canonical scalar field in the two-dimensional
spacetime. We search for a generalized model that is twin of the standard
model, supporting the same defect structure with the same energy density. We
also study the stability of the defect solution under small fluctuations, which
is governed by a Sturm-Liouville equation, and show how to make it stable. The
model is then modified and used in the five-dimensional spacetime to construct
a thick brane that engenders the first order framework and preserves the
twinlike behavior, under tensorial fluctuations of the metric in its
gravitational sector.
|
Novel higher-curvature variations of $R^2$ inflation: We put forward novel extensions of Starobinsky inflation, involving a class
of 'geometric' higher-curvature corrections that yield second-order
Friedmann-Lema\^itre equations and second-order-in-time linearized equations
around cosmological backgrounds. We determine the range of models within this
class that admit an extended phase of slow roll inflation as an attractor. By
embedding these theories in anti-de Sitter space, we derive holographic
'unitarity' bounds on the two dominant higher-order curvature corrections.
Finally we compute the leading corrections to the spectral properties of scalar
and tensor primordial perturbations, including the modified consistency
relation $r=-8n_{T}$. Remarkably, the range of models singled out by holography
nearly coincides with the current observational bounds on the scalar spectral
tilt. Our results indicate that future observations have the potential to
discriminate between different higher-curvature corrections considered here.
|
On generalized Macdonald polynomials: Generalized Macdonald polynomials (GMP) are eigenfunctions of
specifically-deformed Ruijsenaars Hamiltonians and are built as triangular
polylinear combinations of Macdonald polynomials. They are orthogonal with
respect to a modified scalar product, which could be constructed with the help
of an increasingly important triangular perturbation theory, showing up in a
variety of applications. A peculiar feature of GMP is that denominators in this
expansion are fully factorized, which is a consequence of a hidden symmetry
resulting from the special choice of the Hamiltonian deformation. We introduce
also a simplified but deformed version of GMP, which we call generalized Schur
functions. Our basic examples are bilinear in Macdonald polynomials.
|
A microscopic description of absorption in high-energy string-brane
collisions: We study the collision of a highly energetic light closed string off a stack
of Dp-branes at (sub)string-scale impact parameters and in a regime justifying
a perturbative treatment. Unlike at larger impact parameters - where elastic
scattering and/or tidal excitations dominate - here absorption of the closed
string by the brane system, with the associated excitation of open strings
living on it, becomes important. As a first step, we study this phenomenon at
the disk level, in which the energetic closed string turns into a single heavy
open string at rest whose particularly simple properties are described.
|
Two-loop Integrability of Planar N=6 Superconformal Chern-Simons Theory: Bethe ansatz equations have been proposed for the asymptotic spectral problem
of AdS_4/CFT_3. This proposal assumes integrability, but the previous
verification of weak-coupling integrability covered only the su(4) sector of
the ABJM gauge theory. Here we derive the complete planar two-loop dilatation
generator of N=6 superconformal Chern-Simons theory from osp(6|4)
superconformal symmetry. For the osp(4|2) sector, we prove integrability
through a Yangian construction. We argue that integrability extends to the full
planar two-loop dilatation generator, confirming the applicability of the Bethe
equations at weak coupling. Further confirmation follows from an analytic
computation of the two-loop twist-one spectrum.
|
Conformal a-charge, correlation functions and conical defects: In this note we demonstrate that, as we conjectured earlier in [1], the
a-charge in the conformal anomaly in dimension $d=2n$ manifests in a $n$-point
correlation function of energy momentum tensor of a CFT considered in flat
spacetime with a conical defect. We consider in detail dimensions $d=2,\, 4,\,
6$ and give a general formula for arbitrary $n$.
|
Kink Crystal: We describe a one-dimensional kink crystal, which represents a collection of
equal and equally localized kinks forming a lattice in the real axis. The
results are analytical, original and may motivate other studies on localized
structures in high energy physics.
|
A Note on Quiver Quantum Toroidal Algebra: Recently, Li and Yamazaki proposed a new class of infinite-dimensional
algebras, quiver Yangian, which generalizes the affine Yangian
$\mathfrak{gl}_{1}$. The characteristic feature of the algebra is the action on
BPS states for non-compact toric Calabi-Yau threefolds, which are in one-to-one
correspondence with the crystal melting models. These algebras can be
bootstrapped from the action on the crystals and have various truncations.
