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Involution requirement on a boundary makes massless fermions
compactified on a finite flat disk mass protected: The genuine Kaluza-Klein-like theories--with no fields in addition to
gravity--have difficulties with the existence of massless spinors after the
compactification of some space dimensions \cite{witten}. We proposed (Phys.
Lett. B 633 (2006)771) such a boundary condition for spinors in 1+5
compactified on a flat disk that ensures masslessness of spinors in d=1+3 as
well as their chiral coupling to the corresponding background gauge field
(which solves equations of motion for a free field linear in the Riemann
curvature). In this paper we study the same toy model: M^{(1+3)} x M^{(2)},
looking this time for an involution which transforms a space of solutions of
Weyl equations in d=1+5 from the outside of the flat disk in x^5 and x^6 into
its inside, allowing massless spinor of only one handedness--and accordingly
assures mass protection--and of one charge--1/2--and infinitely many massive
spinors of the same charge, chirally coupled to the corresponding background
gauge field. We reformulate the operator of momentum so that it is Hermitean on
the vector space of spinor states obeying the involution boundary condition. | General Composite Non-Abelian Strings and Flag Manifold Sigma Models: We fully investigate the symmetry breaking patterns occurring upon creation
of composite non-Abelian strings: vortex strings in non-Abelian theories where
different sets of colours have different amounts of flux. After spontaneous
symmetry breaking, there remains some internal colour degrees of freedom
attached to these objects, which we argue must exist in a Flag manifold, a more
general kind of projective space than both $\mathbb{CP}(N)$ and the
Grassmannian manifold. These strings are expected to be BPS, since its
constituents are. We demonstrate that this is true and construct a low-energy
effective action for the fluctuations of the internal Flag moduli, which we
then re-write it in two different ways for the dynamics of these degrees of
freedom: a gauged linear sigma model with auxiliary fields and a non-linear
sigma model with an explicit target space metric for the Flag Manifolds, both
of which $\mathcal{N}=(2,2)$ supersymmetric. We finish by performing some
groundwork analysis of the resulting theory. |
Finite Temperature Large N Gauge Theory with Quarks in an External
Magnetic Field: Using a ten dimensional dual string background, we study aspects of the
physics of finite temperature large N four dimensional SU(N) gauge theory,
focusing on the dynamics of fundamental quarks in the presence of a background
magnetic field. At vanishing temperature and magnetic field, the theory has N=2
supersymmetry, and the quarks are in hypermultiplet representations. In a
previous study, similar techniques were used to show that the quark dynamics
exhibit spontaneous chiral symmetry breaking. In the present work we begin by
establishing the non-trivial phase structure that results from finite
temperature. We observe, for example, that above the critical value of the
field that generates a chiral condensate spontaneously, the meson melting
transition disappears, leaving only a discrete spectrum of mesons at any
temperature. We also compute several thermodynamic properties of the plasma. | Nonabelian noncommutative gauge theory via noncommutative extra
dimensions: The concept of covariant coordinates on noncommutative spaces leads directly
to gauge theories with generalized noncommutative gauge fields of the type that
arises in string theory with background B-fields. The theory is naturally
expressed in terms of cochains in an appropriate cohomology; we discuss how it
fits into the framework of projective modules. The equivalence of star products
that arise from the background field with and without fluctuations and
Kontsevich's formality theorem allow an explicitly construction of a map that
relates ordinary gauge theory and noncommutative gauge theory (Seiberg-Witten
map.) As application we show the exact equality of the Dirac-Born-Infeld action
with B-field in the commutative setting and its semi-noncommutative cousin in
the intermediate picture. Using noncommutative extra dimensions the
construction is extended to noncommutative nonabelian gauge theory for
arbitrary gauge groups; an explicit map between abelian and nonabelian gauge
fields is given. All constructions are also valid for non-constant B-field,
Poisson structure and metric. |
Decoupling limits of N=4 super Yang-Mills on R x S^3: We find new decoupling limits of N=4 super Yang-Mills (SYM) on R x S^3 with
gauge group SU(N). These decoupling limits lead to decoupled theories that are
much simpler than the full N=4 SYM but still contain many of its interesting
features. The decoupling limits correspond to being in a near-critical region,
near a point with zero temperature and critical chemical potentials. The new
decoupling limits are found by generalizing the limits of hep-th/0605234 to
include not only the chemical potentials for the SU(4) R-symmetry of N=4 SYM
but also the chemical potentials corresponding to the SO(4) symmetry. In the
decoupled theories it is possible to take a strong coupling limit in a
controllable manner since the full effective Hamiltonian is known. For planar
N=4 SYM on R x S^3 all the decoupled theories correspond to fully integrable
spin chains. We study the thermodynamics of the decoupled theories and find the
Hagedorn temperature for small and large values of the effective coupling. We
find an alternative formulation of the decoupling limits in the microcanonical
ensemble. This leads to a characterization of certain regimes of weakly coupled
N=4 SYM in which there are string-like states. Finally, we find a similar
decoupling limit for pure Yang-Mills theory, which for the planar limit leads
to a fully integrable decoupled theory. | Complex Linear Effective Theory and Supersymmetry Breaking Vacua: We calculate the low energy effective action of massless and massive complex
linear superfields coupled to a massive U(1) vector multiplet. Our calculations
include superspace higher derivative corrections and therefore go beyond
previous results. Among the superspace higher derivatives we find that terms
which lead to a deformation of the auxiliary field potential and may break
supersymmetry are also generated. We show that the supersymmetry breaking vacua
can only be trusted if there exists a hierarchy between the higher order terms.
