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Analytic (non)integrability of Arutyunov-Bassi-Lacroix model: We use the notion of the gauge/string duality and discuss the Liouvillian
(non) integrability criteria for string sigma models in the context of recently
proposed Arutyunov-Bassi-Lacroix (ABL) model [JHEP \textbf{03} (2021), 062].
Our analysis complements those previous results due to numerical analysis as
well as Lax pair formulation. We consider a winding string ansatz for the
deformed torus $T^{\qty(\lambda_{1},\lambda_{2},\lambda)}_{k}$ which can be
interpreted as a system of coupled pendulums. Our analysis reveals the
Liouvillian nonintegrablity of the associated sigma model. We also obtain the
\emph{generalized} decoupling limit and confirm the analytic integrability for
the decoupled sector.
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Quantum Group Schrödinger Field Theory: We show that a quantum deformation of quantum mechanics given in a previous
work is equivalent to quantum mechanics on a nonlinear lattice with step size
$\Delta x=~(1-q)x$. Then, based on this, we develop the basic formalism of
quantum group Schr\"{o}dinger field theory in one spatial quantum dimension,
and explicitly exhibit the $SU_{q}(2)$ covariant algebras satisfied by the
$q$-bosonic and $q$-fermionic Schr\"{o}dinger fields. We generalize this result
to an arbitrary number of fields.
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Diff-invariant Kinetic Terms in Arbitrary Dimensions: We study the physical content of quadratic diff-invariant Lagrangians in
arbitrary dimensions by using covariant symplectic techniques. This paper
extends previous results in dimension four. We discuss the difference between
the even and odd dimensional cases.
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AdS Bubbles, Entropy and Closed String Tachyons: We study the conjectured connection between AdS bubbles (AdS solitons) and
closed string tachyon condensations. We confirm that the entanglement entropy,
which measures the degree of freedom, decreases under the tachyon condensation.
The entropies in supergravity and free Yang-Mills agree with each other
remarkably. Next we consider the tachyon condensation on the AdS twisted circle
and argue that its endpoint is given by the twisted AdS bubble, defined by the
double Wick rotation of rotating black 3-brane solutions. We calculated the
Casimir energy and entropy and checked the agreements between the gauge and
gravity results. Finally we show an infinite boost of a null linear dilaton
theory with a tachyon wall (or bubble), leads to a solvable time-dependent
background with a bulk tachyon condensation. This is the simplest example of
spacetimes with null boundaries in string theory.
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Scalar-Graviton Amplitudes and Celestial Holography: We compute scattering amplitudes involving one massive scalar and two, three,
or four gravitons. We show that when the conformal dimension of the massive
scalar is set to zero, the resulting celestial correlators depend {\it only} on
the coordinates of the gravitons. Such correlators of gravitons are
well-defined and do not suffer from divergences associated with the Mellin
transform of usual graviton amplitudes. Moreover, they are non-distributional
and take the form of standard CFT correlators. We show that they are consistent
with the usual OPEs but the statement of the soft theorem is modified.
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Some Examples of Chiral Moduli Spaces and Dynamical Supersymmetry
Breaking: We investigate the low-energy dynamics of $SU(N)$ gauge theories with one
antisymmetric tensor field, $N - 4 + N_f$ antifundamentals and $N_f$
fundamentals, for $N_f \le 3$. For $N_f = 3$ we construct the quantum moduli
space, and for $N_f < 3$ we find the exact quantum superpotentials. We find two
large classes of models with dynamical supersymmetry breaking. The odd $N$
theories break supersymmetry once appropriate mass terms are added in the
superpotential.
The even $N$ theories break supersymmetry after gauging an extra chiral
$U(1)$ symmetry.
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Quasi-integrability in deformed sine-Gordon models and infinite towers
of conserved charges: We have studied the space-reflection symmetries of some soliton solutions of
deformed sine-Gordon models in the context of the quasi-integrability concept.
Considering a dual pair of anomalous Lax representations of the deformed model
we compute analytically and numerically an infinite number of alternating
conserved and asymptotically conserved charges through a modification of the
usual techniques of integrable field theories. The charges associated to
two-solitons with a definite parity under space-reflection symmetry, i.e.
kink-kink (odd parity) and kink-antikink (even parity) scatterings with equal
and opposite velocities, split into two infinite towers of conserved and
asymptotically conserved charges. For two-solitons without definite parity
under space-reflection symmetry (kink-kink and kink-antikink scatterings with
unequal and opposite velocities) our numerical results show the existence of
the asymptotically conserved charges only. However, we show that in the
center-of-mass reference frame of the two solitons the parity symmetries and
their associated set of exactly conserved charges can be restored. Moreover,
the positive parity breather-like (kink-antikink bound state) solution exhibits
a tower of exactly conserved charges and a subset of charges which are periodic
in time. We back up our results with extensive numerical simulations which also
demonstrate the existence of long lived breather-like states in these models.
The time evolution has been simulated by the 4th order Runge-Kutta method
supplied with non-reflecting boundary conditions.
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From the planar limit to M-theory: The large-N limit of gauge theories has been playing a crucial role in
theoretical physics over the decades. Despite its importance, little is known
outside the planar limit where the 't Hooft coupling $\lambda=g_{YM}^2N$ is
fixed. In this Letter we consider more general large-N limit --- $\lambda$
grows with N, e.g., $g_{YM}^2$ is fixed. Such a limit is important particularly
in recent attempts to find the nonpertubative formulation of M-theory. Based on
various supporting evidence, we propose this limit is essentially identical to
the planar limit, in the sense the order of the large-N limit and the strong
coupling limit commute. For a wide class of large-N gauge theories, these two
limits are smoothly connected, and the analytic continuation from the planar
limit is justified. As simple examples, we reproduce a few properties of the
six-dimensional N=(2, 0) theory on S^1 from the five-dimensional maximal super
Yang-Mills theory, supporting the recent conjecture by Douglas and Lambert et
al. that these two theories are identical.
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On Fast Charged Particles Scattering on a Flat Relativistic Beam of
Charged Particles in Approximation of Continuous Potential: The differential scattering cross section for the problem of fast charged
particles motion near a flat relativistic beam of charged particles was
obtained. The problem is considered in the eikonal approximation in the
representation of the beam by a continuous potential.
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Dipole-Deformed Bound States and Heterotic Kodaira Surfaces: We study a particular N = 1 confining gauge theory with fundamental flavors
realised as seven branes in the background of wrapped five branes on a rigid
two-cycle of a non-trivial global geometry. In parts of the moduli space, the
five branes form bound states with the seven branes. We show that in this
regime the local supergravity solution is surprisingly tractable, even though
the background topology is non-trivial. New effects such as dipole deformations
may be studied in detail, including the full backreactions. Performing the
dipole deformations in other ways leads to different warped local geometries.
In the dual heterotic picture, which is locally given by a C* fibration over a
Kodaira surface, we study details of the geometry and the construction of
bundles. We also point out the existence of certain exotic bundles in our
framework.
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Q-stars in scalar-tensor gravitational theories in extra dimensions: We present Jordan-Brans-Dicke and general scalar-tensor gravitational theory
in extra dimensions in an asymptotically flat or anti de Sitter spacetime. We
consider a special gravitating, boson field configuration, a $q$-star, in 3, 4,
5 and 6 dimensions, within the framework of the above gravitational theory and
find that the parameters of the stable stars are a few per cent different from
the case of General Relativity.
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Emergent Dimensions and Braneworlds from Large-N Confinement: $\mathcal{N}=1$ $SU(N)$ super-Yang-Mills theory on $\mathbb{R}^3\times S^1$
is believed to have a smooth dependence on the circle size $L$. Making $L$
small leads to calculable non-perturbative color confinement, mass gap, and
string tensions. For finite $N$, the small-$L$ low-energy dynamics is described
by a three-dimensional effective theory. The large-$N$ limit, however, reveals
surprises: the infrared dual description is in terms of a theory with an
emergent fourth dimension, curiously reminiscent of T-duality in string theory.
Here, however, the emergent dimension is a lattice, with momenta related to the
$S^1$-winding of the gauge field holonomy, which takes values in
$\mathbb{Z}_N$. Furthermore, the low-energy description is given by a
non-trivial gapless theory, with a space-like $z=2$ Lifshitz scale invariance
and operators that pick up anomalous dimensions as $L$ is increased.
Supersymmetry-breaking deformations leave the long-distance theory
scale-invariant, but change the Lifshitz scaling exponent to $z=1$, and lead to
an emergent Lorentz symmetry at small $L$. Adding a small number of fundamental
fermion fields leads to matter localized on three-dimensional branes in the
emergent four-dimensional theory.
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Gauge symmetry breaking in orbifold model building: We review the gauge symmetry breaking mechanism due to orbifold projections
in orbifold model building. We explicitly show the existence of a scale of
breaking if such a symmetry breaking is due to freely-acting orbifold operators
only, i.e. in case the breaking is realized non-locally in the internal space.
We show that such a scale is related to the compactification moduli only, and
that there are no extra continuous parameters, at least in semirealistic models
with N=1 SUSY in four dimensions. In this sense, the mechanism is peculiarly
different from the standard Higgs (or Hosotani) symmetry breaking mechanism. We
show that the mechanism also differs from that present in standard orbifold
models where, even in presence of discrete Wilson lines, a scale of breaking is
generically missing, since the breaking is localized in specific points in the
internal space.
We review a set of background geometries where the described non-local
breaking is realized, both in the case of two and six extra dimensions. In the
latter case, relevant in string model building, we consider both heterotic and
open string compactifications.
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The Starobinsky Model from Superconformal D-Term Inflation: We point out that in the large field regime, the recently proposed
superconformal D-term inflation model coincides with the Starobinsky model. In
this regime, the inflaton field dominates over the Planck mass in the
gravitational kinetic term in the Jordan frame. Slow-roll inflation is realized
in the large field regime for sufficiently large gauge couplings. The
Starobinsky model generally emerges as an effective description of slow-roll
inflation if a Jordan frame exists where, for large inflaton field values, the
action is scale invariant and the ratio \hat {\lambda} of the inflaton
self-coupling and the nonminimal coupling to gravity is tiny. The
interpretation of this effective coupling is different in different models. In
superconformal D-term inflation it is determined by the scale of grand
unification, \hat {\lambda} ~ (\Lambda_{GUT}/M_P)^4.
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Nonlinear symmetries of black hole entropy in gauged supergravity: Freudenthal duality in N=2, D=4 ungauged supergravity is generated by an
anti-involutive operator that acts on the electromagnetic fluxes, and results
to be a symmetry of the Bekenstein-Hawking entropy. We show that, with a
suitable extension, this duality can be generalized to the abelian gauged case
as well, even in presence of hypermultiplets. By defining Freudenthal duality
along the scalar flow, one can prove that two configurations of charges and
gaugings linked by the Freudenthal operator share the same set of values of the
scalar fields at the black hole horizon. Consequently, Freudenthal duality is
promoted to a nonlinear symmetry of the black hole entropy. We explicitly show
this invariance for the model with prepotential $F=-i X^0 X^1$ and
Fayet-Iliopoulos gauging.
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On D3-brane Dynamics at Strong Warping: We study the dynamics of a D3 brane in generic IIB warped compactifications,
using the Hamiltonian formulation discussed in arXiv:0805.3700 [hep-th]. Taking
into account of both closed and open string fluctuations, we derive the warped
Kahler potential governing the motion of a probe D3 brane. By including the
backreaction of D3, we also comment on how the problem of defining a
holomorphic gauge coupling on wrapped D7 branes in warped background can be
resolved.
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On a Unified Theory of Generalized Branes Coupled to Gauge Fields,
Including the Gravitational and Kalb-Ramond Fields: We investigate a theory in which fundamental objects are branes described in
terms of higher grade coordinates X^{\mu_1 ... \mu_n} encoding both the motion
of a brane as a whole, and its volume evolution. We thus formulate a dynamics
which generalizes the dynamics of the usual branes. Geometrically, coordinates
X^{\mu_1 ... \mu_n} and associated coordinate frame fields {\gamma_{\mu_1 ...
\mu_n}} extend the notion of geometry from spacetime to that of an enlarged
space, called Clifford space or C-space. If we start from 4-dimensional
spacetime, then the dimension of C-space is 16. The fact that C-space has more
than four dimensions suggests that it could serve as a realization of
Kaluza-Klein idea. The "extra dimensions" are not just the ordinary extra
dimensions, they are related to the volume degrees of freedom, therefore they
are physical, and need not be compactified. Gauge fields are due to the metric
of Clifford space. It turns out that amongst the latter gauge fields there also
exist higher grade, antisymmetric fields of the Kalb-Ramond type, and their
non-Abelian generalization. All those fields are naturally coupled to the
generalized branes, whose dynamics is given by a generalized Howe-Tucker action
in curved C-space.
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Instabilities of Thin Black Rings: Closing the Gap: We initiate the study of dynamical instabilities of higher-dimensional black
holes using the blackfold approach, focusing on asymptotically flat boosted
black strings and singly-spinning black rings in $D\ge5$. We derive novel
analytic expressions for the growth rate of the Gregory-Laflamme instability
for boosted black strings and its onset for arbitrary boost parameter. In the
case of black rings, we study their stability properties in the region of
parameter space that has so far remained inaccessible to numerical approaches.
In particular, we show that very thin (ultraspinning) black rings exhibit a
Gregory-Laflamme instability, giving strong evidence that black rings are
unstable in the entire range of parameter space. For very thin rings, we show
that the growth rate of the instability increases with increasing
non-axisymmetric mode $m$ while for thicker rings, there is competition between
the different modes. However, up to second order in the blackfold
approximation, we do not observe an elastic instability, in particular for
large modes $m\gg1$, where this approximation has higher accuracy. This
suggests that the Gregory-Laflamme instability is the dominant instability for
very thin black rings. Additionally, we find a long-lived mode that describes a
wiggly time-dependent deformation of a black ring. We comment on disagreements
between our results and corresponding ones obtained from a large $D$ analysis
of black ring instabilities.
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D1 and D5-Brane Actions in AdS_m x S^n: The kappa-invariant and supersymmetric actions of D1 and D5-branes in AdS_3 x
S^3 are investigated, as well as the action of a D5-brane in an AdS_5 x S^5
background. The action of a D5-brane lying totally in an AdS_3 x S^3 background
is found. Some progress was made towards finding the action for the D5-brane
free to move in the whole AdS_3 x S^3 x T^4 space, however the supersymmetric
action found here is not kappa-invariant and the reasons the method used did
not find a kappa-invariant solution are discussed.
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Scenario for Seeding a Singularity in $d = 2$ String Black Hole with
Tachyon: The $d = 2$ string admits a black hole solution and also a singular solution
when tachyon back reaction is included. It is of importance to know if the
former solution can evolve into a later one. An explicit solution describing
this process is difficult to obtain. We present here a scenario in which such
an evolution is very likely to occur. In essence, it takes place when a
derivative discontinuity is seeded in the dilaton field by an incident tachyon
pulse. An application of this scenario to $1 + 1$ dimensional toy models
suggests that a black hole can evolve into a massive remnant, strengthening its
candidacy for the end state of a black hole.
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On the Thermodynamic Geometry of BTZ Black Holes: We investigate the Ruppeiner geometry of the thermodynamic state space of a
general class of BTZ black holes. It is shown that the thermodynamic geometry
is flat for both the rotating BTZ and the BTZ Chern Simons black holes in the
canonical ensemble. We further investigate the inclusion of thermal
fluctuations to the canonical entropy of the BTZ Chern Simons black holes and
show that the leading logartithmic correction due to Carlip is reproduced. We
establish that the inclusion of thermal fluctuations induces a non zero scalar
curvature to the thermodynamic geometry.
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Dilatonic Black Holes, Naked Singularities and Strings: We extend a previous calculation which treated Schwarschild black hole
horizons as quantum mechanical objects to the case of a charged, dilaton black
hole. We show that for a unique value of the dilaton parameter `a', which is
determined by the condition of unitarity of the S matrix, black holes transform
at the extremal limit into strings.
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Brill-Noether-general Limit Root Bundles: Absence of vector-like Exotics
in F-theory Standard Models: Root bundles appear prominently in studies of vector-like spectra of 4d
F-theory compactifications. Of particular importance to phenomenology are the
Quadrillion F-theory Standard Models (F-theory QSMs). In this work, we analyze
a superset of the physical root bundles whose cohomologies encode the
vector-like spectra for the matter representations $(\mathbf{3},
\mathbf{2})_{1/6}$, $(\mathbf{\overline{3}}, \mathbf{1})_{-2/3}$ and
$(\mathbf{1}, \mathbf{1})_{1}$. For the family $B_3( \Delta_4^\circ )$
consisting of $\mathcal{O}(10^{11})$ F-theory QSM geometries, we argue that
more than $99.995\%$ of the roots in this superset have no vector-like exotics.
This indicates that absence of vector-like exotics in those representations is
a very likely scenario.
The QSM geometries come in families of toric 3-folds $B_3( \Delta^\circ )$
obtained from triangulations of certain 3-dimensional polytopes $\Delta^\circ$.