In this paper, we propose a $q$-deformed version of the quiver Yangian,
referred to as the quiver quantum toroidal algebra (QQTA). We examine some of
the consistency conditions of the algebra. In particular, we show that QQTA is
a Hopf superalgebra with a formal super coproduct, like known quantum toroidal
algebras. QQTA contains an extra central charge $C$. When it is trivial
($C=1$), QQTA has a representation acting on the three-dimensional crystals,
like Li-Yamazaki's quiver Yangian. While we focus on the toric Calabi-Yau
threefolds without compact 4-cycles, our analysis can likely be generalized to
all toric Calabi-Yau threefolds.
|
N=1 supersymmetric sigma model with boundaries, II: We consider the N=1 supersymmetric two-dimensional non-linear sigma model
with boundaries and nonzero B-field. By analysing the appropriate currents we
describe the full set of boundary conditions compatible with N=1 superconformal
symmetry. Using this result the problem of finding a correct action is
discussed. We interpret the supersymmetric boundary conditions as a maximal
integral submanifold of the target space manifold, and speculate about a new
geometrical structure, the deformation of an almost product structure.
|
On generalizations of Verlinde's formula: It is shown that traces of mapping classes of finite order may be expressed
by Verlinde-like formulae. The 3D topological argument is explained, and the
resulting trace identities for modular matrix elements are presented.
|
No-birefringence conditions for spacetime: Within the axiomatic premetric approach to classical electrodynamics, we
derive under which covariant conditions the quartic Fresnel surface represents
a unique light cone without birefringence in vacuum.
|
Tropical Mirror: We describe the tropical curves in toric varieties and define the tropical
Gromov-Witten invariants. We introduce amplitudes for the higher topological
quantum mechanics (HTQM) on special trees and show that the amplitudes are
equal to the tropical Gromov-Witten invariants. We show that the sum over the
amplitudes in A-model HTQM equals to the total amplitude in B-model HTQM,
defined as a deformation of the A-model HTQM by the mirror superpotential. We
derive the mirror superpotentials for the toric varieties and showed that they
coincide with the superpotentials in the mirror Landau-Ginzburg theory. We
construct the mirror dual states to the evaluation observables in the tropical
Gromov-Witten theory.
|
Consistent Anti-de Sitter-Space/Conformal-Field-Theory Dual for a
Time-Dependent Finite Temperature System: We propose a consistent setup for the holographic dual of the strongly
coupled large-Nc N=4 super Yang-Mills theory plasma which undergoes the Bjorken
flow relevant to the quark-gluon plasma at BNL Relativistic Heavy Ion Collider
and CERN LHC. The dual geometry is constructed order by order in a well-defined
late-time expansion. The transport coefficients are determined by the
regularity of the geometry. We prove, for the first time, that the dual
geometry has an apparent horizon hence an event horizon, which covers a
singularity at the origin. Further we prove that the dual geometry is regular
to all orders in the late-time expansion under an appropriate choice of the
transport coefficients. This choice is also shown to be unique. Our model
serves as a concrete well-defined example of a time-dependent AdS/CFT dual.
|
The beat of a fuzzy drum: fuzzy Bessel functions for the disc: The fuzzy disc is a matrix approximation of the functions on a disc which
preserves rotational symmetry. In this paper we introduce a basis for the
algebra of functions on the fuzzy disc in terms of the eigenfunctions of a
properly defined fuzzy Laplacian. In the commutative limit they tend to the
eigenfunctions of the ordinary Laplacian on the disc, i.e. Bessel functions of
the first kind, thus deserving the name of fuzzy Bessel functions.
|
(N,p,q) Harmonic Superspace: A family of harmonic superspaces associated with four-dimensional spacetime
is described. Some applications to supersymmetric field theories, including
supergravity, are given.
|
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