A renormalization group analysis shows that generically a hierarchy is not
generated by the quantum corrections. |
Renormalization Group Flow of the Holst Action: The renormalization group (RG) properties of quantum gravity are explored,
using the vielbein and the spin connection as the fundamental field variables.
The scale dependent effective action is required to be invariant both under
space time diffeomorphisms and local frame rotations. The nonperturbative RG
equation is solved explicitly on the truncated theory space defined by a three
parameter family of Holst-type actions which involve a running Immirzi
parameter. We find evidence for the existence of an asymptotically safe
fundamental theory, probably inequivalent to metric quantum gravity constructed
in the same way. | Sasakian quiver gauge theories and instantons on Calabi-Yau cones: We consider SU(2)-equivariant dimensional reduction of Yang-Mills theory on
manifolds of the form $M\times S^3/\Gamma$, where $M$ is a smooth manifold and
$S^3/\Gamma$ is a three-dimensional Sasaki-Einstein orbifold. We obtain new
quiver gauge theories on $M$ whose quiver bundles are based on the affine ADE
Dynkin diagram associated to $\Gamma$. We relate them to those arising through
translationally-invariant dimensional reduction over the associated Calabi-Yau
cones $C(S^3/\Gamma)$ which are based on McKay quivers and ADHM matrix models,
and to those arising through SU(2)-equivariant dimensional reduction over the
leaf spaces of the characteristic foliations of $S^3/\Gamma$ which are K\"ahler
orbifolds of $\mathbb{C} P^1$ whose quiver bundles are based on the unextended
Dynkin diagram corresponding to $\Gamma$. We use Nahm equations to describe the
vacua of SU(2)-equivariant quiver gauge theories on the cones as moduli spaces
of spherically symmetric instantons. We relate them to the Nakajima quiver
varieties which can be realized as Higgs branches of the worldvolume quiver
gauge theories on D$p$-branes probing D$(p+4)$-branes which wrap an ALE space,
and to the moduli spaces of spherically symmetric solutions in putative
non-abelian generalizations of two-dimensional affine Toda field theories. |
Anomalies and Wess-Zumino Terms in an Extended, Regularized
Field-Antifield Formalism: Quantization of anomalous gauge theories with closed, irreducible gauge
algebra within the extended Field-Antifield formalism is further pursued. Using
a Pauli-Villars (PV) regularization of the generating functional at one loop
level, an alternative form for the anomaly is found which involves only the
regulator. The analysis of this expression allows to conclude that recently
found ghost number one cocycles with nontrivial antifield dependence can not
appear in PV regularization. Afterwards, the extended Field-Antifield formalism
is further completed by incorporating quantum effects of the extra variables,
i.e., by explicitly taking into account the regularization of the extra sector.
In this context, invariant PV regulators are constructed from non-invariant
ones, leading to an alternative interpretation of the Wess-Zumino action as the
local counterterm relating invariant and non-invariant regularizations.