The matter curves in $X_\Sigma \in B_3( \Delta^\circ )$ can be deformed to
nodal curves which are the same for all spaces in $B_3( \Delta^\circ )$.
Therefore, one can probe the vector-like spectra on the entire family $B_3(
\Delta^\circ )$ from studies of a few nodal curves. We compute the cohomologies
of all limit roots on these nodal curves.
In our applications, for the majority of limit roots the cohomologies are
determined by line bundle cohomology on rational tree-like curves. For this, we
present a computer algorithm. The remaining limit roots, corresponding to
circuit-like graphs, are handled by hand. The cohomologies are independent of
the relative position of the nodes, except for a few circuits. On these
\emph{jumping circuits}, line bundle cohomologies can jump if nodes are
specially aligned. This mirrors classical Brill-Noether jumps. $B_3(
\Delta_4^\circ )$ admits a jumping circuit, but the root bundle constraints
pick the canonical bundle and no jump happens.
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The complete worldsheet S matrix of superstrings on AdS_3 x S^3 x T^4
with mixed three-form flux: We determine the off-shell symmetry algebra and representations of Type IIB
superstring theory on $AdS_3\times S^3 \times T^4$ with mixed R-R and NS-NS
three-form flux. We use these to derive the non-perturbative worldsheet S
matrix of fundamental excitations of the superstring theory. Our analysis
includes both massive and massless modes and shows how turning on mixed
three-form flux results in an integrable deformation of the S matrix of the
pure R-R theory.
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Covariant Quantization of the Brink-Schwarz Superparticle: The quantization of the Brink-Schwarz-Casalbuoni superparticle is performed
in an explicitly covariant way using the antibracket formalism. Since an
infinite number of ghost fields are required, within a suitable off-shell
twistor-like formalism, we are able to fix the gauge of each ghost sector
without modifying the physical content of the theory. The computation reveals
that the antibracket cohomology contains only the physical degrees of freedom.
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String Theory and Integrable Systems: This is mainly a brief review of some key achievements in a `hot'' area of
theoretical and mathematical physics. The principal aim is to outline the basic
structures underlying {\em integrable} quantum field theory models with {\em
infinite-dimensional} symmetry groups which display a radically new type of
{\em quantum group} symmetries. Certain particular aspects are elaborated upon
with some detail: integrable systems of Kadomtsev-Petviashvili type and their
reductions appearing in matrix models of strings; Hamiltonian approach to
Lie-Poisson symmetries; quantum field theory approach to two-dimensional
relativistic integrable models with dynamically broken conformal invariance.
All field-theoretic models in question are of primary relevance to diverse
branches of physics ranging from nonlinear hydrodynamics to string theory of
fundamental particle interactions at ultra-high energies.
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Page Curve for Eternal Schwarzschild Black Hole in Dimensionally-Reduced
Model of Dilaton Gravity: As a contribution to the subject of the information loss paradox in
(1+1)-dimensional gravitational systems, we study a model of (1+1)-dimensional
dilaton gravity derived from the four-dimensional Einstein-Hilbert action by
dimensional reduction. The reduced action involves the cosmological constant
and admits black hole solutions. After including the back-reaction of quantum
fields to 1-loop order, we solve the semi-classical field equations
perturbatively and compute the quantum correction to the Hawking temperature.
We consider the quantum extremal surface approach and invoke the ``island
rule'' to compute the fine-grained entropy of the Hawking radiation for an
eternal Schwarzschild black hole and demonstrate that it follows the unitary
Page curve.
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Central charges and RG flow of strongly-coupled N=2 theory: We calculate the central charges a, c and k_G of a large class of
four-dimensional N=2 superconformal field theories arising from compactifying
the six-dimensional N=(2,0) theory on a Riemann surface with regular and
irregular punctures. We also study the renormalization group flows between the
general Argyres-Douglas theories, which all agree with the a-theorem.
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A Tale of Two Saddles: We find a new on-shell replica wormhole in a computation of the generating
functional of JT gravity coupled to matter. We show that this saddle has lower
action than the disconnected one, and that it is stable under restriction to
real Lorentzian sections, but can be unstable otherwise. The behavior of the
classical generating functional thus may be strongly dependent on the signature
of allowed perturbations. As part of our analysis, we give an LM-style
construction for computing the on-shell action of replicated manifolds even as
the number of boundaries approaches zero, including a type of one-step replica
symmetry breaking that is necessary to capture the contribution of the new
saddle. Our results are robust against quantum corrections; in fact, we find
evidence that such corrections may sometimes stabilize this new saddle.
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Holomorphically Covariant Matrix Models: We present a method to construct matrix models on arbitrary simply connected
oriented real two dimensional Riemannian manifolds. The actions and the path
integral measure are invariant under holomorphic transformations of matrix
coordinates.
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On the influence of three-point functions on the propagators of Landau
gauge Yang-Mills theory: We solve the Dyson-Schwinger equations of the ghost and gluon propagators of
Landau gauge Yang-Mills theory together with that of the ghost-gluon vertex.
The latter plays a central role in many truncation schemes for functional
equations. By including it dynamically we can determine its influence on the
propagators. We also suggest a new model for the three-gluon vertex motivated
by lattice data which plays a crucial role to obtain stable solutions when the
ghost-gluon vertex is included. We find that both vertices have a sizable
quantitative impact on the mid-momentum regime and contribute to the reduction
of the gap between lattice and Dyson-Schwinger equation results. Furthermore,
we establish that the three-gluon vertex dressing turns negative at low momenta
as suggested by lattice results in three dimensions.
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The Inflationary Wavefunction and its Initial Conditions: We explore the effect of initial conditions on the inflationary wavefunction
and their consequences for the observed spectrum of primordial fluctuations. In
a class of models with a sudden transition into inflation we find that, for a
reasonable set of assumptions about the reheat temperature and the number of
e-foldings, it is possible for initial conditions set by a pre-inflationary
epoch to have an observable effect.
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Standard Grand Unification from Superstrings: Recent developments about the construction of standard $SO(10)$ and $SU(5)$
grand unified theories from 4-dimensional superstrings are presented. Explicit
techniques involving higher level affine Lie algebras, for obtaining such
stringGUTs from symmetric orbifolds are discussed. Special emphasis is put on
the different constraints and selection rules for model building in this string
framework, trying to disentangle those which are generic from those depending
on the orbifold construction proposed. Some phenomenological implications from
such constraints are briefly discussed.
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From massive gravity to dark matter density: Massive gravity previously constructed as the spin-2 quantum gauge theory is
studied in the classical limit. The vector-graviton field v which does not
decouple in the limit of vanishing graviton mass gives rise to a modification
of general relativity. The modified Schwarzschild solution contains a
contribution which can be interpreted as the dark mass density. We calculate
the density profile in the simplest spherically symmetric geometry.
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On the type of the temperature phase transition in O(N) models within a
perturbative analysis: We investigate the type of the temperature phase transition in the $N$
component $\la \phi^4$ ($O(N)$) model of scalar fields. Actual calculations are
carried out in the beyond-super-daisy approximation (BSDA). The cases $N = 1$
and larger $N$ are considered separately. Using the solutions of gap equations
we show that the character of the phase transition depends on the account for
graphs BSDA. The role of different kinds of diagrams (especially the "sunset"
one) is clarified. It is shown in a perturbation theory in the effective
expansion parameter $N^{- 1/3}$ that the kind of the phase transition depends
on the value of coupling $\la$. It turns from a weak first-order to the
second-order one for increasing $\la$. This is in agreement with the
observation found recently for the $O(1)$ model in Monte Carlo simulations on a
lattice. Comparison with results of other authors is given.
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Flow Equations In Arbitrary Signature: We discuss general bosonic configurations of four-dimensional N=2
supergravity coupled to vector multiplets in (t,s) space-time. The supergravity
theories with Euclidean and neutral signature are described by the so-called
para-special K\"ahler geometry. For extremal solutions, we derive in a unified
fashion, using the equations of motion, the flow equations for all space-time
signatures. Demanding that the solutions with neutral and Euclidean signatures
admit unbroken supersymmetry, we derive the constraints, known as the
stabilisation equations, on the para-covariantly holomorphic sections expressed
in terms of the adapted coordinates. The stabilisation equations expressed in
terms of the para-complex sections imply generalised flow equations in terms of
para-complex central charge. For Euclidean and neutral signature, it is
demonstrated that solutions for either signs of gauge kinetic terms are mapped
into each other via field redefinitions.
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Fast Scramblers Of Small Size: We investigate various geometrical aspects of the notion of `optical depth'
in the thermal atmosphere of black hole horizons. Optical depth has been
proposed as a measure of fast-crambling times in such black hole systems, and
the associated optical metric suggests that classical chaos plays a leading
role in the actual scrambling mechanism. We study the behavior of the optical
depth with the size of the system and find that AdS/CFT phase transitions with
topology change occur naturally as the scrambler becomes smaller than its
thermal length. In the context of detailed AdS/CFT models based on D-branes,
T-duality implies that small scramblers are described in terms of matrix
quantum mechanics.
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Toy Model for Tachyon Condensation in Bosonic String Field Theory: We study tachyon condensation in a baby version of Witten's open string field
theory. For some special values of one of the parameters of the model, we are
able to obtain closed form expressions for the stable vacuum state and for the
value of the potential at the minimum. We study the convergence rate of the
level truncation method and compare our exact results with the numerical
results found in the full string field theory.
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New analytic solutions in String Field Theory: towards collective Higher
Spin vacuum: We construct analytic solutions in cubic open superstring field theory at
higher superconformal ghost numbers.The solutions are the pure ghost ones and
are given by combinations of Bell polynomials of bosonized superconformal ghost
fields multiplied by exponents of the bosonized ghosts. Based on the structure
of the solutions, we conjecture them to describe the ghost part of collective
vacuum for higher spin modes in open string theory.
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Holographic duality and the resistivity of strange metals: We present a strange metal, described by a holographic duality, which
reproduces the famous linear resistivity of the normal state of the copper
oxides, in addition to the linear specific heat. This holographic metal reveals
a simple and general mechanism for producing such a resistivity, which requires
only quenched disorder and a strongly interacting, locally quantum critical
state. The key is the minimal viscosity of the latter: unlike in a
Fermi-liquid, the viscosity is very small and therefore is important for the
electrical transport. This mechanism produces a resistivity proportional to the
electronic entropy.
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R^4 corrections to conifolds and G_2 holonomy metrics: Motivated by examples that appeared in the context of string theory - gauge
theory duality, we consider corrections to supergravity backgrounds induced by
higher derivative R^4+... terms in superstring effective action. We argue that
supersymmetric solutions that solve BPS conditions at the leading
(supergravity) order continue to satisfy a 1-st order ``RG-type'' system of
equations with extra source terms encoding string (or M-theory) corrections. We
illustrate this explicitly on the examples of R^4 corrections to the
generalized resolved and deformed 6-d conifolds and to a class of non-compact
7-d spaces with G_2 holonomy. Both types of backgrounds get non-trivial
modifications which we study in detail, stressing analogies between the two
cases.
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Gauge Theory and the Excision of Repulson Singularities: We study brane configurations that give rise to large-N gauge theories with
eight supersymmetries and no hypermultiplets. These configurations include a
variety of wrapped, fractional, and stretched branes or strings. The
corresponding spacetime geometries which we study have a distinct kind of
singularity known as a repulson. We find that this singularity is removed by a
distinctive mechanism, leaving a smooth geometry with a core having an enhanced
gauge symmetry. The spacetime geometry can be related to large-N Seiberg-Witten
theory.
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ABJM Mirrors and a Duality of Dualities: We clarify how mirror symmetry acts on 3d theories with N=2,3 or 4
supersymmetries and non-abelian Chern-Simons terms and then construct many new
examples. We identify a new duality, geometric duality, that allows us to
generate large families of gauge theories, with and without Chern-Simons term,
that all flow to the same conformal field theory in the infrared. In
particular, we find an interesting duality of dualities: a pair of theories
related via mirror symmetry can be mapped, via geometric duality, into a pair
of gauge theories related by Seiberg duality. This network of dualities can be
understood as the simple result that all of these theories are different
realizations of one and the same system in M-theory.
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Bright branes for strongly coupled plasmas: We use holographic techniques to study photon production in a class of finite
temperature, strongly coupled, large-Nc SU(Nc) quark-gluon plasmas with Nf <<
Nc quark flavours. Our results are valid to leading order in the
electromagnetic coupling constant but non-perturbatively in the SU(Nc)
interactions. The spectral function of electromagnetic currents and other
related observables exhibit an interesting structure as a function of the
photon frequency and the quark mass. We discuss possible implications for heavy
ion collision experiments.
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Horizons, holography and condensed matter: The holographic correspondence creates an interface between classical
gravitational physics and the dynamics of strongly interacting quantum field
theories. This chapter will relate the physics of charged, asymptotically
Anti-de Sitter spacetimes to the phenomenology of low temperature critical
phases of condensed matter. Common essential features will characterise both
the gravitational and field theoretic systems. Firstly, an emergent scaling
symmetry at the lowest energy scales appears as an emergent isometry in the
interior, `near horizon' regime of the spacetime. Secondly, the field theoretic
distinction between fractionalized and mesonic phases appears as the presence
or absence of a charge-carrying horizon in the spacetime. A perspective
grounded in these two characteristics allows a unified presentation of
`holographic superconductors', `electron stars' and `charged dilatonic
spacetimes'.
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Hydrodynamics and beyond in the strongly coupled N=4 plasma: We continue our investigations on the relation between hydrodynamic and
higher quasinormal modes in the AdS black hole background started in
arXiv:0710.4458 [hep-th]. As is well known, the quasinormal modes can be
interpreted as the poles of the retarded Green functions of the dual N=4 gauge
theory at finite temperature. The response to a generic perturbation is
determined by the residues of the poles. We compute these residues numerically
for energy-momentum and R-charge correlators. We find that the diffusion modes
behave in a similar way: at small wavelengths the residues go over into a form
of a damped oscillation and therefore these modes decouple at short distances.
The sound mode behaves differently: its residue does not decay and at short
wavelengths this mode behaves as the higher quasinormal modes. Applications of
our findings include the definition of hydrodynamic length and time scales. We
also show that the quasinormal modes, including the hydrodynamic diffusion
modes, obey causality.
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Unitarity in three-dimensional flat space higher spin theories: We investigate generic flat-space higher spin theories in three dimensions
and find a no-go result, given certain assumptions that we spell out. Namely,
it is only possible to have at most two out of the following three properties:
unitarity, flat space, non-trivial higher spin states. Interestingly, unitarity
provides an (algebra-dependent) upper bound on the central charge, like c=42
for the Galilean $W_4^{(2-1-1)}$ algebra. We extend this no-go result to rule
out unitary "multi-graviton" theories in flat space. We also provide an example
circumventing the no-go result: Vasiliev-type flat space higher spin theory
based on hs(1) can be unitary and simultaneously allow for non-trivial
higher-spin states in the dual field theory.
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Dynamical Mass Generation for Non-Abelian Gauge Fields without the Higgs: We present an alternative to the Higgs mechanism to generate masses for
non-abelian gauge fields in (3+1)-dimensions. The initial Lagrangian is
composed of a fermion with current-current and dipole-dipole type
self-interactions minimally coupled to non-abelian gauge fields. The mass
generation occurs upon the fermionic functional integration. We show that by
fine-tuning the coupling constants the effective theory contains massive
non-abelian gauge fields without any residual scalars or other degrees of
freedom.
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An Invitation to Higher Gauge Theory: In this easy introduction to higher gauge theory, we describe parallel
transport for particles and strings in terms of 2-connections on 2-bundles.
Just as ordinary gauge theory involves a gauge group, this generalization
involves a gauge '2-group'. We focus on 6 examples. First, every abelian Lie
group gives a Lie 2-group; the case of U(1) yields the theory of U(1) gerbes,
which play an important role in string theory and multisymplectic geometry.
Second, every group representation gives a Lie 2-group; the representation of
the Lorentz group on 4d Minkowski spacetime gives the Poincar\'e 2-group, which
leads to a spin foam model for Minkowski spacetime. Third, taking the adjoint
representation of any Lie group on its own Lie algebra gives a 'tangent
2-group', which serves as a gauge 2-group in 4d BF theory, which has
topological gravity as a special case. Fourth, every Lie group has an 'inner
automorphism 2-group', which serves as the gauge group in 4d BF theory with
cosmological constant term. Fifth, every Lie group has an 'automorphism
2-group', which plays an important role in the theory of nonabelian gerbes. And
sixth, every compact simple Lie group gives a 'string 2-group'. We also touch
upon higher structures such as the 'gravity 3-group' and the Lie 3-superalgebra
that governs 11-dimensional supergravity.
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Differential calculus and gauge theory on finite sets: We develop differential calculus and gauge theory on a finite set G. An
elegant formulation is obtained when G is supplied with a group structure and
in particular for a cyclic group. Connes' two-point model (which is an
essential ingredient of his reformulation of the standard model of elementary
particle physics) is recovered in our approach. Reductions of the universal
differential calculus to `lower-dimensional' differential calculi are
considered. The `complete reduction' leads to a differential calculus on a
periodic lattice which is related to q-calculus.