Finally, application of the above ideas to the bosonic string reproduces the
well-known Liouville action and the shift $(26-D)\rightarrow(25-D)$ at one
loop. | Non-Commutative Instantons and the Information Metric: By using the so-called Information Metric on the moduli space of an
anti-selfdual (ASD) Instanton in a Self-Dual (SD) Non-Commutative background,
we investigate the geometry of moduli space. The metric is evaluated
perturbatively in non-commutativity parameter and we show that by putting a
cut-off in the location of instanton in the definition of Information Metric we
can recover the five dimensional space time in the presence of a B-field. This
result shows that the non-commutative YM-Instanton Moduli corresponds to
D-Instanton Moduli in the gravity side where the radial and transverse location
of D-Instanton are corresponding to YM-Instanton size and location,
respectively. The match is shown in the first order of non-commutativity
parameter. |
Fermion Number 1/2 of Sphalerons and Spectral Mirror Symmetry: We present a rederivation of the baryon and lepton numbers $\frac{1}{2}$ of
the $SU(2)_L$ S sphaleron of the standard electroweak theory based on spectral
mirror symmetry. We explore the properties of a fermionic Hamiltonian under
discrete transformations along a noncontractible loop of field configurations
that passes through the sphaleron and whose endpoints are the vacuum. As is
well known, CP transformation is not a symmetry of the system anywhere on the
loop, except at the endpoints. By augmenting CP with a chirality
transformation, we observe that the Dirac Hamiltonian is odd under the new
transformation precisely at the sphaleron, and this ensures the mirror symmetry
of the spectrum, including the continua. As a consistency check, we show that
the fermionic zero mode presented by Ringwald in the sphaleron background is
invariant under the new transformation. The spectral mirror symmetry which we
establish here, together with the presence of the zero mode, are the two
necessary conditions whence the fermion number $\frac{1}{2}$ of the sphaleron
can be inferred using the reasoning presented by Jackiw and Rebbi or,
equivalently, using the spectral deficiency $\frac{1}{2}$ of the Dirac sea. The
relevance of this analysis to other solutions is also discussed. | SYMMETRIES OF THE DIMENSIONALLY REDUCED STRING EFFECTIVE ACTION: A two dimensional string effective action is obtained by dimensionally
reducing the bosonic part of the ten dimensional heterotic string effective
action. It is shown that this effective action, with a few restrictions on some
backgrounds describes a two dimensional model which admits an infinite sequence
of nonlocal conserved currents. |
Chern-Simons gravity, based on a non-semisimple group: The gauge theory-formulation of string-motivated lineal gravity proposed by
Cangemi and Jackiw is obtained by dimensional reduction from $(2+1)$
dimensional gravity with a Chern-Simons Lagrangian. | Electromagnetic Duality and Entanglement Anomalies: Duality is an indispensable tool for describing the strong-coupling dynamics
of gauge theories. However, its actual realization is often quite subtle:
quantities such as the partition function can transform covariantly, with
degrees of freedom rearranged in a nonlocal fashion. We study this phenomenon
in the context of the electromagnetic duality of abelian $p$-forms. A careful
calculation of the duality anomaly on an arbitrary $D$-dimensional manifold
shows that the effective actions agree exactly in odd $D$, while in even $D$
they differ by a term proportional to the Euler number. Despite this anomaly,
the trace of the stress tensor agrees between the dual theories. We also
compute the change in the vacuum entanglement entropy under duality, relating
this entanglement anomaly to the duality of an "edge mode" theory in two fewer
dimensions. Previous work on this subject has led to conflicting results; we
explain and resolve these discrepancies. |
Comments on the Boundary Scattering Phase: We present a simple solution to the crossing equation for an open string
worldsheet reflection matrix, with boundaries preserving a SU(1|2)^2 residual
symmetry, which constrains the boundary dressing factor. In addition, we also
propose an analogous crossing equation for the dressing factor where extra
boundary degrees of freedom preserve a SU(2|2)^2 residual symmetry. | Geometric Approaches to Quantum Fields and Strings at Strong Couplings: Geometric structures and dualities arise naturally in quantum field theories
and string theory. In fact, these tools become very useful when studying strong
coupling effects, where standard perturbative techniques can no longer be used.
In this thesis we look at several conformal field theories in various
dimensions. We first discuss the structure of the nilpotent networks stemming
from T-brane deformations in 4D $\mathcal{N}=1$ theories and then go to the
stringy origins of 6D superconformal field theories to realize deformations
associated with T-branes in terms of simple combinatorial data. We then analyze
non-perturbative generalizations of orientifold 3-planes (i.e. S-folds) in
order to produce different 4D $\mathcal{N}=2$ theories. Afterwards, we turn our
attention towards a few dualities found at strong coupling. For instance,
abelian T-duality is known to be a full duality in string theory between type
IIA and type IIB. Its nonabelian generalization, Poisson-Lie T-duality, has
only been conjectured to be so. We show that Poisson-Lie symmetric
$\sigma$-models are at least two-loop renormalizable and their
$\beta$-functions are invariant under Poisson-Lie T-duality. Finally, we review
recent progress leading to phenomenologically relevant dualities between
M-theory on local $G_2$ spaces and F-theory on locally elliptically fibered
Calabi-Yau fourfolds. In particular, we find that the 3D $\mathcal{N}=1$
effective field theory defined by M-theory on a local $Spin(7)$ space unifies
the Higgs bundle data associated with 4D $\mathcal{N}=1$ M-theory and F-theory
vacua. We finish with some comments on 3D interfaces at strong coupling. |
Quantum Equivalence of Auxiliary Field Methods in Supersymmetric
Theories: Quantum corrections to Legendre transformations are shown to cancel to all
orders in supersymmetric theories in path integral formalism. Using this
result, lagrangians for auxiliary fields are generalized to non-quadratic
forms. In supersymmetric effective nonlinear lagrangians, the arbitrariness due
to the existence of quasi Nambu-Goldstone bosons is shown to disappear when
local auxiliary gauge fields are introduced. | A_{N-1} conformal Toda field theory correlation functions from conformal
N=2 SU(N) quiver gauge theories: We propose a relation between correlation functions in the 2d A_{N-1}
conformal Toda theories and the Nekrasov instanton partition functions in
certain conformal N=2 SU(N) 4d quiver gauge theories. Our proposal generalises
the recently uncovered relation between the Liouville theory and SU(2) quivers.