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Proposal for Background Independent Berkovits' Superstring Field Theory: In this paper we would like to propose the background independent formulation
of Berkovits' superstring field theory. Then we will show that the solution of
equation of motion of this theory leads to the Berkovits' superstring field
theory formulated around particular CFT background.
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Averaging over moduli in deformed WZW models: WZW models live on a moduli space parameterized by current-current
deformations. The moduli space defines an ensemble of conformal field theories,
which generically have $N$ abelian conserved currents and central charge $c >
N$. We calculate the average partition function and show that it can be
interpreted as a sum over 3-manifolds. This suggests that the ensemble-averaged
theory has a holographic dual, generalizing recent results on Narain CFTs. The
bulk theory, at the perturbative level, is identified as $U(1)^{2N}$
Chern-Simons theory coupled to additional matter fields. From a mathematical
perspective, our principal result is a Siegel-Weil formula for the characters
of an affine Lie algebra.
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The Imaginary Part of the Static Potential in Strongly Coupled
Anisotropic Plasma: Using the gauge/gravity duality we study the imaginary part of the static
potential associated to the thermal width in finite temperature strongly
coupled anisotropic plasma. We firstly derive the potential for a generic
anisotropic background. Then we apply our formulas to a theory where the
anisotropy has been generated by a space dependent axion term. We find that
using our method there exist a peculiar turning point in the imaginary part of
the potential, similar to the one appearing in the real part. The presence of
anisotropy leads to decrease of the imaginary potential, where larger decrease
happens along the anisotropic direction when the temperature is kept fixed.
When the entropy density is fixed, increase happens along the parallel
direction while along the transverse plane we observe a decrease. To estimate
the thermal width we use an approximate extrapolation beyond the turning point
and we find a decrease in presence of the anisotropy, independently of the
comparison scheme used.
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Relative Entanglement Entropies in 1+1-dimensional conformal field
theories: We study the relative entanglement entropies of one interval between excited
states of a 1+1 dimensional conformal field theory (CFT). To compute the
relative entropy $S(\rho_1 \| \rho_0)$ between two given reduced density
matrices $\rho_1$ and $\rho_0$ of a quantum field theory, we employ the replica
trick which relies on the path integral representation of ${\rm Tr} ( \rho_1
\rho_0^{n-1} )$ and define a set of R\'enyi relative entropies $S_n(\rho_1 \|
\rho_0)$. We compute these quantities for integer values of the parameter $n$
and derive via the replica limit, the relative entropy between excited states
generated by primary fields of a free massless bosonic field. In particular, we
provide the relative entanglement entropy of the state described by the primary
operator $i \partial\phi$, both with respect to the ground state and to the
state generated by chiral vertex operators. These predictions are tested
against exact numerical calculations in the XX spin-chain finding perfect
agreement.
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The renormalisation group for the truncated conformal space approach on
the cylinder: In this paper we continue the study of the truncated conformal space approach
to perturbed conformal field theories, this time applied to bulk perturbations
and focusing on the leading truncation-dependent corrections to the spectrum.
We find expressions for the leading terms in the ground state energy
divergence, the coupling constant renormalisation and the energy rescaling. We
apply these methods to problems treated in two seminal papers and show how
these RG improvements greatly increase the predictive power of the TCSA
approach. One important outcome is that the TCSA spectrum of excitations is
predicted not to converge for perturbations of conformal weight greater than
3/4, but the ratios of excitation energies should converge.
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Scattering of twist fields from D-branes and orientifolds: We compute the two-point function for Z_N orbifold twist fields on the disk
and RP2. We apply this to a computation of the O(g_s) correction to the Kahler
potential for (the symmetric combination of) blow-up modes in type I string
theory on T^6/Z_3. This is related by supersymmetry to the one-loop field
dependent correction to the Fayet-Iliopoulos D-term for the anomalous U(1)
factor. We find this correction to be non-vanishing away from the orbifold
point.
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Chiral Primordial Gravitational Waves from a Lifshitz Point: We study primordial gravitational waves produced during inflation in quantum
gravity at a Lifshitz point proposed by Ho${\rm\check{r}}$ava. Assuming
power-counting renormalizability, foliation preserving diffeomorphism
invariance, and the condition of detailed balance, we show that primordial
gravitational waves are circularly polarized due to parity violation. The
chirality of primordial gravitational waves is a quite robust prediction of
quantum gravity at a Lifshitz point which can be tested through observations of
cosmic microwave background radiation and stochastic gravitational waves.
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Comments on the anti-Hawking effect on a BTZ black hole spacetime: We compute the transition rate of an Unruh-DeWitt detector coupled both to a
ground state and to a KMS state of a massless, conformally coupled scalar field
on a static BTZ black hole with Robin boundary conditions. We observe that,
although the anti-Hawking effect is manifest for the ground state, this is not
the case for the KMS state. In addition, we show that our analysis applies with
minor modifications also to the anti-Unruh effect on Rindler-AdS$_3$ spacetime.
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Non-Perturbative Decoupling of Heavy Fermions: We show that heavy fermions decouple from the low energy physics also in
non-perturbative instanton effects. Provided the heavy fermions are lighter
than the symmetry breaking scale, all the instanton effects should be expressed
as local operators in the effective Lagrangian. The effective theory itself
doesn't admit instantons. We present the mechanism which suppresses instantons
in the effective theory.
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A Renormalized Supersymmetry in the Topological Yang-Mills Field Theory: We reconsider the algebraic BRS renormalization of Witten's topological
Yang-Mills field theory by making use of a vector supersymmetry Ward identity
which improves the finiteness properties of the model. The vector
supersymmetric structure is a common feature of several topological theories.
The most general local counterterm is determined and is shown to be a trivial
BRS-coboundary.
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Twisted K-theory and K-theory of bundle gerbes: In this note we introduce the notion of bundle gerbe K-theory and investigate
the relation to twisted K-theory. We provide some examples. Possible
applications of bundle gerbe K-theory to the classification of D-brane charges
in non-trivial backgrounds are discussed.
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Black strings in AdS_5: We present non-extremal magnetic black string solutions in five-dimensional
gauged supergravity. The conformal infinity is the product of time and S^1xS_h,
where S_h denotes a compact Riemann surface of genus h. The construction is
based on both analytical and numerical techniques. We compute the holographic
stress tensor, the Euclidean action and the conserved charges of the solutions
and show that the latter satisfy a Smarr-type formula. The phase structure is
determined in the canonical ensemble, and it is shown that there is a first
order phase transition from small to large black strings, which disappears
above a certain critical magnetic charge that is obtained numerically. For
another particular value of the magnetic charge, that corresponds to a twisting
of the dual super Yang-Mills theory, the conformal anomalies coming from the
background curvature and those arising from the coupling to external gauge
fields exactly cancel. We also obtain supersymmetric solutions describing waves
propagating on extremal BPS magnetic black strings, and show that they possess
a Siklos-Virasoro reparametrization invariance.
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Jack superpolynomials, superpartition ordering and determinantal
formulas: We call superpartitions the indices of the eigenfunctions of the
supersymmetric extension of the trigonometric Calogero-Moser-Sutherland model.
We obtain an ordering on superpartitions from the explicit action of the
model's Hamiltonian on monomial superfunctions. This allows to define Jack
superpolynomials as the unique eigenfunctions of the model that decompose
triangularly, with respect to this ordering, on the basis of monomial
superfunctions. This further leads to a simple and explicit determinantal
expression for the Jack superpolynomials.
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Zero Modes in a $c = 2$ Matrix Model: Recently \REF\dk{Simon Dalley and Igor Klebanov,'Light Cone Quantization of
the $c=2$ Matrix Model', PUPT-1333, hepth@xxx/920705} \refend Dalley and
Klebanov proposed a light-cone quantized study of the $c=2$ matrix model, but
which ignores $k^{+}=0$ contributions. Since the non-critical string limit of
the matrix model involves taking the parameters $\lambda$ and $\mu$ of the
matrix model to a critical point, zero modes of the field might be important in
this study. The constrained light-cone quantization (CLCQ) approach of Heinzl,
Krusche and Werner is applied . It is found that there is coupling between the
zero mode sector and the rest of the theory, hence CLCQ should be implemented.
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Nilpotent superfields for broken abelian symmetries: We find new solutions to real cubic constraints on $N=1$ chiral superfields
transforming under global abelian symmetries. These solutions describe the
low-energy dynamics of a goldstino interacting with an axion (both belonging to
the same chiral superfield) with non-linearly realized supersymmetry. We show
the relation between our model and the approach of Komargodski and Seiberg for
describing goldstino-axion dynamics which uses orthogonal nilpotent
superfields.
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Operator Identities, Representations of Algebras and the Problem of
Normal Ordering: Families of operator identities appeared as a consequence of an existence of
finite-dimensional representation of (super) Lie algebras of first-order
differential operators and $q$-deformed (quantum) algebras of first-order
finite-difference operators are presented. It is shown that those identities
can be rewritten in terms of creation/annihilation operators and it leads to a
simplification of the problem of the normal ordering in the second quantization
method.
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Canonical Deformation of $N=2$ $AdS_{4}$ SUGRA: It is known that one can define a consistent theory of extended, $N=2$
anti-de Sitter (AdS) Supergravity (SUGRA) in $D=4$. Besides the standard
gravitational part, this theory involves a single $U(1)$ gauge field and a pair
of Majorana vector-spinors that can be mixed into a pair of charged spin-$3/2$
gravitini. The action for $N=2$ $AdS_{4}$ SUGRA is invariant under
$SO(1,3)\times U(1)$ gauge transformations, and under local SUSY. We present a
geometric action that involves two "inhomogeneous" parts: an orthosymplectic
$OSp(4\vert 2)$ gauge-invariant action of the Yang-Mills type, and a
supplementary action invariant under purely bosonic $SO(2,3)\times U(1)\sim
Sp(4)\times SO(2)$ sector of $OSp(4\vert 2)$, that needs to be added for
consistency. This action reduces to $N=2$ $AdS_{4}$ SUGRA after gauge fixing,
for which we use a constrained auxiliary field in the manner of Stelle and
West. Canonical deformation is performed by using the Seiberg-Witten approach
to noncommutative (NC) gauge field theory with the Moyal product. The
NC-deformed action is expanded in powers of the deformation parameter
$\theta^{\mu\nu}$ up to the first order. We show that $N=2$ $AdS_{4}$ SUGRA has
non-vanishing linear NC correction in the physical gauge, originating from the
additional, purely bosonic action. For comparison, simple $N=1$ Poinacar\'{e}
SUGRA can be obtained in the same manner, directly from an $OSp(4\vert 1)$
gauge-invariant action. The first non-vanishing NC correction is quadratic in
$\theta^{\mu\nu}$ and therefore exceedingly difficult to calculate. Under
Wigner-In\"{o}n\"{u} (WI) contraction, $N=2$ AdS superalgebra reduces to $N=2$
Poincar\'{e} superalgebra, and it is not clear whether this relation holds
after canonical deformation. We present the linear NC correction to $N=2$
$AdS_{4}$ SUGRA explicitly, discuss its low-energy limit, and what remains of
it after WI contraction.
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Solvability of the $F_4$ Integrable System: It is shown that the $F_4$ rational and trigonometric integrable systems are
exactly-solvable for {\it arbitrary} values of the coupling constants. Their
spectra are found explicitly while eigenfunctions by pure algebraic means. For
both systems new variables are introduced in which the Hamiltonian has an
algebraic form being also (block)-triangular. These variables are invariant
with respect to the Weyl group of $F_4$ root system and can be obtained by
averaging over an orbit of the Weyl group. Alternative way of finding these
variables exploiting a property of duality of the $F_4$ model is presented. It
is demonstrated that in these variables the Hamiltonian of each model can be
expressed as a quadratic polynomial in the generators of some
infinite-dimensional Lie algebra of differential operators in a
finite-dimensional representation. Both Hamiltonians preserve the same flag of
polynomials and each subspace of the flag coincides with the finite-dimensional
representation space of this algebra. Quasi-exactly-solvable generalization of
the rational $F_4$ model depending on two continuous and one discrete
parameters is found.
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Braided Matrix Structure of the Sklyanin Algebra and of the Quantum
Lorentz Group: Braided groups and braided matrices are novel algebraic structures living in
braided or quasitensor categories. As such they are a generalization of
super-groups and super-matrices to the case of braid statistics. Here we
construct braided group versions of the standard quantum groups $U_q(g)$. They
have the same FRT generators $l^\pm$ but a matrix braided-coproduct $\und\Delta
L=L\und\tens L$ where $L=l^+Sl^-$, and are self-dual. As an application, the
degenerate Sklyanin algebra is shown to be isomorphic to the braided matrices
$BM_q(2)$; it is a braided-commutative bialgebra in a braided category. As a
second application, we show that the quantum double $D(\usl)$ (also known as
the `quantum Lorentz group') is the semidirect product as an algebra of two
copies of $\usl$, and also a semidirect product as a coalgebra if we use braid
statistics. We find various results of this type for the doubles of general
quantum groups and their semi-classical limits as doubles of the Lie algebras
of Poisson Lie groups.
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Finite dimensional AKSZ-BV theories: We describe a canonical reduction of AKSZ-BV theories to the cohomology of
the source manifold. We get a finite dimensional BV theory that describes the
contribution of the zero modes to the full QFT. Integration can be defined and
correlators can be computed. As an illustration of the general construction we
consider two dimensional Poisson sigma model and three dimensional Courant
sigma model. When the source manifold is compact, the reduced theory is a
generalization of the AKSZ construction where we take as source the cohomology
ring. We present the possible generalizations of the AKSZ theory.
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Non-local Thirring model at finite-temperature: We extend a recently proposed non-local and non-covariant version of the
Thirring model to the finite-temperature case. We obtain a completely bosonized
expression for the partition function, describing the thermodynamics of the
collective modes which are the underlying excitations of this system. From this
result we derive closed formulae for the free-energy, specific-heat, two-point
correlation functions and momentum distribution, as functionals of
electron-electron coupling potentials.
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"Peireles Substitution" and Chern-Simons Quantum Mechanics: An elementary derivation is given for the ``Peierles substitution'' used in
projecting dynamics in a strong magnetic field onto the lowest Landau level.
The projection of wavefunctions and the ordering prescription for the projected
Hamiltonian is explained.
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Discrete-time Calogero-Moser Model and Lattice KP Equations: We introduce an integrable time-discretized version of the classical
Calogero-Moser model, which goes to the original model in a continuum limit.
This discrete model is obtained from pole solutions of a semi-discretized
version of the Kadomtsev-Petviashvili equation, leading to a finite-dimensional
symplectic mapping. Lax pair, symplectic structure and sufficient set of
invariants of the discrete Calogero-Moser model are constructed for both the
rational and elliptic cases. The classical $r$-matrix is the same as for the
continuum model. An exact solution of the initial value problem is given for
the rational discrete-time Calogero-Moser model. The pole-expansion and
elliptic solutions of the fully discretized Kadomtsev-Petviashvili equation are
also discussed.
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Universal low temperature theory of charged black holes with AdS$_2$
horizons: We consider the low temperature quantum theory of a charged black hole of
zero temperature horizon radius $R_h$, in a spacetime which is asymptotically
AdS$_{D}$ ($D > 3$) far from the horizon. At temperatures $T \ll 1/R_h$, the
near-horizon geometry is AdS$_2$, and the black hole is described by a
universal 0+1 dimensional effective quantum theory of time diffeomorphisms with
a Schwarzian action, and a phase mode conjugate to the U(1) charge. We obtain
this universal 0+1 dimensional effective theory starting from the full
$D$-dimensional Einstein-Maxwell theory, while keeping quantitative track of
the couplings. The couplings of the effective theory are found to be in
agreement with those expected from the thermodynamics of the $D$-dimensional
black hole.
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Long Lived Large Type II Strings: decay within compactification: Motivated also by recent revival of interest about metastable string states
(as cosmic strings or in accelerator physics), we study the decay, in presence
of dimensional compactification, of a particular superstring state, which was
proven to be remarkably long-lived in the flat uncompactified scenario. We
compute the decay rate by an exact numerical evaluation of the imaginary part
of the one-loop propagator. For large radii of compactification, the result
tends to the fully uncompactified one (lifetime T = const M^5/g^2), as
expected, the string mainly decaying by massless radiation. For small radii,
the features of the decay (emitted states, initial mass dependence,....)
change, depending on how the string wraps on the compact dimensions.
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Representation-theoretic proof of the inner product and symmetry
identities for Macdonald's polynomials: This paper is a continuation of our papers \cite{EK1, EK2}. In \cite{EK2} we
showed that for the root system $A_{n-1}$ one can obtain Macdonald's
polynomials as weighted traces of intertwining operators between certain
finite-dimensional representations of $U_q(sl_n)$. The main goal of the present
paper is to use this construction to give a representation-theoretic proof of
Macdonald's inner product and symmetry identities for the root system
$A_{n-1}$. The proofs are based on the techniques of ribbon graphs developed by
Reshetikhin and Turaev. We also use the symmetry identities to derive recursive
relations for Macdonald's polynomials.