New features appear in the analysis that have no counterparts in the Liouville
case. |
Towards a $Z_3$-graded approach to quarks' symmetries: Colour $SU(3)$ group is an exact symmetry of Quantum Chromodynamics, which
describes strong interactions between quarks and gluons. Supplemented by two
internal symmetries, $SU(2)$ and $U(1)$, it serves as the internal symmetry of
the Standard Model, describing as well the electroweak interactions of quarks
and leptons. The colour$SU(3)$ symmetry is exact, while two other symmetries
are broken by means of the Higgs-Kibble mechanism. The three colours and
fractional quarks charges with values $1/3$ and $2/3$ suggest that the cyclic
group $Z_3$ may play a crucial role in quark field dynamics. In this paper we
consequently apply the $Z_3$ symmetry to field multiplets describing colour
quark fields. Generalized Dirac equation for coloured $12$-component spinors is
introduced and its properties are discussed. Imposing $Z_3$-graded Lorentz and
Poincar\'e covariance leads to enlargement of quark fields multiplets and
incorporates additional $Z_2 \times Z_3$ symmetry which leads to the appearance
of three generations (families) of distinct quark doublets. | On Macroscopic Energy Gap for $q$-Quantum Mechanical Systems: The q-deformed harmonic oscillator within the framework of the recently
introduced Schwenk-Wess $q$-Heisenberg algebra is considered. It is shown, that
for "physical" values $q\sim1$, the gap between the energy levels decreases
with growing energy. Comparing with the other (real) $q$-deformations of the
harmonic oscillator, where the gap instead increases, indicates that the
formation of the macroscopic energy gap in the Schwenk-Wess $q$-Quantum
Mechanics may be avoided. |
Quadratic supersymmetric transformations of the Dirac Green functions: We consider the quadratic supersymmetric aspect of the Darboux transformation
for the Green functions of the one-dimensional Dirac equation with a
generalized form of the potential. We obtain the relation between the initial
and the transformed Green functions on the whole real line. We also construct
the formula for the unabridged trace of the difference of the transformed and
the initial Green functions of the boundary problem on the whole real line. We
present an example illustrated our developments. | On spectrum of ILW hierarchy in conformal field theory: We consider a system of Integrals of Motion in conformal field theory related
to the gl(2) Intermediate Long Wave equation. It interpolates between the
system studied by Bazhanov, Lukyanov and Zamolodchikov and the one studied by
the author and collaborators. We find Bethe anzatz equations for the spectrum
of this system and its gl(n) generalizations. |
Dualities of Adjoint QCD$_3$ from Branes: We consider an 'electric' $U(N)$ level $k$ QCD$_3$ theory with one adjoint
Majorana fermion. Inspired by brane dynamics, we suggest that for $k \ge N/2$
the massive $m<0$ theory, in the vicinity of the supersymmetric point, admits a
$U(k-\frac{N}{2})_{-(\frac{1}{2}k+\frac{3}{4}N),-(k+\frac{N}{2})}$ 'magnetic'
dual with one adjoint Majorana fermion. The magnetic theory flows in the IR to
a topological $U(k-\frac{N}{2})_{-N,-(k+\frac{N}{2})}$ pure Chern-Simons theory
in agreement with the dynamics of the electric theory. When $k<N/2$ the
magnetic dual is $U(\frac{N}{2}-k)_{\frac{1}{2}k+\frac{3}{4}N,N}$ with one
adjoint Majorana fermion. Depending on the sign of the fermion mass, the
magnetic theory flows to either $U(\frac{N}{2}-k)_{N,N}$ or
$U(\frac{N}{2}-k)_{\frac{1}{2}N+k,N}$ TQFT. A second magnetic theory,
$U(N/2+k)_{\frac{1}{2}k-\frac{3}{4}N,-N}$, flows to either
$U(\frac{N}{2}+k)_{-N,-N}$ or $U(\frac{N}{2}+k)_{-(\frac{1}{2}N-k),-N}$ TQFT.
Dualities for $SO$ and $USp$ theories with one adjoint fermion are also
discussed. | Black Hole Thermodynamics with Dynamical Lambda: We study evolution and thermodynamics of a slow-roll transition between early
and late time de Sitter phases, both in the homogeneous case and in the
presence of a black hole, in a scalar field model with a generic potential
having both a maximum and a positive minimum. Asymptotically future de Sitter
spacetimes are characterized by ADM charges known as cosmological tensions. We
show that the late time de Sitter phase has finite cosmological tension when
the scalar field oscillation around its minimum is underdamped, while the
cosmological tension in the overdamped case diverges. We compute the variation
in the cosmological and black hole horizon areas between the early and late
time phases, finding that the fractional change in horizon area is proportional
to the corresponding fractional change in the effective cosmological constant.
We show that the extended first law of thermodynamics, including variation in
the effective cosmological constant, is satisfied between the initial and final
states, and discuss the dynamical evolution of the black hole temperature. |
A Note on Background (In)dependence: In general quantum systems there are two kinds of spacetime modes, those that
fluctuate and those that do not. Fluctuating modes have normalizable
wavefunctions. In the context of 2D gravity and ``non-critical'' string theory
these are called macroscopic states. The theory is independent of the initial
Euclidean background values of these modes. Non-fluctuating modes have
non-normalizable wavefunctions and correspond to microscopic states. The theory
depends on the background value of these non-fluctuating modes, at least to all
orders in perturbation theory. They are superselection parameters and should
not be minimized over. Such superselection parameters are well known in field
theory. Examples in string theory include the couplings $t_k$ (including the
cosmological constant) in the matrix models and the mass of the two-dimensional
Euclidean black hole. We use our analysis to argue for the finiteness of the
string perturbation expansion around these backgrounds. | Holographic complexity of local quench at finite temperature: This paper is devoted to the study of the evolution of holographic complexity
after a local perturbation of the system at finite temperature. We calculate
the complexity using both the complexity=action(CA) and the
complexity=volume(CA) conjectures and find that the CV complexity of the total
state shows the unbounded late time linear growth. The CA computation shows
linear growth with fast saturation to a constant value. We estimate the CV and
CA complexity linear growth coefficients and show, that finite temperature
leads to violation of the Lloyd bound for CA complexity. Also it is shown that
for composite system after the local quench the state with minimal entanglement
may correspond to the maximal complexity. |
Functional renormalization group for $p=2$ like glassy matrices in the
planar approximation: II. Ward identities method in the deep IR: This paper, as a continuation of our previous investigation
[arXiv:2403.07577] aims to study the glassy random matrices with quenched
Wigner disorder. In this previous work, we have constructed a renormalization
group based on the effective deterministic kinetic spectrum emerging from large
$N$ limit, and we extended approximate solutions using standard vertex
expansion, at the leading order of the derivative expansion. Now in the
following work, by introducing the non-trivial Ward identities which come from
the $(\mathcal{U}(N))^{\times 2}$ symmetry broken of the effective kinetic
action, we provide in the deep IR the explicit solution of the functional
renormalization group for a model with quartic coupling by solving the
Hierarchy to all orders in the local sector, which in particular imply the
vanishing of the anomalous dimension. The numerical investigations confirm the
first-order phase transition discovered in the vertex expansion framework, both
in the active and passive schemes. Finally, we extend the discussion to
hermitian matrices. | Higgs Inflation in Horava-Lifshitz Gravity: We study the possibility of standard model Higgs boson acting as an inflaton
field in the framework of Horava-Lifshitz Gravity. Under this framework, we
showed that it is possible for the Higgs field to produce right amount of
inflation and generate scale invariant power spectrum with the correct
experimental value. Thanks to the foliation preserving diffeomorphism and
anisotropic space-time scaling, it essentially helps us to construct this model
without the pre-existing inconsistency coming from cosmological and particle
physics constraints. We do not need to introduce any non-minimal or higher
derivative coupling term in an arbitrary basis either. |
Anomaly-free scale symmetry and gravity: In this Letter, we address the question of whether the conformal invariance
can be considered as a global symmetry of a theory of fundamental interactions.