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Destruction of a metastable string by particle collisions: We calculate the probability of destruction of a metastable string by
collisions of the Goldstone bosons, corresponding to the transverse waves on
the string. We find a general formula that allows to determine the probability
of the string breakup by a collision of arbitrary number of the bosons. We find
that the destruction of a metastable string takes place only in collisions of
even number of the bosons, and we explicitly calculate the energy dependence of
such process in a two-particle collision for an arbitrary relation between the
energy and the largest infrared scale in the problem, the length of the
critical gap in the string.
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Spherically Symmetric Braneworld Solutions with R_{4} term in the Bulk: An analysis of a spherically symmetric braneworld configuration is performed
when the intrinsic curvature scalar is included in the bulk action; the
vanishing of the electric part of the Weyl tensor is used as the boundary
condition for the embedding of the brane in the bulk. All the solutions outside
a static localized matter distribution are found; some of them are of the
Schwarzschild-(A)dS_{4} form. Two modified Oppenheimer-Volkoff interior
solutions are also found; one is matched to a Schwarzschild-(A)dS_{4} exterior,
while the other does not. A non-universal gravitational constant arises,
depending on the density of the considered object; however, the conventional
limits of the Newton's constant are recovered. An upper bound of the order of
TeV for the energy string scale is extracted from the known solar system
measurements (experiments). On the contrary, in usual brane dynamics, this
string scale is calculated to be larger than TeV.
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Klebanov-Witten theory with massive dynamical flavors: We consider the addition of a large number of massive dynamical flavors to
the Klebanov-Witten theory, the quiver gauge theory describing the low energy
dynamics of Nc D3-branes at the conifold singularity. Massive flavors are
introduced by means of Nf D7-branes which are holomorphically embedded and
smeared along the transverse directions. After some general comments on the
validity of the smearing procedure, we find the full backreacted supergravity
solution corresponding to a particular class of massive embeddings. The
solution depends on a running effective number of flavors, whose functional
form follows from the smeared embedding. The running reflects the integrating
in/out of massive degrees of freedom in the dual field theory as the energy
scale is changed. We study how the dynamics of the theory depends on the flavor
parameters, mainly focusing on the static quark-antiquark potential. As
expected, we find that the dynamical flavors tend to screen the static color
charges.
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Algebraic Structures Related to Reflection Equations: Quadratic algebras related to the reflection equations are introduced. They
are quantum group comodule algebras. The quantum group $F_q(GL(2))$ is taken as
the example. The properties of the algebras (center, representations,
realizations, real forms, fusion procedure etc) as well as the generalizations
are discussed.
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Soft supersymmetry breaking with tiny cosmological constant in flux
compactified N=1 Supergravity: Using the flux compactification scenario in a generic supergravity model we
construct a set of conditions which are necessary to generate de-Sitter or anti
de-Sitter vacua for appropriate choices of the parameters in superpotential. It
is shown that a mass spectrum consistent with softly broken TeV scale
supersymmetry in a minimal supersymmetric standard model at the observable
sector can be obtained along with a tiny cosmological constant when the Kahler
and superpotential of the hidden sector satisfy a set of general constraints.
Constructing a specific model with Kahler and superpotentials which satisfy the
above constraints, it is demonstrated that all the hidden sector fields have
vacuum expectation values close to Planck scale and the resulting low energy
potential does not have any flat direction.
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Aspects of screening and confinement in a topologically massive
$U{\left( 1 \right)_{\cal W}} \times U{(1)_{\cal Y}}$ Chern-Simons-Higgs
theory: By using the gauge-invariant but path-dependent, variables formalism, we
consider a recently proposed topologically massive $U{\left( 1 \right)_{\cal
W}} \times U{(1)_{\cal Y}}$ Chern-Simons-Higgs theory in $2+1$ dimensions. In
particular, we inspect the impact of a Chern-Simons mixing term between two
Abelian gauge fields on physical observables. We pursue our investigation by
analysing the model in two different situations. In the first case, where we
integrate out the massive excitation and consider an effective model for the
massless field, we show that the interaction energy contains a linear term
leading to the confinement of static charge probes along with a screening
contribution. The second situation, where the massless field can be exactly
integrated over with its constraint duly taken into account, the interesting
feature is that the resulting effective model describes a purely screening
phase, without any trace of a confining regime.
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Integrable Open Spin Chains in Defect Conformal Field Theory: We demonstrate that the one-loop dilatation generator for the scalar sector
of a certain perturbation of N=4 Super Yang-Mills with fundamentals is the
Hamiltonian of an integrable spin chain with open boundary conditions. The
theory is a supersymmetric defect conformal field theory (dCFT) with the
fundamentals in hypermultiplets confined to a codimension one defect. We obtain
a K-matrix satisfying a suitably generalized form of the boundary Yang-Baxter
equation, study the Bethe ansatz equations and demonstrate how Dirichlet and
Neumann boundary conditions arise in field theory, and match to existing
results in the plane wave limit.
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Perturbative gauge theory at null infinity: We describe a theory living on the null conformal boundary of
four-dimensional Minkowski space, whose states include the radiative modes of
Yang-Mills theory. The action of a Kac-Moody symmetry algebra on the
correlators of these states leads to a Ward identity for asymptotic 'large'
gauge transformations which is equivalent to the soft gluon theorem. The
subleading soft gluon behavior is also obtained from a Ward identity for
charges acting as vector fields on the sphere of null generators of the
boundary. Correlation functions of the Yang-Mills states are shown to produce
the full classical S-matrix of Yang-Mills theory. The model contains additional
states arising from non-unitary gravitational degrees of freedom, indicating a
relationship with the twistor-string of Berkovits & Witten.
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Exact S-matrices for d_{n+1}^{(2)} affine Toda solitons and their bound
states: We conjecture an exact S-matrix for the scattering of solitons in
$d_{n+1}^{(2)}$ affine Toda field theory in terms of the R-matrix of the
quantum group $U_q(c_n^{(1)})$. From this we construct the scattering
amplitudes for all scalar bound states (breathers) of the theory. This S-matrix
conjecture is justified by detailed examination of its pole structure. We show
that a breather-particle identification holds by comparing the S-matrix
elements for the lowest breathers with the S-matrix for the quantum particles
in real affine Toda field theory, and discuss the implications for various
forms of duality.
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Finite Group Modular Data: In a remarkable variety of contexts appears the modular data associated to
finite groups. And yet, compared to the well-understood affine algebra modular
data, the general properties of this finite group modular data has been poorly
explored. In this paper we undergo such a study. We identify some senses in
which the finite group data is similar to, and different from, the affine data.
We also consider the data arising from a cohomological twist, and write down,
explicitly in terms of quantities associated directly with the finite group,
the modular S and T matrices for a general twist, for what appears to be the
first time in print.
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Hairy Black Holes in a Box: We do a systematic study of the phases of gravity coupled to an
electromagnetic field and charged scalar in flat space, with box boundary
conditions. The scalar-less box has previously been investigated by Braden,
Brown, Whiting and York (and others) before AdS/CFT and we elaborate and extend
their results in a language more familiar from holography. The phase diagram of
the system is analogous to that of AdS black holes, but we emphasize the
differences and explain their origin. Once the scalar is added, we show that
the system admits both boson stars as well as hairy black holes as solutions,
providing yet another way to evade flat space no-hair theorems. Furthermore
both these solutions can exist as stable phases in regions of the phase
diagram. The final picture of the phases that emerges is strikingly similar to
that found recently for holographic superconductors in global AdS, arXiv:
1602.07211. Our construction lays bare certain previously unnoticed subtleties
associated to the definition quasi-local charges for gravitating scalar fields
in finite regions.
|
Y-Systems for Generalised Gibbs Ensembles in Integrable Quantum Field
Theory: The thermodynamic Bethe ansatz approach to the study of integrable quantum
field theories was introduced in the early 90s. Since then it has been known
that the thermodynamic Bethe ansatz equations can be recast in the form of
$Y$-systems. These $Y$-systems have a number of interesting properties, notably
in the high-temperature limit their solutions are constants from which the
central charge of the ultraviolet fixed point can be obtained and they are
typically periodic functions, with period proportional to the dimension of the
perturbing field. In this letter we discuss the derivation of $Y$-systems when
the standard thermodynamic Bethe ansatz equations are replaced by generalised
versions, describing generalised Gibbs ensembles. We shown that for many
integrable quantum field theories, there is a large class of distinct
generalised Gibbs ensembles which share the same $Y$-system.
|
Duality Transformations for Generalized WDVV equations in Seiberg-Witten
theory: It is known that electric-magnetic duality transformations are symmetries of
the generalized Witten-Dijkgraaf-Verlinde-Verlinde (WDVV) equations. In
Seiberg-Witten theory the solutions to these equations come in certain sets
according to the gauge group. We show that the duality transformations
transform solutions within a set to another solution within the same set, by
using a subset of the Picard-Fuchs equations on the Seiberg-Witten family of
Riemann surfaces. The electric-magnetic duality transformations can be thought
of as changes of a canonical homology basis on the surfaces which in our
derivation is clearly responsible for the covariance of the generalized WDVV
system.
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On the addition of torsion to chiral gravity: Three-dimensional gravity in Anti-de Sitter space is considered, including
torsion. The derivation of the central charges of the algebra that generates
the asymptotic isometry group of the theory is reviewed, and a special point of
the theory, at which one of the central charges vanishes, is compared with the
chiral point of topologically massive gravity. This special point corresponds
to a singular point in Chern-Simons theory, where one of the two coupling
constants of the SL(2,R) actions vanishes. A prescription to approach this
point in the space of parameters is discussed, and the canonical structure of
the theory is analyzed.
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Frame-like Actions for Massless Mixed-Symmetry Fields in Minkowski space: A frame-like action for arbitrary mixed-symmetry bosonic massless fields in
Minkowski space is constructed. The action is given in a simple form and
consists of two terms for a field of any spin. The fields and gauge parameters
are certain tensor-valued differential forms. The formulation is based on the
unfolded form of equations for mixed-symmetry fields.
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Manifestly gauge-covariant representation of scalar and fermion
propagators: A new way to write the massive scalar and fermion propagators on a background
of a weak gauge field is presented. They are written in a form that is
manifestly gauge-covariant up to several additional terms that can be written
as boundary terms in momentum space. These additional terms violate
Ward-Takahashi identities and need to be renormalized by appropriate
counterterms if the complete theory is to be gauge-covariant. This form makes
it possible to calculate many amplitudes in a manifestly gauge-covariant way
(at the same time reducing the number of Feynman diagrams). It also allows to
express some counterterms in a way independent of the regularization scheme and
provides an easy way to derive the anomalous term affecting the chiral current
conservation.
|
The Supersymmetry of Higher-Derivative Supergravity in AdS$_4$
Holography: An action for the higher-derivative corrections to minimal gauged
supergravity in four dimensions has been recently proposed. We demonstrate that
the supersymmetric solutions of this model are those of the two-derivative
action, and investigate some of their properties. In particular, we prove a
formula for the renormalised on-shell action in terms of contributions from
fixed points of a $U(1)$ action, and confirm that it is invariant under
deformations which preserve the boundary almost contact structure.
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The Sakai-Sugimoto soliton: The Sakai-Sugimoto model is the preeminent example of a string theory
description of holographic QCD, in which baryons correspond to topological
solitons in the bulk. Here we investigate the validity of various
approximations of the Sakai-Sugimoto soliton that are used widely to study the
properties of holographic baryons. These approximations include the flat space
self-dual instanton, a linear expansion in terms of eigenfunctions in the
holographic direction and an asymptotic power series at large radius. These
different approaches have produced contradictory results in the literature
regarding properties of the baryon, such as relations for the electromagnetic
form factors. Here we determine the regions of validity of these various
approximations and show how to relate different approximations in contiguous
regions of applicability. This analysis clarifies the source of the
contradictory results in the literature and resolves some outstanding issues,
including the use of the flat space self-dual instanton, the detailed
properties of the asymptotic soliton tail, and the role of the UV cutoff
introduced in previous investigations. A consequence of our analysis is the
discovery of a new large scale, that grows logarithmically with the 't Hooft
coupling, at which the soliton fields enter a nonlinear regime. Finally, we
provide the first numerical computation of the Sakai-Sugimoto soliton and
demonstrate that the numerical results support our analysis.
|
Creation of Magnetic Monopoles in Classical Scattering: We consider the creation of 't Hooft-Polyakov magnetic monopoles by
scattering classical wave packets of gauge fields. An example with eight
clearly separated magnetic poles created with parity violating helical initial
conditions is shown. No clear separation of topological charge is observed with
corresponding parity symmetric initial conditions.
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Supersymmetry in Lorentzian Curved Spaces and Holography: We consider superconformal and supersymmetric field theories on
four-dimensional Lorentzian curved space-times, and their five-dimensional
holographic duals. As in the Euclidean signature case, preserved supersymmetry
for a superconformal theory is equivalent to the existence of a charged
conformal Killing spinor. Differently from the Euclidean case, we show that the
existence of such spinors is equivalent to the existence of a null conformal
Killing vector. For a supersymmetric field theory with an R-symmetry, this
vector field is further restricted to be Killing. We demonstrate how these
results agree with the existing classification of supersymmetric solutions of
minimal gauged supergravity in five dimensions.
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Dynamics of Brane-World Cosmological Models: We show that generically the initial singularity is isotropic in spatially
homogeneous cosmological models in the brane-world scenario. We then argue that
it is plausible that the initial singularity is isotropic in typical brane
world cosmological models. Therefore, brane cosmology naturally gives rise to a
set of initial data that provide the conditions for inflation to subsequently
take place, thereby solving the initial conditions problem and leading to a
self--consistent and viable cosmology.
|
Bosonization at Finite Temperature and Anyon Condensation: An operator formalism for bosonization at finite temperature and density is
developed. We treat the general case of anyon statistics. The exact $n$-point
correlation functions, satisfying the Kubo-Martin-Schwinger condition, are
explicitly constructed. The invariance under both vector and chiral
transformations allows to introduce two chemical potentials. Investigating the
exact momentum distribution, we discover anyon condensation in certain range of
the statistical parameter. Another interesting feature is the occurrence of a
non-vanishing persistent current. As an application of the general formalism,
we solve the massless Thirring model at finite temperature, deriving the charge
density and the persistent current.
|
Minimalisation of uncertainty relations in noncommutative quantum
mechanics: The explicit constrtuction of states saturating uncertainty relations
following from basic commutation rules of NCQM is given both in Fock space and
coordinate representation
|
S-duality and Topological Strings: In this paper we show how S-duality of type IIB superstrings leads to an
S-duality relating A and B model topological strings on the same Calabi-Yau as
had been conjectured recently: D-instantons of the B-model correspond to
A-model perturbative amplitudes and D-instantons of the A-model capture
perturbative B-model amplitudes.
Moreover this confirms the existence of new branes in the two models.
As an application we explain the recent results concerning A-model
topological strings on Calabi-Yau and its equivalence to the statistical
mechanical model of melting crystal.
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Pulsating strings on $(AdS_3 \times S^3)_\varkappa$: We derive the energy of pulsating strings as a function of adiabatic
invariant oscillation number, which oscillates in $S^2_{\varkappa}$. We find
similar solutions for the strings oscillating in deformed $AdS_3$. Furthermore,
we generalize the result to the oscillating strings in anti-de Sitter space in
the presence of extra angular momentum in $(AdS_3 \times S^1)_\varkappa$.
|
Generalized Dualities in 1T-Physics as Holographic Predictions from
2T-Physics: In the conventional formalism of physics, with 1-time, systems with different
Hamiltonians or Lagrangians have different physical interpretations and are
considered to be independent systems unrelated to each other. However, in this
paper we construct explicitly canonical maps in 1T phase space (including
timelike components, specifically the Hamiltonian) to show that it is
appropriate to regard various 1T-physics systems, with different Lagrangians or
Hamiltonians, as being duals of each other. This concept is similar in spirit
to dualities discovered in more complicated examples in field theory or string
theory. Our approach makes it evident that such generalized dualities are
widespread. This suggests that, as a general phenomenon, there are hidden
relations and hidden symmetries that conventional 1T-physics does not capture,
implying the existence of a more unified formulation of physics that naturally
supplies the hidden information. In fact, we show that 2T-physics in
(d+2)-dimensions is the generator of these dualities in 1T-physics in
d-dimensions by providing a holographic perspective that unifies all the dual
1T systems into one. The unifying ingredient is a gauge symmetry in phase
space. Via such dualities it is then possible to gain new insights toward new
physical predictions not suspected before, and suggest new methods of
computation that yield results not obtained before. As an illustration, we will
provide concrete examples of 1T-systems in classical mechanics that are solved
analytically for the first time via our dualities. These dualities in classical
mechanics have counterparts in quantum mechanics and field theory, and in some
simpler cases they have already been constructed in field theory. We comment on
the impact of our approach on the meaning of spacetime and on the development
of new computational methods based on dualities.
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The O(N) vector model in the large N limit revisited: multicritical
points and double scaling limit: The multicritical points of the $O(N)$ invariant $N$ vector model in the
large $N$ limit are reexamined. Of particular interest are the subtleties
involved in the stability of the phase structure at critical dimensions. In the
limit $N \to \infty$ while the coupling $g \to g_c$ in a correlated manner (the
double scaling limit) a massless bound state $O(N)$ singlet is formed and
powers of $1/N$ are compensated by IR singularities. The persistence of the $N
\to \infty$ results beyond the leading order is then studied with particular
interest in the possible existence of a phase with propagating small mass
vector fields and a massless singlet bound state. We point out that under
certain conditions the double scaled theory of the singlet field is
non-interacting in critical dimensions.
|
High-dimensional Lifshitz-type spacetimes, universal horizons and black
holes in Hořava-Lifshitz gravity: In this paper, we present all $[(d+1)+1]$-dimensional static diagonal vacuum
solutions of the non-projectable Ho\v{r}ava-Lifshitz gravity in the IR limit,
and show that they give rise to very rich Lifshitz-type structures, depending
on the choice of the free parameters of the solutions. These include the
Lifshitz spacetimes with or without hyperscaling violation, Lifshitz solitons,
and black holes. Remarkably, even the theory breaks explicitly the Lorentz
symmetry and allows generically instantaneous propagations, universal horizons
still exist, which serve as one-way membranes for signals with any large
velocities. In particular, particles even with infinitely large velocities
would just move around on these boundaries and cannot escape to infinity.
Another remarkable feature appearing in the Lifshitz-type spacetimes is that
the dynamical exponent $z$ can take its values only in the ranges $1 \le z < 2$
for $d \ge 3$ and $1 \le z <\infty$ for $d = 2$, due to the stability and
ghost-free conditions of the theory.
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Confinement in N=1 SUSY Gauge Theories and Model Building Tools: We develop a systematic approach to confinement in N=1 supersymmetric
theories. We identify simple necessary conditions for theories to confine
without chiral symmetry breaking and to generate a superpotential
non-perturbatively (s-confine). Applying these conditions we identify all N=1
theories with a single gauge group and no tree-level superpotential which
s-confine. We give a complete list of the confined spectra and superpotentials.
Some of these theories are of great interest for model building. We give
several new examples of models which break supersymmetry dynamically.
|
On Abelianization of First Class Constraints: The systematic method for the conversion of first class constraints to the
equivalent set of Abelian one based on the Dirac equivalence transformation is
developed. The representation for the corresponding matrix performing this
transformation is proposed. This representation allows one to lead the problem
of abelianization to the solution of a certain system of first order {\it
linear } differential equations for matrix elements .
|
Three-loop Correction to the Instanton Density. II. The Sine-Gordon
potential: In this second paper on quantum fluctuations near the classical instanton
configurations, see {\em Phys. Rev. D \bf 92}, 025046 (2015) and
arXiv:1501.03993, we focus on another well studied quantum-mechanical problem,
the one-dimensional Sine-Gordon potential (the Mathieu potential). Using only
the tools from quantum field theory, the Feynman diagrams in the instanton
background, we calculate the tunneling amplitude (the instanton density) to the
three-loop order. The result confirms (to seven significant figures) the one
recently recalculated by G. V. Dunne and M. \"{U}nsal, {\it Phys. Rev. \bf D
89}, 105009 (2014) from the resurgence perspective. As in the double well
potential case, we found that the largest contribution is given by the diagrams
originating from the Jacobian. We again observe that in the three-loop case
individual Feynman diagrams contain irrational contributions, while their sum
does not.
|
Variations of Infinite Derivative Modified Gravity: We consider nonlocal modified Einstein gravity without matter, where nonlocal
term has the form $P(R) F(\Box) Q(R)$. For this model, in this paper we give
the derivation of the equations of motion in detail. This is not an easy task
and presented derivation should be useful to a researcher who wants to
investigate nonlocal gravity. Also, we present the second variation of the
related Einstein-Hilbert modified action and basics of gravity perturbations.
|
Bjorken and threshold limit of a space-like structure function in the 2D
$U(N)$ Gross-Neveu model: In this note, we investigate a simple coordinate-space structure function
$f_a(z^2m^2,\lambda)$ in the 2D $U(N)$ Gross-Neveu model to next-to-leading
order in the large $N$ expansion. We analytically perform the twist expansion
in the Bjorken limit through double Mellin-representations. Hard and
non-perturbative scaling functions at various powers are naturally generated in
their Borel representations. At leading power (LP), the collinear factorization
formula is explicitly verified, and the issue of ``scale-dependency'' of
perturbative and non-perturbative functions is explained naturally. At NLP,
there are three series of non-perturbative functions and the related hard
functions. At higher powers, explicit forms for all the contributions are also
obtained. The renormalon cancellation at $t=n$ between hard functions at powers
$p$ and the non-perturbative functions at powers $p+n$ are explicitly verified
to all powers. Simple expressions for the leading power non-perturbative
functions are also provided both in coordinate space and momentum-fraction
spaces ($0<\alpha<1$) with ``zero-mode-type'' subtractions at $\alpha=0$
discussed in detail. We also investigate the threshold expansion of the
structure function and its relation to the twist expansion.
|
Bosonization and generalized Mandelstam soliton operators: The generalized massive Thirring model (GMT) with three fermion species is
bosonized in the context of the functional integral and operator formulations
and shown to be equivalent to a generalized sine-Gordon model (GSG) with three
interacting soliton species. The generalized Mandelstam soliton operators are
constructed and the fermion-boson mapping is established through a set of
generalized bosonization rules in a quotient positive definite Hilbert space of
states. Each fermion species is mapped to its corresponding soliton in the
spirit of particle/soliton duality of Abelian bosonization. In the
semi-classical limit one recovers the so-called SU(3) affine Toda model coupled
to matter fields (ATM) from which the classical GSG and GMT models were
recently derived in the literature. The intermediate ATM like effective action
possesses some spinors resembling the higher grading fields of the ATM theory
which have non-zero chirality. These fields are shown to disappear from the
physical spectrum, thus providing a bag model like confinement mechanism and
leading to the appearance of the massive fermions (solitons). The ordinary
MT/SG duality turns out to be related to each SU(2) sub-group. The higher rank
Lie algebra extension is also discussed.
|
Holographic Studies of The Generic Massless Cubic Gravities: We consider the generic massless cubic gravities coupled to a negative bare
cosmological constant mainly in $D=5$ and $D=4$ dimensions, which are Einstein
gravity extended with cubic curvature invariants where the linearized excited
spectrum around the AdS background contains no massive modes. The generic
massless cubic gravities are more general than Myers quasi-topological gravity
in $D=5$ and Einsteinian cubic gravity in $D=4$. It turns out that the massless
cubic gravities admit the black holes at least in a perturbative sense with the
coupling constants of the cubic terms becoming infinitesimal. The first order
approximate black hole solutions with arbitrary boundary topology $k$ are
presented, and in addition, the second order approximate planar black holes are
exhibited as well. We then establish the holographic dictionary for such
theories by presenting $a$-charge, $C_T$-charge and energy flux parameters
$t_2$ and $t_4$. By perturbatively discussing the holographic R\'enyi entropy,
we find $a$, $C_T$ and $t_4$ can somehow determine the R\'enyi entropy with the
limit $q\rightarrow 1$, $q\rightarrow 0$ and $q\rightarrow \infty$ up to the
first order, where $q$ is the order of the R\'enyi entropy. For holographic
hydrodynamics, we discuss the shear-viscosity-entropy-ratio and find that the
patterns deviating from the KSS bound $1/(4\pi)$ can somehow be controlled by
$((c-a)/c,t_4)$ up to the first order in $D=5$, and
$((\mathcal{C}_T-\tilde{a})/\mathcal{C}_T,t_4)$ up to the second order in
$D=4$, where $\mathcal{C}_T$ and $\tilde{a}$ differ from $C_T$-charge and
$a$-charge by inessential overall constants.
|
Maximally supersymmetric solutions of ten- and eleven-dimensional
supergravities: We classify (up to local isometry) the maximally supersymmetric solutions of
the eleven- and ten-dimensional supergravity theories. We find that the AdS
solutions, the Hpp-waves and the flat space solutions exhaust them.
|
Corrugated Multi-Supersheets: We explore the multi-superthreads and supersheets solutions of
six-dimensional N=1 supergravity coupled to a tensor multiplet. The solutions
carry D1-D5-P charges, but no Kaluza-Klein monopole. We lay down the formalism
to construct multiple supersheets with arbitrary and independent profiles. The
solution is by construction free of Dirac strings in contrast to the
five-dimensional construction where one has to separately solve integrability
conditions. We explore this formalism to construct supersheets that fluctuate
in both directions allowing a more general choice of profiles. These new
solutions are genuinely six-dimensional, singular, fluctuating BPS solutions
and by analyzing them we expect to learn more about the conjectured
superstrata. We also derive the conditions under which different supersheets
can touch, or even intersect through each other.
|
Operator mixing, UV asymptotics of nonplanar/planar $2$-point
correlators, and nonperturbative large-$N$ expansion of QCD-like theories: We work out the interplay between lowest-order perturbative computations in
the 't Hooft coupling, $g^2=g^2_{YM} N$, operator mixing, renormalization-group
(RG) improved ultraviolet (UV) asymptotics of leading-order (LO)
nonplanar/planar contributions to $2$-point correlators, and nonperturbative
large-$N$ expansion of perturbatively massless QCD-like theories. As concrete
examples, we compute to the lowest perturbative order in $SU(N)$ YM theory the
ratios, $r_i$, of LO-nonplanar to planar contributions to the $2$-point
correlators in the orthogonal basis in the coordinate representation of the
gauge-invariant dimension-$8$ scalar operators and all the twist-$2$ operators.
We demonstrate that -- if $\frac{\gamma_0}{\beta_0}$ has no LO-nonplanar
contribution, with $\gamma_0$ and $\beta_0$ the one-loop coefficients of the
anomalous-dimension matrix and beta function respectively -- $r_i$ actually
coincides with the corresponding ratio in the large-$N$ expansion of the
RG-improved UV asymptotics of the $2$-point correlators, provided that a
certain canonical nonresonant diagonal renormalization scheme exists for the
corresponding operators. Contrary to the aforementioned scalar operators, for
the first $10^3$ twist-$2$ operators we actually verify the above conditions,
and we get the universal value $r_i=-\frac{1}{N^2}$. Hence, nonperturbatively
such $r_i$ must coincide with the UV asymptotics of the ratio of the glueball
self-energy loop to the glueball tree contribution to the $2$-point correlators
above. As a consequence, the universality of $r_i$ reflects the universality of
the effective coupling in the nonperturbative large-$N$ YM theory for the
twist-$2$ operators in the coordinate representation.
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JuliBootS: a hands-on guide to the conformal bootstrap: We introduce {\tt JuliBootS}, a package for numerical conformal bootstrap
computations coded in {\tt Julia}. The centre-piece of {\tt JuliBootS} is an
implementation of Dantzig's simplex method capable of handling arbitrary
precision linear programming problems with continuous search spaces. Current
supported features include conformal dimension bounds, OPE bounds, and
bootstrap with or without global symmetries. The code is trivially
parallelizable on one or multiple machines. We exemplify usage extensively with
several real-world applications. In passing we give a pedagogical introduction
to the numerical bootstrap methods.
|
Holographic superconductivity in Einsteinian Cubic Gravity: We study the condensation of a charged scalar field in a $(3+1)$-dimensional
asymptotically AdS background in the context of Einsteinian cubic gravity,
featuring a holographic superconductor with higher curvature corrections
corresponding to a CFT with a non-vanishing value of the stress tensor
three-point function $t_4$. As it was previously noticed for higher dimensional
Gauss-Bonnet theory, we observe that the critical temperature of the
superconducting phase transition is lowered as the higher curvature coupling
grows.
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Holographic plasma and anyonic fluids: We use alternative quantisation of the $D3/D5$ system to explore properties
of a strongly coupled charged plasma and strongly coupled anyonic fluids. The
$S$-transform of the $D3/D5$ system is used as a model for charged matter
interacting with a U(1) gauge field in the large coupling regime, and we
compute the dispersion relationship of the propagating electromagnetic modes as
the density and temperature are changed. A more general $SL(2,\mathbb{Z})$
transformation gives a strongly interacting anyonic fluid, and we study its
transport properties as we change the statistics of the anyons and the
background magnetic field.
|
Breakdown of emergent Lifshitz symmetry in holographic matter with
Harris-marginal disorder: We revisit the theory of strongly correlated quantum matter perturbed by
Harris-marginal random-field disorder, using the simplest holographic model. We
argue that for weak disorder, the ground state of the theory is not Lifshitz
invariant with a non-trivial disorder-dependent dynamical exponent, as
previously found. Instead, below a non-perturbatively small energy scale, we
predict infrared physics becomes independent of the disorder strength.
|
Stringy (Galilei) Newton-Hooke Chern-Simons Gravities: We construct Chern-Simons gravities in $(2+1)$-dimensional space-time
considering the Stringy Galilei algebra both with and without non-central
extensions. In the first case, there is an invariant and non-degenerate
bilinear form, however, the field equations do not allow to express the spin
connections in terms of the dreibeins. In the second case, there is no
invariant non-degenerate bilinear form. Therefore, in both cases, we do not
have an ordinary gravity theory. Instead, if we consider the stringy
Newton-Hooke algebra with extensions as gauge group we have an invariant
non-degenerate metric and from the field equations, we express the spin
connections in terms of the geometric fields.
|
Vector-Field Domain Walls: We argue that spontaneous Lorentz violation may generally lead to metastable
domain walls related to the simultaneous violation of some accompanying
discrete symmetries. Remarkably, such domain wall solutions exist for
space-like Lorentz violation and do not exist for the time-like violation.
Because a preferred space direction is spontaneously induced, these domain
walls have no planar symmetry and produce a peculiar static gravitational field
at small distances, while their long-distance gravity appears the same as for
regular scalar-field walls. Some possible applications of vector-field domain
walls are briefly discussed.
|
Vortices on the Higgs Branch of the Seiberg-Witten Theory: We study the mechanism of confinement via formation of
Abrikosov-Nielsen-Olesen vortices on the Higgs branch of N=2 supersymmetric
SU(2) gauge theory with massive fundamental matter. Higgs branch represents a
limiting case of superconductor of type I with vanishing Higgs mass. We show
that in this limit vortices still exist although they become logarithmically
"thick". Because of this the confining potential is not linear any longer. It
behaves as $L/\log L$ with a distance $L$ between confining heavy charges
(monopoles). This new confining regime can occur only in supersymmetric
theories. We also address the problem of quantum stability of vortices. To this
end we develop string representation for a vortex and use it to argue that
vortices remain stable.
|
Nonrelativistic Limit of Dirac Theory From Effective Field Theory: In this work we analyze the low energy nonrelativistic limit of Dirac theory
in the framework of effective field theory. By integrating out the high energy
modes of Dirac field, given in terms of a combination of the two-components
Weyl spinors, we obtain a low energy effective action for the remaining
components, whose equation of motion can then be compared to the
Pauli-Schr\"odinger equation after demanding normalization of the wave
function. We then discuss the relevance of the terms in the effective action in
the context of an anisotropic dimensional analysis which is suitable for
nonrelativistic theories.
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Absorption of scalars by extremal black holes in string theory: We show that the low frequency absorption cross section of minimally coupled
test massless scalar fields by extremal spherically symmetric black holes in d
dimensions is equal to the horizon area, even in the presence of
string--theoretical $\alpha'$ corrections. Classically one has the relation
$\sigma = 4 G S$ between that absorption cross section and the black hole
entropy. By comparing in each case the values of the horizon area and Wald's
entropy, we discuss the validity of such relation in the presence of higher
derivative corrections for extremal black holes in many different contexts: in
the presence of electric and magnetic charges, for nonsupersymmetric and
supersymmetric black holes, in d=4 and d=5 dimensions. The examples we consider
seem to indicate that this relation is not verified in the presence of
$\alpha'$ corrections in general, although being valid in some specific cases
(electrically charged maximally supersymmetric black holes in d=5). We argue
that the relation $\sigma = 4 G S$ should in general be valid for the
absorption cross section of scalar fields which, although being independent
from the black hole solution, have their origin from string theory, and
therefore are not minimally coupled.
|
Infinite N phase transitions in continuum Wilson loop operators: We define smoothed Wilson loop operators on a four dimensional lattice and
check numerically that they have a finite and nontrivial continuum limit. The
continuum operators maintain their character as unitary matrices and undergo a
phase transition at infinite N reflected by the eigenvalue distribution closing
a gap in its spectrum when the defining smooth loop is dilated from a small
size to a large one. If this large N phase transition belongs to a solvable
universality class one might be able to calculate analytically the string
tension in terms of the perturbative Lambda-parameter. This would be achieved
by matching instanton results for small loops to the relevant large-N-universal
function which, in turn, would be matched for large loops to an effective
string theory. Similarities between our findings and known analytical results
in two dimensional space-time indicate that the phase transitions we found only
affect the eigenvalue distribution, but the traces of finite powers of the
Wilson loop operators stay smooth under scaling.