To describe Nature, this theory must contain a mechanism of spontaneous
breaking of the scale symmetry. Besides that, the fundamental theory must
include gravity, whereas all known extensions of the conformal invariance to
the curved space-time suffer from the Weyl anomaly. We show that conformal
symmetry can be made free from the quantum anomaly only in the flat space. The
presence of gravity would reduce the global symmetry group of the fundamental
theory to the scale invariance only. We discuss how the effective Lagrangian
respecting the scale symmetry can be used for the description of particle
phenomenology and cosmology. | How to Classify Reflexive Gorenstein Cones: Two of my collaborations with Max Kreuzer involved classification problems
related to string vacua. In 1992 we found all 10,839 classes of polynomials
that lead to Landau-Ginzburg models with c=9 (Klemm and Schimmrigk also did
this); 7,555 of them are related to Calabi-Yau hypersurfaces. Later we found
all 473,800,776 reflexive polytopes in four dimensions; these give rise to
Calabi-Yau hypersurfaces in toric varieties. The missing piece - toric
constructions that need not be hypersurfaces - are the reflexive Gorenstein
cones introduced by Batyrev and Borisov. I explain what they are, how they
define the data for Witten's gauged linear sigma model, and how one can modify
our classification ideas to apply to them. I also present results on the first
and possibly most interesting step, the classification of certain basic weights
systems, and discuss limitations to a complete classification. |
Magnetic flux tube models in superstring theory: Superstring models describing curved 4-dimensional magnetic flux tube
backgrounds are exactly solvable in terms of free fields. We first consider the
simplest model of this type (corresponding to `Kaluza-Klein' Melvin
background). Its 2d action has a flat but topologically non-trivial
10-dimensional target space (there is a mixing of angular coordinate of the
2-plane with an internal compact coordinate). We demonstrate that this theory
has broken supersymmetry but is perturbatively stable if the radius R of the
internal coordinate is larger than R_0=\sqrt{2\a'}. In the Green-Schwarz
formulation the supersymmetry breaking is a consequence of the presence of a
flat but non-trivial connection in the fermionic terms in the action. For R <
R_0 and the magnetic field strength parameter q > R/2\a' there appear
instabilities corresponding to tachyonic winding states. The torus partition
function Z(q,R) is finite for R > R_0 (and vanishes for qR=2n, n=integer). At
the special points qR=2n (2n+1) the model is equivalent to the free superstring
theory compactified on a circle with periodic (antiperiodic) boundary condition
for space-time fermions. Analogous results are obtained for a more general
class of static magnetic flux tube geometries including the a=1 Melvin model. | Non-minimal couplings in two dimensional gravity: a quantum
investigation: We investigate the quantum effects of the non-minimal matter-gravity
couplings derived by Cangemi and Jackiw in the realm of a specific fermionic
theory, namely the abelian Thirring model on a Riemann surface of genus zero
and one. The structure and the strength of the new interactions are seen to be
highly constrained, when the topology of the underlying manifold is taken into
account. As a matter of fact, by requiring to have a well-defined action, we
are led both to quantization rules for the coupling constants and to selection
rules for the correlation functions. Explicit quantum computations are carried
out in genus one (torus). In particular the two-point function and the chiral
condensate are carefully derived for this case. Finally the effective
gravitational action, coming from integrating out the fermionic degrees of
freedoom, is presented. It is different from the standard Liouville one: a new
non-local functional of the conformal factor arises and the central charge is
improved, depending also on the Thirring coupling constant. This last feature
opens the possibility of giving a new explicit representation of the minimal
series in terms of a fermionic interacting model. |
Conical Casimir Pistons with Hybrid Boundary Conditions: In this paper we compute the Casimir energy and force for massless scalar
fields endowed with hybrid boundary conditions, in the setting of the bounded
generalized cone. By using spectral zeta function regularization methods, we
obtain explicit expressions for the Casimir energy and force in arbitrary
dimensions in terms of the zeta function defined on the piston. Our general
formulas are, subsequently, specialized to the case in which the piston is
modelled by a $d$-dimensional sphere. In this particular situation, explicit
results are given for $d=2,3,4,5$. | Lumpy cosmic strings: We outline a model of abelian-Higgs strings with variable scalar and vector
core radii. In general, the functions determining the time and
position-dependent core widths may be expressed as arbitrary left or right
movers, of which the usual constant values are a particular solution. In this
case the string may carry momentum, even if the embedding of its central axis
remains fixed, and the resulting objects resemble "necklaces". Some possible
astrophysical applications of lumpy strings, including as potential engines for
anomalous gamma ray bursts, are also discussed. |
Massive Gauge Field Theory Without Higgs Mechanism I. .Quantization: According to the conventional concept of the gauge field theory, the local
gauge invariance excludes the possibility of giving a mass to the gauge boson
without resorting to the Higgs mechanism because the Lagrangian constructed by
adding a mass term to the Yang-Mills Lagrangian is not only
gauge-non-invariant, but also unrenormalizable. On the contrary, we argue that
the principle of gauge invariance actually allows a mass term to enter the
Lagrangian if the Lorentz constraint condition is taken into account at the