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An Infinite Set of Tree Amplitudes in Higgs-Yang-Mills: It is pointed out that the Parke-Taylor or maximally helicity violating
amplitudes in the pure Yang-Mills can, after some specifications, be
interpreted as amplitudes of scattering of massive vector bosons in the
Higgs-Yang-Mills system.
|
A Comment on Holographic Luttinger Theorem: Robustness of the Luttinger theorem for fermionic liquids is examined in
holography. The statement of the Luttinger theorem, the equality between the
fermion charge density and the volume enclosed by the Fermi surface, can be
mapped to a Gauss's law in the gravity dual, a la Sachdev. We show that various
deformations in the gravity dual, such as inclusion of magnetic fields, a
parity-violating theta-term, dilatonic deformations, and higher-derivative
corrections, do not violate the holographic derivation of the Luttinger
theorem, as long as the theory is in a confining phase. Therefore a robustness
of the theorem is found for strongly correlated fermions coupled with strongly
coupled sectors which admit gravity duals. On the other hand, in the deconfined
phase, we also show that the deficit appearing in the Luttinger theorem is
again universal. It measures a total deficit which measures the charge of the
deconfined ("fractionalized") fermions, independent of the deformation
parameters.
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Anyons and Deformed Lie Algebras: We discuss the connection between anyons (particles with fractional
statistics) and deformed Lie algebras (quantum groups). After a brief review of
the main properties of anyons, we present the details of the anyonic
realization of all deformed classical Lie algebras in terms of anyonic
oscillators. The deformation parameter of the quantum groups is directly
related to the statistics parameter of the anyons. Such a realization is a
direct generalization of the Schwinger construction in terms of fermions and is
based on a sort of bosonization formula which yields the generators of the
deformed algebra in terms of the undeformed ones. The entire procedure is well
defined on two-dimensional lattices, but it can be consistently reduced also to
one-dimensional chains.
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Correlation functions for some conformal theories on Riemann surfaces: We discuss the geometrical connection between 2D conformal field theories,
random walks on hyperbolic Riemann surfaces and knot theory. For the wide class
of CFTs with monodromies being the discrete subgroups of SL(2,R), the
determination of four-point correlation functions are related to construction
of topological invariants for random walks on multipunctured Riemann surfaces
|
A new method to solve the Non Perturbative Renormalization Group
equations: We propose a method to solve the Non Perturbative Renormalization Group
equations for the $n$-point functions. In leading order, it consists in solving
the equations obtained by closing the infinite hierarchy of equations for the
$n$-point functions. This is achieved: i) by exploiting the decoupling of modes
and the analyticity of the $n$-point functions at small momenta: this allows us
to neglect some momentum dependence of the vertices entering the flow
equations; ii) by relating vertices at zero momenta to derivatives of lower
order vertices with respect to a constant background field. Although the
approximation is not controlled by a small parameter, its accuracy can be
systematically improved. When it is applied to the O(N) model, its leading
order is exact in the large $N$ limit; in this case, one recovers known results
in a simple and direct way, i.e., without introducing an auxiliary field.
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Magnetic Monopoles with No Strings Attached: A Portal to the Dark Side
of Dual Electrodynamics: It has long been known that in the absence of electric charges and currents,
Maxwell's electromagnetism in 4 dimensional vacuum Minkowski space-time is
invariant under SO(2) dual transformations that mix its electric and magnetic
fields. Extending this symmetry to include the coupling to electrically charged
matter, requires a dual coupling to magnetically charged matter as well,
leading to Maxwell equations for SO(2) dual electrodynamics. Based on a doubled
ensemble of SO(2) dual 4-vector gauge potentials which does away with the need
of Dirac string singularities for magnetic monopoles, a local Lagrangian action
principle for SO(2) dual electromagnetism is known, which manifestly displays
all the required space-time and internal symmetries, and reduces to the
experimentally well established Maxwell electrodynamics in the absence of
magnetic charges and currents. Applying the same considerations for the matter
action of electrically and magnetically charged point particles, a unique SO(2)
dual generalised Lorentz force is identified for SO(2) dual electrodynamics,
truly different from the usual SO(2) dual invariant choice motivated by
simplicity, but yet made arbitrarily and which does not derive from some action
principle. This generalised Lorentz force involves a single real and new
coupling constant of unknown value, without the requirement of a
Dirac-Schwinger-Zwanziger quantisation condition for electric and magnetic
charges of dyons. A physical consequence for SO(2) dual electrodynamics of this
coupling constant if nonvanishing, is to open a channel, or portal between the
otherwise mutually totally ``dark'' sectors of electric and magnetic charges
for electromagnetic interactions.
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Spin group and almost commutative geometry: For Connes' spectral triples, the group of automorphisms lifted to the
Hilbert space is defined and used to fluctuate the metric. A few commutative
examples are presented including Chamseddine and Connes' spectral unification
of gravity and electromagnetism. One almost commutative example is treated: the
full standard model. Here the lifted automorphisms explain O'Raifeartaigh's
reduction $SU(2)\times U(3)/\zz_2.$
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Photon Masses in the Landscape and the Swampland: In effective quantum field theory, a spin-1 vector boson can have a
technically natural small mass that does not originate from the Higgs
mechanism. For such theories, which may be written in St\"uckelberg form, there
is no point in field space at which the mass is exactly zero. I argue that
quantum gravity differs from, and constrains, effective field theory:
arbitrarily small St\"uckelberg masses are forbidden. In particular, the limit
in which the mass goes to zero lies at infinite distance in field space, and
this distance is correlated with a tower of modes becoming light according to
the Swampland Distance Conjecture. Application of Tower or Sublattice variants
of the Weak Gravity Conjecture makes this statement more precise: for a spin-1
vector boson with coupling constant $e$ and St\"uckelberg mass $m$, local
quantum field theory breaks down at energies at or below $\Lambda_{\rm UV} =
\min((m M_{\rm Pl}/e)^{1/2}, e^{1/3} M_{\rm Pl})$. Combined with
phenomenological constraints, this argument implies that the Standard Model
photon must be exactly massless. It also implies that much of the parameter
space for light dark photons, which are the target of many experimental
searches, is compatible only with Higgs and not St\"uckelberg mass terms. This
significantly affects the experimental limits and cosmological histories of
such theories. I explain various caveats and weak points of the arguments,
including loopholes that could be targets for model-building.
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Is Bimetric Gravity Really Ghost Free?: We perform the Hamiltonian analysis of the bimetric theory of gravity
introduced in [arXiv:1109.3515 [hep-th]]. We carefully analyze the requirement
of the preservation of all constraints and we find that there is no additional
constraint that could eliminate the ghost mode.
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Black hole entropy in string-generated gravity models: The Euclidean action and entropy are computed in string-generated gravity
models with quadratic curvatures, and used to argue that a negative mass
extremal metric is the background for hyperbolic (k=-1) black hole spacetimes,
k being the curvature constant of the event horizon. The entropy associated
with a black hole is always positive for k=(0,1) family. The positivity of
energy condition also ensures that the k=-1 (extremal) entropy is non-negative.
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The six-point remainder function to all loop orders in the multi-Regge
limit: We present an all-orders formula for the six-point amplitude of planar
maximally supersymmetric N=4 Yang-Mills theory in the leading-logarithmic
approximation of multi-Regge kinematics. In the MHV helicity configuration, our
results agree with an integral formula of Lipatov and Prygarin through at least
14 loops. A differential equation linking the MHV and NMHV helicity
configurations has a natural action in the space of functions relevant to this
problem---the single-valued harmonic polylogarithms introduced by Brown. These
functions depend on a single complex variable and its conjugate, w and w*,
which are quadratically related to the original kinematic variables. We
investigate the all-orders formula in the near-collinear limit, which is
approached as |w|->0. Up to power-suppressed terms, the resulting expansion may
be organized by powers of log|w|. The leading term of this expansion agrees
with the all-orders double-leading-logarithmic approximation of Bartels,
Lipatov, and Prygarin. The explicit form for the sub-leading powers of log|w|
is given in terms of modified Bessel functions.
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Heterotic Kink Solitons and their Worldvolume Action: We present a formalism for computing the higher-order corrections to the
worldvolume action of a co-dimension one kink soliton embedded in
five-dimensional heterotic M-theory. The geometry of heterotic M-theory, as
well as the effective theory which describes a five-brane wrapping a
holomorphic curve by a topological kink in a scalar field, is reviewed. Using
this formalism, the explicit worldvolume action is computed to second order in
two expansion parameters--one describing the "warp" of the heterotic geometry
and the second the fluctuation length of the soliton hypersurface. The result
is expressed in terms of the trace of the extrinsic curvature and the intrinsic
curvature scalar.
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Doubled Field Approach to Yang - Mills Requires Non-Locality: Doubling a Yang-Mills field we apply the pattern which has been found to
construct a "duality-symmetric" gravity with matter to the "duality-symmetric"
Yang - Mills theory in five space-time dimensions. Constructing the action we
conclude that dualizing a non-abelian theory requires non-locality. We analyze
the symmetries of the theory and equations of motion. Extension to the
supersymmetric theory is also demonstrated.
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Hadron physics as Seiberg dual of QCD: We try to identify the light hadron world as the magnetic picture of QCD. We
take both phenomenological and theoretical approaches to this hypothesis, and
find that the interpretation seems to show interesting consistencies. In
particular, one can identify the rho and omega mesons as the magnetic gauge
bosons, and the Higgs mechanism for them provides a dual picture of the color
confinement.
|
Landau energy spectrum and quantum oscillator model for twisted
N-enlarged Newton-Hooke space-time: We derive the energy levels for oscillator model defined on the twisted
N-enlarged Newton-Hooke space-time, i.e., we find time-dependent eigenvalues
and corresponding time-dependent eigenstates. We also demonstrate that for a
particular choice of deformation parameters of phase space the above spectrum
can be identified with the time-dependent Landau one.
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A Covariant Approach to Noncommutative M5-branes: We briefly review how to discuss noncommutative (NC) M5-branes and
intersecting NC M5-branes from kappa-invariance of an open supermembrane action
with constant three-form fluxes. The kappa-invariance gives rise to possible
Dirichlet brane configurations. We shortly summarize a construction of
projection operators for NC M5-branes and some intersecting configurations of
NC M5-branes. A strong flux limit of them is also discussed.
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Holographic entanglement entropy and the internal space: We elaborate on the role of extremal surfaces probing the internal space in
AdS/CFT. Extremal surfaces in AdS quantify the "geometric" entanglement between
different regions in physical space for the dual CFT. This, however, is just
one of many ways to split a given system into subsectors, and extremal surfaces
in the internal space should similarly quantify entanglement between subsectors
of the theory. For the case of AdS$_5\times$S$^5$, their area was interpreted
as entanglement entropy between U(n) and U(m) subsectors of U(n+m) N=4 SYM.
Making this proposal precise is subtle for a number of reasons, the most
obvious being that from the bulk one usually has access to gauge-invariant
quantities only, while a split into subgroups is inherently gauge variant. We
study N=4 SYM on the Coulomb branch, where some of the issues can be mitigated
and the proposal can be sharpened. Continuing back to the original
AdS$_5\times$S$^5$ geometry, we obtain a modified proposal, based on the
relation of the internal space to the R-symmetry group.
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Massive Vector Chern-Simons Gravity: We present a second order gravity action which consists of ordinary Einstein
action augmented by a first-order, vector like, Chern-Simons quasi topological
term.This theory is ghost-free and propagates a pure spin-2 mode. It is
diffeomorphism invariant, although its local Lorentz invariance has been
spontaneously broken.
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Four-qubit entanglement from string theory: We invoke the black hole/qubit correspondence to derive the classification of
four-qubit entanglement. The U-duality orbits resulting from timelike reduction
of string theory from D=4 to D=3 yield 31 entanglement families, which reduce
to nine up to permutation of the four qubits.
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Cosmic No Hair for Braneworlds with a Bulk Dilaton Field: Braneworld cosmology supported by a bulk scalar field with an exponential
potential is developed. A general class of separable backgrounds for both
single and two-brane systems is derived, where the bulk metric components are
given by products of world-volume and bulk coordinates and the world-volumes
represent any anisotropic and inhomogeneous solution to an effective
four-dimensional Brans-Dicke theory of gravity. We deduce a cosmic no hair
theorem for all ever expanding, spatially homogeneous Bianchi world-volumes and
find that the spatially flat and isotropic inflationary scaling solution
represents a late-time attractor when the bulk potential is sufficiently flat.
The dependence of this result on the separable nature of the bulk metric is
investigated by applying the techniques of Hamilton-Jacobi theory to
five-dimensional Einstein gravity. We employ the spatial gradient expansion
method to determine the asymptotic form of the bulk metric up to third-order in
spatial gradients. It is found that the condition for the separable form of the
metric to represent the attractor of the system is precisely the same as that
for the four-dimensional world-volume to isotropize. We also derive the
fourth-order contribution to the Hamilton-Jacobi generating functional.
Finally, we conclude by placing our results within the context of the
holographic approach to braneworld cosmology.
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Brane gaugino condensate in 10d: We analyze the structure of gaugino interactions on D7-branes from a 10d
perspective. This is essential if one wants to lift the standard 4d approach to
type IIB moduli stabilization to 10d. In particular, a 10d picture has recently
been used to raise concerns about the KKLT proposal for constructing de Sitter
vacua, and to lend support to swampland conjectures against de Sitter. However,
the analyses of brane gaugino condensation so far are plagued by UV divergences
and do not include local 4-fermion terms. They also fail to reproduce the
4-fermion terms required by supergravity when compactified to four dimensions.
Motivated by the structure of heterotic and Horava-Witten theories, we suggest
an extension of the brane action by a particular 4-fermion operator that
resolves the above problems. Crucially, the UV divergence is cancelled and the
expected structure of the 4d effective action is reproduced. We believe that
attempts at a 10d description of KKLT have to be reconsidered in this new
light.
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Complete integrability of geodesic motion in Sasaki-Einstein toric
$Y^{p,q}$ spaces: We construct explicitly the constants of motion for geodesics in the
$5$-dimensional Sasaki-Einstein spaces $Y^{p,q}$. To carry out this task we use
the knowledge of the complete set of Killing vectors and Killing-Yano tensors
on these spaces. In spite of the fact that we generate a multitude of constants
of motion, only five of them are functionally independent implying the complete
integrability of geodesic flow on $Y^{p,q}$ spaces. In the particular case of
the homogeneous Sasaki-Einstein manifold $T^{1,1}$ the integrals of motion have
simpler forms and the relations between them are described in detail.
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Bounds on the local energy density of holographic CFTs from bulk
geometry: The stress tensor is a basic local operator in any field theory; in the
context of AdS/CFT, it is the operator which is dual to the bulk geometry
itself. Here we exploit this feature by using the bulk geometry to place
constraints on the local energy density in static states of holographic
$(2+1)$-dimensional CFTs living on a closed (but otherwise generally curved)
spatial geometry. We allow for the presence of a marginal scalar deformation,
dual to a massless scalar field in the bulk. For certain vacuum states in which
the bulk geometry is well-behaved at zero temperature, we find that the bulk
equations of motion imply that the local energy density integrated over
specific boundary domains is negative. In the absence of scalar deformations,
we use the inverse mean curvature flow to show that if the CFT spatial geometry
has spherical topology but non-constant curvature, the local energy density
must be positive somewhere. This result extends to other topologies, but only
for certain types of vacuum; in particular, for a generic toroidal boundary,
the vacuum's bulk dual must be the zero-temperature limit of a toroidal black
hole.
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Semitransparent pistons: We consider semitransparent pistons in the presence of extra dimensions. It
is shown that the piston is always attracted to the closest wall irrespective
of details of the geometry and topology of the extra dimensions and of the
cross section of the piston. Furthermore, we evaluate the zeta regularized
determinant for this configuration.
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Spread of entanglement in a Sachdev-Ye-Kitaev chain: We study the spread of R\'enyi entropy between two halves of a
Sachdev-Ye-Kitaev (SYK) chain of Majorana fermions, prepared in a thermofield
double (TFD) state. The SYK chain model is a model of chaotic many-body
systems, which describes a one-dimensional lattice of Majorana fermions, with
spatially local random quartic interaction. We find that for integer R\'enyi
index $n>1$, the R\'enyi entanglement entropy saturates at a parametrically
smaller value than expected. This implies that the TFD state of the SYK chain
does not rapidly thermalize, despite being maximally chaotic: instead, it
rapidly approaches a prethermal state. We compare our results to the signatures
of thermalization observed in other quenches in the SYK model, and to intuition
from nearly-$\mathrm{AdS}_2$ gravity.
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High temperature dimensional reduction in Snyder space: In this paper, we formulate the statistical mechanics in Snyder space that
supports the existence of a minimal length scale. We obtain the corresponding
invariant Liouville volume which properly determines the number of microstates
in the semiclassical regime. The results show that the number of accessible
microstates drastically reduces at the high energy regime such that there is
only one degree of freedom for a particle. Using the Liouville volume, we
obtain the deformed partition function and we then study the thermodynamical
properties of the ideal gas in this setup. Invoking the equipartition theorem,
we show that $2/3$ of the degrees of freedom freeze at the high temperature
regime when the thermal de Broglie wavelength becomes of the order of the
Planck length. This reduction of the number of degrees of freedom suggests an
effective dimensional reduction of the space from $3$ to $1$ at the Planck
scale.
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Mean lifetime of a false vacuum in terms of the Krylov-Fock non-escape
probability: The Krylov-Fock expression of non-decay (or survival) probability, which
allows to evaluate the deviations from the exponential decay law (nowadays well
established experimentally), is more informative as it readily provides the
distribution function for the lifetime as a random quantity. Guided by the well
established formalism for describing nuclear alpha decay, we use this
distribution function to figure out the mean value of lifetime and its
fluctuation rate. This theoretical framework is of considerable interest
inasmuch as it allows an experimental verification. Next, we apply the
Krylov-Fock approach to the decay of a metastable state at a finite temperature
in the framework of thermo-field dynamics. In contrast to the existing
formalism, this approach shows the interference effect between the tunnelings
from different metastable states as well as between the tunneling and the
barrier hopping. This effect looks quite natural in the framework of consistent
quantum mechanical description as a manifestation of the "double-slit
experiment". In the end we discuss the field theory applications of the results
obtained.
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Variations of the Hidden Sector in a Realistic Intersecting Brane Model: Recently, we discussed the first example of a phenomenologically realistic
intersecting D6-brane model. In this model, the gauge symmetry in the hidden
sector is USp(2)_1 x USp(2)_2 x USp(2)_3 x USp(2)_4. However, we find that the
USp(2)_1 x USp(2)_2 gauge symmetry can be replaced by an U(2)_{12} gauge
symmetry, and/or the USp(2)_3 x USp(2)_4 gauge symmetry can be replaced by an
U(2)_{34} gauge symmetry since the USp(2)^2 stacks of D6-branes contribute to
the same Ramond-Ramond tadpoles as those of the U(2) stacks. Thus, there are
three non-equivalent variations of the hidden sector, and the corresponding
gauge symmetries are U(2)_{12} x USp(2)_3 x USp(2)_4, U(2)_{34} x USp(2)_1 x
USp(2)_2, and U(2)_{12} x U(2)_{34}, respectively. Moreover, we study the
hidden sector gauge symmetry breaking, discuss how to decouple the additional
exotic particles, and briefly comment on the phenomenological consequences.
|
Two-Matrix model with ABAB interaction: Using recently developed methods of character expansions we solve exactly in
the large N limit a new two-matrix model of hermitean matrices A and B with the
action S={1\over 2}(\tr A^2+\tr B^2)-{\alpha\over 4}(\tr A^4+\tr B^4)
-{\beta\over 2} \tr(AB)^2. This model can be mapped onto a special case of the
8-vertex model on dynamical planar graphs. The solution is parametrized in
terms of elliptic functions. A phase transition is found: the critical point is
a conformal field theory with central charge c=1 coupled to 2D quantum gravity.
|
Massless Boundary Sine-Gordon at the Free Fermion Point: Correlation and
Partition Functions with Applications to Quantum Wires: In this report we compute the boundary states (including the boundary
entropy) for the boundary sine-Gordon theory. From the boundary states, we
derive both correlation and partition functions. Through the partition
function, we show that boundary sine-Gordon maps onto a doubled boundary Ising
model. With the current-current correlators, we calculate for finite system
size the ac-conductance of tunneling quantum wires with dimensionless free
conductance 1/2 (or, alternatively interacting quantum Hall edges at filling
fraction 1/2). In the dc limit, the results of C. Kane and M. Fisher, Phys.
Rev. B46 (1992) 15233, are reproduced.
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Explicit de Sitter Flux Vacua for Global String Models with Chiral
Matter: We address the open question of performing an explicit stabilisation of all
closed string moduli (including dilaton, complex structure and Kaehler moduli)
in fluxed type IIB Calabi-Yau compactifications with chiral matter. Using toric
geometry we construct Calabi-Yau manifolds with del Pezzo singularities.
D-branes located at such singularities can support the Standard Model gauge
group and matter content. In order to control complex structure moduli
stabilisation we consider Calabi-Yau manifolds which exhibit a discrete
symmetry that reduces the effective number of complex structure moduli. We
calculate the corresponding periods in the symplectic basis of invariant
three-cycles and find explicit flux vacua for concrete examples. We compute the
values of the flux superpotential and the string coupling at these vacua.
Starting from these explicit complex structure solutions, we obtain AdS and dS
minima where the Kaehler moduli are stabilised by a mixture of D-terms,
non-perturbative and perturbative alpha'-corrections as in the LARGE Volume
Scenario. In the considered example the visible sector lives at a dP_6
singularity which can be higgsed to the phenomenologically interesting class of
models at the dP_3 singularity.
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A Lower Estimate for the Modified Steiner Functional: We prove inequality (1) for the modified Steiner functional A(M), which
extends the notion of the integral of mean curvature for convex surfaces.We
also establish an exression for A(M) in terms of an integral over all
hyperplanes intersecting the polyhedralral surface M.
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Tall tales from de Sitter space I: Renormalization group flows: We study solutions of Einstein gravity coupled to a positive cosmological
constant and matter, which are asymptotically de Sitter and homogeneous.
Regarded as perturbations of de Sitter space, a theorem of Gao and Wald implies
that generically these solutions are `tall,' meaning that the perturbed
universe lives through enough conformal time for an entire spherical Cauchy
surface to enter any observer's past light cone. Such observers will realize
that their universe is spatially compact. An interesting fact, which we
demonstrate with an explicit example, is that this Cauchy surface can have
arbitrarily large volume for fixed asymptotically de Sitter behavior. Our main
focus is on the implications of tall universes for the proposed dS/CFT
correspondence. Particular attention is given to the associated renormalization
group flows, leading to a more general de Sitter `c-theorem.' We find, as
expected, that a contracting phase always represents a flow towards the
infrared, while an expanding phase represents a `reverse' flow towards the
ultraviolet. We also discuss the conformal diagrams for various classes of
homogeneous flows.
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Non-minimal Kinetic coupling to gravity and accelerated expansion: We study a scalar field with kinetic term coupled to itself and to the
curvature, as a source of dark energy, and analyze the role of this new
coupling in the accelerated expansion at large times. In the case of scalar
field dominance, the scalar field and potential giving rise to power-law
expansion are found in some cases, and a dynamical equation of state is
calculated for a given solution of the field equations. A behavior very close
to that of the cosmological constant was found.
|
Tachyon Condensation and Brane Descent Relations in p-adic String Theory: It has been conjectured that an extremum of the tachyon potential of a
bosonic D-brane represents the vacuum without any D-brane, and that various
tachyonic lump solutions represent D-branes of lower dimension. We show that
the tree level effective action of p-adic string theory, the expression for
which is known exactly, provides an explicit realisation of these conjectures.
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Nonabelian N=2 Superstrings: The Green-Schwarz covariant N=2 superstring action can be consistently
deduced as the action of the Wess-Zumino-Witten (WZW) sigma model defined on
the direct product of two N=1, D=10 Poincar\'e supertranslation groups.
Generalizing this result, we construct new WZW sigma models on the supergroups
with a nonabelian even part and interpret them as models of superstrings moving
on the supergroup manifolds. We show that these models are completely
integrable and in some special cases possess fermionic kappa-symmetry.
|
Viscosity of an ideal relativistic quantum fluid: A perturbative study: We show that a quantized ideal fluid will generally exhibit a small but
non-zero viscosity due to the backreaction of quantum soundwaves on the
background. We use an effective field theory expansion to estimate this
viscosity to first order in perturbation theory. We discuss our results, and
whether this estimate can be used to obtain a more model-independent estimate
of the "quantum bound" on the viscosity of physical systems
|
Trace and chiral anomalies in string and ordinary field theory from
Feynman diagrams for nonlinear sigma models: We write general one-loop anomalies of string field theory as path integrals
on a torus for the corresponding nonlinear sigma model. This extends the work
of Alvarez-Gaum\'e and Witten from quantum mechanics to two dimensions. Higher
world-volume loops contribute in general to nontopological anomalies and a
formalism to compute these is developed. We claim that (i) for general
anomalies one should not use the propagator widely used in string theory but
rather the one obtained by generalization from quantum mechanics, but (ii) for
chiral anomalies both propagators give the same result. As a check of this
claim in a simpler model we compute trace anomalies in quantum mechanics. The
propagator with a center-of-mass zero mode indeed does not give the correct
result for the trace anomaly while the propagator for fluctuations $q^i (\tau)$
satisfying $q^i (\tau = -1) = q^i (\tau = 0) = 0$ yields in $d=2$ and $d=4$
dimensions the correct results from two- and three-loop graphs.
We then return to heterotic string theory and calculate the contributions to
the anomaly from the different spin structures for $d=2$. We obtain agreement
with the work of Pilch, Schellekens and Warner and that of Li in the sector
with spacetime fermions. In the other sectors, where no explicit computations
have been performed in the past and for which one needs higher loops, we find a
genuine divergence, whose interpretation is unclear to us. We discuss whether
or not this leads to a new anomaly.
|
Nonlinear Brownian Motion and Higgs Mechanism: An extension of the stochastic quantization scheme is proposed by adding
nonlinear terms to the field equations. Our modification is motivated by the
recently established theory of active Brownian motion. We discuss a way of
promoting this theory to the case of infinite degrees of freedom. Equilibrium
distributions can be calculated exactly and are interpreted as path integral
densities of quantum field theories. By applying our procedure to scalar QED,
the symmetry breaking potential of the Higgs mechanism arises as the
equilibrium solution.
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Beta-ensembles for toric orbifold partition function: We investigate combinatorics of the instanton partition function for the
generic four dimensional toric orbifolds. It is shown that the orbifold
projection can be implemented by taking the inhomogeneous root of unity limit
of the q-deformed partition function. The asymptotics of the combinatorial
partition function yields the multi-matrix model for a generic $\beta$.
|
IIB or not IIB: We consider Type IIB superstring theory with the addition of n 9-branes and n
anti-9-branes (and no orientifolds). The result is a ten-dimensional chiral
theory of open and closed oriented strings with gauge group U(n) \times U(n).
There is, however, a tachyonic instability which can be understood as the
consequence of brane-antibrane annihilation. We therefore expect to recover the
usual IIB theory as the tachyon rolls to infinity.
|
Global Aspects of p-Branes: We generalize to dimension $p>1$ the notion of string structure and discuss
the related obstruction. We apply our results to a model of bosonic $p$-branes
propagating on a principal $G$-bundle, coupled to a Yang--Mills field and an
antisymmetric tensor field and in the presence of a Wess-Zumino term in the
Lagrangian. We construct the quantization line bundle and discuss the action of
background gauge transformations on wave functions.
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Component Decompositions and Adynkra Libraries for Supermultiplets in
Lower Dimensional Superspaces: We present Adynkra Libraries that can be used to explore the embedding of
multiplets of component field (whether on-shell or partial on-shell) within
Salam-Strathdee superfields for theories in dimension nine through four.
|
$T^3$ deformations and $β$-deformed geometries: We discuss $\beta$-deformed geometries on two types of $T^3$'s where the
direction along the third coordinate is not orthogonal to the direction along
the second coordinate or the direction along the first coordinate. We show that
the intersection angle between the direction along the third coordinate and the
direction along the second coordinate corresponds to the parameter of the
S-duality of the $\beta$-deformation while the intersection angle between the
direction along the third coordinate and the direction along the first
coordinate generalizes the $\beta$-deformed geometry.
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Nonabelian (2,0) Tensor Multiplets and 3-algebras: Using 3-algebras we obtain a nonabelian system of equations that furnish a
representation of the (2,0)-supersymmetric tensor multiplet. The on-shell
conditions are quite restrictive so that the system can be reduced to
five-dimensional gauge theory along with six-dimensional abelian (2,0) tensor
multiplets. We briefly discuss possible applications to D4-branes using a
spacelike reduction and M5-branes using a null reduction.
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Shifted Quiver Quantum Toroidal Algebra and Subcrystal Representations: Recently, new classes of infinite-dimensional algebras, quiver Yangian (QY)
and shifted QY, were introduced, and they act on BPS states for non-compact
toric Calabi-Yau threefolds. In particular, shifted QY acts on general
subcrystals of the original BPS crystal. A trigonometric deformation called
quiver quantum toroidal algebra (QQTA) was also proposed and shown to act on
the same BPS crystal. Unlike QY, QQTA has a formal Hopf superalgebra structure
which is useful in deriving representations.
In this paper, we define the shifted QQTA and study a class of their
representations. We define 1d and 2d subcrystals of the original 3d crystal by
removing a few arrows from the original quiver diagram and show how the shifted
QQTA acts on them. We construct the 2d crystal representations from the 1d
crystal representations by utilizing a generalized coproduct acting on
different shifted QQTAs. We provide a detailed derivation of subcrystal
representations of $\mathbb{C}^{3}$, $\mathbb{C}^{3}/\mathbb{Z}_{n}(n\geq 2)$,
conifold, suspended pinch point, and
$\mathbb{C}^{3}/(\mathbb{Z}_{2}\times\mathbb{Z}_{2})$.
|
Gauge fixing problem and the constrained quantization: In this work, the quantization of the Yang-Mills theory is worked out by
means of Dirac's canonical quantization method, using the generalized Coulomb
gauge fixing conditions. Following the construction of the matrix composed of
all the second class constraints of the theory, its convenience within the
framework of the canonical approach is discussed. Although this method can be
used successfully in the quantization of the Abelian theories, it brings along
difficulties for the non-Abelian case, which can not be handled easily even for
the generalized Coulomb gauge of the Yang-Mills theory.
|
Graph Rings and Integrable Perturbations of $N=2$ Superconformal
Theories: We show that the connection between certain integrable perturbations of $N=2$
superconformal theories and graphs found by Lerche and Warner extends to a
broader class. These perturbations are such that the generators of the
perturbed chiral ring may be diagonalized in an orthonormal basis. This allows
to define a dual ring, whose generators are labelled by the ground states of
the theory and are encoded in a graph or set of graphs, that reproduce the
pattern of the ground states and interpolating solitons. All known
perturbations of the $ADE$ potentials and some others are shown to satisfy this
criterion. This suggests a test of integrability.
|
Normalized Fuchsian form on Riemann sphere and differential equations
for multiloop integrals: We consider the question of reducibility of the differential system to
normalized Fuchsian form on the Riemann sphere. The differential equations for
the multiloop integrals in $\epsilon$-form constitute a particular example of
the normalized Fuchsian form. We formulate the algorithmic criterion of
reducibility. We also consider the question of the proper choice of variable in
the differential system suitable for its reduction to $\epsilon$-form.
|
Thermodynamic relations for entropy and temperature of multi-horizons
black holes: We present some entropy and temperature relations of multi-horizons, even
including the "virtual" horizon. These relations are related to product,
division and sum of entropy and temperature of multi-horizons. We obtain the
additional thermodynamic relations of both static and rotating black holes in
three and four dimensional (A)dS spacetime. Especially, a new dimensionless,
charges-independence and $T_+S_+=T_-S_-$ like relation is presented. This
relation does not depend on the mass, electric charge, angular momentum and
cosmological constant, as it is always a constant. These relations lead us to
get some interesting thermodynamic bound of entropy and temperature, including
the Penrose inequality which is the first geometrical inequality of black
holes. Besides, based on these new relations, one can obtain the first law of
thermodynamics and Smarr relation for all horizons of black hole.
|
Why Boltzmann Brains Are Bad: Some modern cosmological models predict the appearance of Boltzmann Brains:
observers who randomly fluctuate out of a thermal bath rather than naturally
evolving from a low-entropy Big Bang. A theory in which most observers are of
the Boltzmann Brain type is generally thought to be unacceptable, although
opinions differ. I argue that such theories are indeed unacceptable: the real
problem is with fluctuations into observers who are locally identical to
ordinary observers, and their existence cannot be swept under the rug by a
choice of probability distributions over observers. The issue is not that the
existence of such observers is ruled out by data, but that the theories that
predict them are cognitively unstable: they cannot simultaneously be true and
justifiably believed.
|
Logarithmic behaviour of connected correlation function in CFT: We study $(m)$-type connected correlation functions of OPE blocks with
respect to one spatial region in two dimensional conformal field theory. We
find logarithmic divergence for these correlation functions. We justify the
logarithmic behaviour from three different approaches: massless free scalar
theory, Selberg integral and conformal block. Cutoff independent coefficients
are obtained from analytic continuation of conformal blocks. A UV/IR relation
has been found in connected correlation functions. We could derive a formal
``first law of thermodynamics'' for a subsystem using deformed reduced density
matrix. Area law of connected correlation function in higher dimensions is also
discussed briefly.
|
Regular non-twisting S-branes: We construct a family of time and angular dependent, regular S-brane
solutions which corresponds to a simple analytical continuation of the
Zipoy-Voorhees 4-dimensional vacuum spacetime. The solutions are asymptotically
flat and turn out to be free of singularities without requiring a twist in
space. They can be considered as the simplest non-singular generalization of
the singular S0-brane solution. We analyze the properties of a representative
of this family of solutions and show that it resembles to some extent the
asymptotic properties of the regular Kerr S-brane. The R-symmetry corresponds,
however, to the general Lorentzian symmetry. Several generalizations of this
regular solution are derived which include a charged S-brane and an additional
dilatonic field.
|
How massless are massless fields in $AdS_d$: Massless fields of generic Young symmetry type in $AdS_d$ space are analyzed.