same time. The Lorentz condition, which implies vanishing of the unphysical
longitudinal field, defines a gauge-invariant physical space for the massive
gauge field. The quantum massive gauge field theory without Higgs mechanism may
well be established by using a BRST-invariant action which is constructed by
the Lagrange undetermined multiplier procedure of incorporating the Lorentz
condition and another condition constraining the gauge group into the original
massive Yang-Mills action. The quantum theory established in this way shows
good renormalizability. | Higher-derivative relations between scalars and gluons: We extend the covariant color-kinematics duality introduced by Cheung and
Mangan to effective field theories. We focus in particular on relations between
the effective field theories of gluons only and of gluons coupled to bi-adjoint
scalars. Maps are established between their respective equations of motion and
between their tree-level scattering amplitudes. An additional rule for the
replacement of flavor structures by kinematic factors realizes the map between
higher-derivative amplitudes. As an example of new relations, the pure-gluon
amplitudes of mass dimension up to eight, featuring insertions of the $F^3$ and
$F^4$ operators which satisfy the traditional color-kinematics duality, can be
generated at all multiplicities from just renormalizable amplitudes of gluons
and bi-adjoint scalars. We also obtain closed-form expressions for the
kinematic numerators of the dimension-six gluon effective field theory, which
are valid in $D$ space-time dimensions. Finally, we find strong evidence that
this extended covariant color-kinematics duality relates the
$(DF)^2+$YM$(+\phi^3)$ theories which, at low energies, generate infinite
towers of operators satisfying the traditional color-kinematics duality, beyond
aforementioned $F^3$ and $F^4$ ones. |
The Cardy Formula from Goldstone Bosons: Two dimensional conformal field theories, can be described by their pseudo
Goldstone bosons when the conformal symmetry is spontaneously and anomalously
broken. We show that the Schwarzian action of these bosons leads to the Cardy
formula without using modular invariance. As a result, the Cardy formula
applies to conformal field theories on a cylinder and chiral theories in one
dimension. This also explains why the Cardy--Verlinde formula for theories on
$S^1 \times S^{d-2}$ can be written in the form of the Cardy formula of an
effective two dimensional theory. | Why Boltzmann Brains Don't Fluctuate Into Existence From the De Sitter
Vacuum: Many modern cosmological scenarios feature large volumes of spacetime in a de
Sitter vacuum phase. Such models are said to be faced with a "Boltzmann Brain
problem" - the overwhelming majority of observers with fixed local conditions
are random fluctuations in the de Sitter vacuum, rather than arising via
thermodynamically sensible evolution from a low-entropy past. We argue that
this worry can be straightforwardly avoided in the Many-Worlds (Everett)
approach to quantum mechanics, as long as the underlying Hilbert space is
infinite-dimensional. In that case, de Sitter settles into a truly stationary
quantum vacuum state. While there would be a nonzero probability for observing
Boltzmann-Brain-like fluctuations in such a state, "observation" refers to a
specific kind of dynamical process that does not occur in the vacuum (which is,
after all, time-independent). Observers are necessarily out-of-equilibrium
physical systems, which are absent in the vacuum. Hence, the fact that
projection operators corresponding to states with observers in them do not
annihilate the vacuum does not imply that such observers actually come into
existence. The Boltzmann Brain problem is therefore much less generic than has
been supposed. |
Scalar correlators and normal modes in holographic neutron stars: We study a scalar field in the background of a holographic neutron star at
finite temperature and analyze its asymptotic behavior to compute the two-point
correlator at the boundary. From the normal modes of the field we determine the
resonances and decay constants of the boundary field theory. We show that the
correlator is dominated by the normal modes in the stable regions of phase
space of the neutron star, becoming a power law as we move into the unstable
zones. | Duality Relations Among Topological Effects In String Theory: We explore two different problems in string theory in which duality relates
an ordinary p-form in one theory to a self-dual (p+1)-form in another theory.
One problem involves comparing D4-branes to M5-branes, and the other involves
comparing the Ramond-Ramond forms in Type IIA and Type IIB superstring theory.
In each case, a subtle topological effect involving the p-form can be recovered
from a careful analysis of the quantum mechanics of the self-dual (p+1)-form. |
Boundary N=2 Theory, Floer Homologies, Affine Algebras, and the Verlinde
Formula: Generalizing our ideas in [arXiv:1006.3313], we explain how
topologically-twisted N=2 gauge theory on a four-manifold with boundary, will
allow us to furnish purely physical proofs of (i) the Atiyah-Floer conjecture,
(ii) Munoz's theorem relating quantum and instanton Floer cohomology, (iii)
their monopole counterparts, and (iv) their higher rank generalizations. In the
case where the boundary is a Seifert manifold, one can also relate its
instanton Floer homology to modules of an affine algebra via a 2d A-model with
target the based loop group. As an offshoot, we will be able to demonstrate an
action of the affine algebra on the quantum cohomology of the moduli space of
flat connections on a Riemann surface, as well as derive the Verlinde formula. | On Orientifolds, Discrete Torsion, Branes and M Theory: We find some lifts to M theory of orientifold and orbifold planes including
the O1, O3 and O5 planes of Type IIB and their transformations under SL(2,Z).