It is demonstrated that in contrast to massless fields in Minkowski space whose
physical degrees of freedom transform in irreps of $o(d-2)$ algebra, $AdS$
massless mixed symmetry fields reduce to a number of irreps of $o(d-2)$
algebra. From the field theory perspective this means that not every massless
field in flat space admits a deformation to $AdS_d$ with the same number of
degrees of freedom, because it is impossible to keep all of the flat space
gauge symmetries unbroken in the AdS space. An equivalent statement is that,
generic irreducible AdS massless fields reduce to certain reducible sets of
massless fields in the flat limit. A conjecture on the general pattern of the
flat space limit of a general $AdS_d$ massless field is made. The example of
the three-cell ``hook'' Young diagram is discussed in detail. In particular, it
is shown that only a combination of the three-cell flat-space field with a
graviton-like field admits a smooth deformation to $AdS_d$.
|
A $U(1)_{B-L}$-extension of the Standard Model from Noncommutative
Geometry: We derive a $U(1)_{B-L}$-extension of the Standard Model from a generalized
Connes-Lott model with algebra ${\mathbb C}\oplus{\mathbb C}\oplus {\mathbb
H}\oplus M_3({\mathbb C})$. This generalization includes the Lorentzian
signature, the presence of a real structure, and a weakening of the order $1$
condition. In addition to the SM fields, the model contains a $Z_{B-L}'$ boson
and a complex scalar field $\sigma$ which spontaneously breaks the new
symmetry. This model is the smallest one which contains the SM fields and is
compatible with both the Connes-Lott theory and the algebraic background
framework.
|
Dynamical Casimir effect for gravitons in bouncing braneworlds: We consider a two-brane system in a five-dimensional anti-de Sitter
spacetime. We study particle creation due to the motion of the physical brane
which first approaches the second static brane (contraction) and then recedes
from it(expansion). The spectrum and the energy density of the generated
gravitons are calculated. We show that the massless gravitons have a blue
spectrum and that their energy density satisfies the nucleosynthesis bound with
very mild constraints on the parameters. We also show that the Kaluza-Klein
modes cannot provide the dark matter in an anti-de-Sitter braneworld. However,
for natural choices of parameters, backreaction from the Kaluza-Klein gravitons
may well become important. The main findings of this work have been published
in the form of a Letter [R. Durrer and M. Ruser, Phys. Rev. Lett. 99, 071601
(2007), arXiv:0704.0756].
|
$n$-point functions of $2d$ Yang-Mills theories on Riemann surfaces: Using the simple path integral method we calculate the $n$-point functions of
field strength of Yang-Mills theories on arbitrary two-dimensional Riemann
surfaces. In $U(1)$ case we show that the correlators consist of two parts , a
free and an $x$-independent part. In the case of non-abelian semisimple compact
gauge groups we find the non-gauge invariant correlators in Schwinger-Fock
gauge and show that it is also divided to a free and an almost $x$-independent
part. We also find the gauge-invariant Green functions and show that they
correspond to a free field theory.
|
The Euler characteristic correction to the Kaehler potential - revisited: We confirm the leading $\alpha'^3$ correction to the 4d, $\mathcal N = 1$
K\"{a}hler potential of type IIB orientifold compactifications, proportional to
the Euler characteristic of the Calabi-Yau threefold (BBHL correction). We
present the explicit solution for the $\alpha'^3$-modified internal background
metric in terms of the non-harmonic part of the third Chern form of the leading
order Calabi-Yau manifold. The corrected internal manifold is almost Calabi-Yau
and admits an $SU(3)$ structure with non-vanishing torsion. We also find that
the full ten-dimensional Einstein frame background metric is multiplied by a
non-trivial Weyl factor. Performing a Kaluza-Klein reduction on the modified
background we derive the $\alpha'^3$-corrected kinetic terms for the dilaton
and the K\"{a}hler deformations of the internal Calabi-Yau threefold for
arbitrary $h^{1,1}$. We analyze these kinetic terms in the 4d, $\mathcal N = 2$
un-orientifolded theory, confirming the expected correction to the K\"ahler
moduli space prepotential, as well as in the 4d, $\mathcal N = 1$ orientifolded
theory, thus determining the corrections to the K\"ahler potential and K\"ahler
coordinates.
|
Modular Groups for Twisted Narain Models: We demonstrate how to find modular discrete symmetry groups for $Z_N$
orbifolds. The $Z_7$ orbifold is treated in detail as a non-trivial example of
a $(2,2)$ orbifold model. We give the generators of the modular group for this
case which, surprisingly, does not contain $\sltz^3$ as had been speculated.
The treatment models with discrete Wilson lines is also discussed. We consider
examples which demonstrate that discrete Wilson lines affect the modular group
in a non-trivial manner. In particular, we show that it is possible for a
Wilson line to break $SL(2,{\bf Z})$.
|
Fermions from the gauge models ground state: We investigate the quantization of pure U(1) and U(2) gauge theories in the
vicinity of non-trivial ground state in four-dimensional Euclidean space-time.
The main goal is to make the simultaneous consideration of many vacuums
possible. It is shown that Fueter (quaternion) analytic and anti analytic
functions can be used as vacuum's collective coordinates. As a result the
ground state describes not a single quasi particle, or finite number of such
particles, but a field. This field satisfies the massless Dirac equation. This
is not a contradiction because it is known that massless spinors can be
quantized either as fermions or as bosons. We choose to quantize the vacuum
anomalously (Fermi--Dirac). The anomalous quantization of the gauge fields
ground state allows non-trivial (anti) self-dual configurations to exist. The
possible connection to the lepton sector of the Standard Model is discussed.
|
Exact Results for 't Hooft Loops in Gauge Theories on S^4: The path integral of a general N=2 supersymmetric gauge theory on S^4 is
exactly evaluated in the presence of a supersymmetric 't Hooft loop operator.
The result we find - obtained using localization techniques - captures all
perturbative quantum corrections as well as non-perturbative effects due to
instantons and monopoles, which are supported at the north pole, south pole and
equator of S^4. As a by-product, our gauge theory calculations successfully
confirm the predictions made for 't Hooft loops obtained from the calculation
of topological defect correlators in Liouville/Toda conformal field theory.
|
In the Woods of M-Theory: We study BPS states which arise in compactifications of M-theory on
Calabi-Yau manifolds. In particular, we are interested in the spectrum of the
particles obtained by wrapping M2-brane on a two-cycle in the CY manifold X. We
compute the Euler characteristics of the moduli space of genus zero curves
which land in a holomorphic four-cycle $S \subset X$. We use M. Kontsevich's
method which reduces the problem to summing over trees and observe the
discrepancy with the predictions of local mirror symmetry. We then turn this
discrepancy into a supporting evidence in favor of existence of extra moduli of
M2-branes which consists of the choice of a flat U(1) connection recently
suggested by C. Vafa and partially confirm this by counting of the arbitrary
genus curves of bi-degree (2,n) in $\IP^1 \times \IP^1$ (this part has been
done together with Barak Kol). We also make a conjecture concerning the
counting of higher genus curves using second quantized Penner model and discuss
possible applications to the string theory of two-dimensional QCD.
|
Random walks on combs: We develop techniques to obtain rigorous bounds on the behaviour of random
walks on combs. Using these bounds we calculate exactly the spectral dimension
of random combs with infinite teeth at random positions or teeth with random
but finite length. We also calculate exactly the spectral dimension of some
fixed non-translationally invariant combs. We relate the spectral dimension to
the critical exponent of the mass of the two-point function for random walks on
random combs, and compute mean displacements as a function of walk duration. We
prove that the mean first passage time is generally infinite for combs with
anomalous spectral dimension.
|
Giant Magnons in Symmetric Spaces: Explicit N-soliton solutions for
CP^n, SU(n) and S^n: Giant magnons are one of the main manifestations of integrability on the
string theory side of the AdS/CFT correspondence. Motivated by the recent
advances in their study, especially in the context of the string theory dual of
ABJM theory, we present and prove explicit N-soliton solutions for the relevant
CP^n, SU(n) and S^n sigma models. The proof is based on solving the dressing
method recursion with the help of determinant operations, and our solutions
hold for any choice of vacuum and soliton parameters. We further specialize our
results for the choices that lead to giant magnons, and as an application, we
calculate the classical time delay due to the scattering of an arbitrary number
of CP^2 elementary dyonic magnons. The determinant expressions for our
N-soliton solutions could possibly be used for the derivation of an effective
particle description of magnon scattering.
|
A quantum circuit interpretation of evaporating black hole geometry: We give a quantum circuit interpretation of evaporating black hole geometry.
We make an analogy between the appearance of island for evaporating black hole
and the transition from two-sided to one-sided black hole in the familiar
example of perturbed thermofield double. If Alice perturbs thermofield double
and waits for scrambling time, she will have a one-sided black hole with
interior of her own. We argue that by similar mechanism the radiation gets
access to the interior (island forms) after Page time. The growth of the island
happens as a result of the constant transitions from two-sided to one-sided
black holes.
|
Permutation operators, entanglement entropy, and the XXZ spin chain in
the limit Δ-> -1: In this paper we develop a new approach to the investigation of the
bi-partite entanglement entropy in integrable quantum spin chains. Our method
employs the well-known replica trick, thus taking a replica version of the spin
chain model as starting point. At each site i of this new model we construct an
operator T_i which acts as a cyclic permutation among the n replicas of the
model. Infinite products of T_i give rise to local operators, precursors of
branch-point twist fields of quantum field theory. The entanglement entropy is
then expressed in terms of correlation functions of such operators. Employing
this approach we investigate the von Neumann and R\'enyi entropies of a
particularly interesting quantum state occurring as a limit (in a compact
convergence topology) of the antiferromagnetic XXZ quantum spin chain. We find
that, for large sizes, the entropy scales logarithmically, but not conformally.
|
Quantum principal commutative subalgebra in the nilpotent part of
$U_q\widehat{s\ell}_2$ and lattice KdV variables: We propose a quantum lattice version of Feigin and E. Frenkel's
constructions, identifying the KdV differential polynomials with functions on a
homogeneous space under the nilpotent part of $\widehat{s\ell}_2$. We construct
an action of the nilpotent part $U_q\widehat n_+$ of $U_q\widehat{s\ell}_2$ on
their lattice counterparts, and embed the lattice variables in a $U_q\widehat
n_+$-module, coinduced from a quantum version of the principal commutative
subalgebra, which is defined using the identification of $U_q\widehat n_+$ with
its coordinate algebra.
|
On Higher-dimensional Carrollian and Galilean Conformal Field Theories: In this paper, we study the Carrollian and Galilean conformal field theories
(CCFT and GCFT) in $d>2$ dimensions. We construct the highest weight
representations (HWR) of Carrollian and Galilean conformal algebra (CCA and
GCA). Even though the two algebras have different structures, their HWRs share
similar structure, because their rotation subalgebras are isomorphic. In both
cases, we find that the finite dimensional representations are generally
reducible but indecomposable, and can be organized into the multiplets.
Moreover, it turns out that the multiplet representations in $d>2$ CCA and GCA
carry not only the simple chain structure appeared in logCFT or $2d$ GCFT, but
also more generally the net structures. We manage to classify all the allowed
chain representations. Furthermore we discuss the two-point and three-point
correlators by using the Ward identities. We mainly focus on the two-point
correlators of the operators in chain representations. Even in this relative
simple case, we find some novel features: multiple-level structure, shortage of
the selection rule on the representations, undetermined 2-pt coefficients,
etc.. We find that the non-trivial correlators could only appear for the
representations of certain structure, and the correlators are generally
polynomials of time coordinates for CCFT (spacial coordinates for GCFT), whose
orders depend on the levels of the correlators.
|
Super D-branes: We present a manifestly Lorentz invariant, spacetime supersymmetric, and
`$\kappa$-invariant' worldvolume action for all type II Dirichlet p-branes,
$p\le9$, in a general type II supergravity background, including massive
backgrounds in the IIA case. The $p=0,2$ cases are rederived from D=11. The
$p=9$ case provides a supersymmetrization of the D=10 Born-Infeld action.
|
Cosmological Perturbations in Brane Worlds: Brane Bending and
Anisotropic Stresses: Using a metric-based formalism to treat cosmological perturbations, we
discuss the connection between anisotropic stress on the brane and brane
bending. First we discuss gauge-transformations, and draw our attention to
gauges, in which the brane-positions remain unperturbed. We provide a unique
gauge, where perturbations both on the brane and in the bulk can be treated
with generality. For vanishing anisotropic stresses on the brane, this gauge
reduces to the generalized longitudinal gauge. We further comment on the
gravitational interaction between the branes and the bulk.
|
On Thermodynamics of 2d Black Holes in Brane Inflationary Potentials: Inspired from the inflation brane world cosmology, we study the
thermodynamics of a black hole solution in two dimensional dilaton gravity with
an arctangent potential background. We first derive the two dimensional black
hole geometry, then we examine its asymptotic behaviors. More precisely, we
find that such behaviors exhibit properties appearing in some known cases
including the Anti de Sitter and the Schwarzchild black holes. Using the
complex path method, we compute the Hawking radiation. The entropy function can
be related to the value of the potential at the horizon.
|
Lamb Shift for static atoms outside a Schwarzschild black hole: We study, by separately calculating the contributions of vacuum fluctuations
and radiation reaction to the atomic energy level shift, the Lamb shift of a
static two-level atom interacting with real massless scalar fields in the
Boulware, Unruh and Hartle-Hawking vacuums outside a Schwarzschild black hole.
We find that in the Boulware vacuum, the Lamb shift gets a correction arising
as a result of the backscattering of vacuum field modes off the space-time
curvature, which is reminiscent of the correction to the Lamb shift induced by
the presence of cavities. However, when the Unruh and Hartle-Hawking vacua are
concerned, our results show that the Lamb shift behaves as if the atom were
irradiated by a thermal radiation or immersed in a thermal bath at the Hawking
temperature, depending on whether the scalar field is in the Unruh or the
Hartle-Hawking vacuum. Remarkably, the thermal radiation is always
backscattered by the space-time geometry.
|
External Fields and the Dynamics of Fundamental Flavours in Holographic
Duals of Large N Gauge Theories: Using the gauge-gravity duality we study strongly coupled dynamics of
fundamental flavours in large N_c gauge theories in a constant external field.
We primarily focus on the effects of an external magnetic field. We use two
holographic models realized in the Type IIB and Type IIA supergravity and
present a comparative case study. In both these models, by studying the
dynamics of probe branes, we explicitly demonstrate and discuss the
magnetically induced chiral symmetry breaking effect ("magnetic catalysis") in
the flavour sector. We also study the associated thermodynamics and the meson
spectrum and realize e.g. Zeeman splitting, stability enhancement of the mesons
in the presence of an external magnetic field etc. By studying the quasinormal
modes of the probe brane fluctuation in the hydrodynamic limit we also obtain
an analytic dispersion relation in the presence of a magnetic field in the Type
IIA model. This dispersion relation consists of a propagating sound mode in the
otherwise diffusive channel and is sourced by the quantum anomaly of the global
U(1) current. We briefly discuss the effects of an external electric field and
observe that the flavour bound states dissociate for sufficiently high electric
fields and an electric current is induced.
|
BRST-BV approach to conformal fields: Using the BRST--BV approach, we consider totally symmetric arbitrary integer
spin conformal fields propagating in flat space. For such fields, we obtain the
ordinary-derivative BRST--BV Lagrangian that is invariant under gauge
transformations. In our approach, the ordinary-derivative Lagrangian and gauge
transformations are constructed in terms of the respective traceless gauge
fields and traceless gauge transformation parameters. We also obtain a
realization of conformal algebra symmetries on the space of fields and
antifields entering the BRST--BV formulation of conformal fields.
|
Field theory actions for ambitwistor string and superstring: We analyze the free ambitwistor string field theory action for the bosonic
string, heterotic string and both GSO sectors of the Type II string. The
spectrum contains non-unitary states and provides an interesting consistency
test for one-loop ambitwistor string computations.
|
Anomaly Matching Across Dimensions and Supersymmetric Cardy Formulae: 't Hooft anomalies are known to induce specific contributions to the
effective action at finite temperature. We present a general method to directly
calculate such contributions from the anomaly polynomial of a given theory,
including a term which involves a $U(1)$ connection for the thermal circle
isometry. Based on this observation, we show that the asymptotic behavior of
the superconformal index of $4d$ $\mathcal{N}=1$ theories on the "second sheet"
can be calculated by integrating the anomaly polynomial on a particular
background. The integration is then performed by an equivariant method to
reproduce known results. Our method only depends on the anomaly polynomial and
therefore the result is applicable to theories without known Lagrangian
formulation. We also present a new formula that relates the behavior of $6d$
$\mathcal{N}=(1,0)$ SCFTs on the second sheet to the anomaly polynomial.
|
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