The possible discrete torsion variants (or K theory classes) are explored, and
are interpreted as arising from brane intersections with planes. We find new
variants of the O0 and of an orbifold line (OF1) and determine their tensions
in some cases. A systematic review of orientifolds, M orientifolds, and known M
lifts, with some new clarifications is included together with a discussion of
the role of T duality. |
Perturbative Understanding of Non-Perturbative Processes and
Quantumization versus Classicalization: In some instances of study of quantum evolution of classical backgrounds it
is considered inevitable to resort to non-perturbative methods at the price of
treating the system semiclassically. We show that a fully quantum perturbative
treatment, in which the background is resolved as a multi-particle state,
recovers the semiclassical non-perturbative results and allows going beyond. We
reproduce particle-creation by a classical field in a theory of two scalars as
well as in scalar QED in terms of scattering processes of high multiplicity.
The multi-particle treatment also gives a transparent picture of why a
single-process transition from a classical to a quantum state, which we call
quantumization, is exponentially suppressed, whereas the opposite process,
classicalization, can take place swiftly if the microstate degeneracy of the
classical state is high. An example is provided by the $N$-graviton portrait of
a black hole: a black hole can form efficiently via a $2\to N$ classicalization
process in the collision of high-energy particles but its quantumization via a
decay $N \to 2$ is exponentially suppressed. | The universality of the shift of the Chern-Simons parameter for a
general class of BRS invariant regularizations: We consider a biparametric family of BRS invariant regularization methods of
SU(N) Chern-Simons theory (the parameters defining the family taking arbitrary
values in $\RR^2$) and show that the shift $k\to k + sign(k) N$ of the
Chern-Simons parameter $k$ occurs for arbitrary values of the family defining
parameters. This supports irrefutably the conjecture that the shift of $k$ is
universal for BRS invariant regulators. |
Crystalline geometries from fermionic vortex lattice with hyperscaling
violation: We analytically consider the spontaneous formation of a fermionic crystalline
geometry in a gravity background with Lifshitz scaling and/or hyperscaling
violation. Fermionic vortex lattice solution sourced by the lowest Laundau
level has been obtained. Thermodynamic analysis shows that the fermionic vortex
lattice favors a triangular configuration, regardless of the values of the
Lifshitz scaling $z$ and the hyperscaling violation exponent $\theta$. Our
results also show that the larger $z$ or lower $\theta$ leads to more stable
lattices thermodynamically. | Null Polygonal Wilson Loops in Full N=4 Superspace: We compute the one-loop expectation value of light-like polygonal Wilson
loops in N=4 super-Yang-Mills theory in full superspace. When projecting to
chiral superspace we recover the known results for tree-level
next-to-maximally-helicity-violating (NMHV) scattering amplitude. The one-loop
MHV amplitude is also included in our result but there are additional terms
which do not immediately correspond to scattering amplitudes. We finally
discuss different regularizations and their Yangian anomalies. |
Relaxing to Three Dimensions: We propose a new selection principle for distinguishing among possible vacua
that we call the "relaxation principle". The idea is that the universe will
naturally select among possible vacua through its cosmological evolution, and
the configuration with the biggest filling fraction is the likeliest. We apply
this idea to the question of the number of dimensions of space. We show that
under conventional (but higher-dimensional) FRW evolution, a universe filled
with equal numbers of branes and antibranes will naturally come to be dominated
by 3-branes and 7-branes. We show why this might help explain the number of
dimensions that are experienced in our visible universe. | The structure of N=3 multiplets in AdS_4 and the complete Osp(3|4) X
SU(3) spectrum of M-theory on AdS_4 X N^{010}: In this paper, relying on previous results of one of us on harmonic analysis,
we derive the complete spectrum of Osp(3|4) X SU(3) multiplets that one obtains
compactifying D=11 supergravity on the unique homogeneous space N^{0,1,0} that
has a tri-sasakian structure, namely leads to N=3 supersymmetry both in the
four-dimensional bulk and on the three-dimensional boundary. As in previously
analyzed cases the knowledge of the Kaluza Klein spectrum, together with
general information on the geometric structure of the compact manifold is an
essential ingredient to guess and construct the corresponding superconformal
field theory. This is work in progress. As a bonus of our analysis we derive
and present the explicit structure of all unitary irreducible representations
of the superalgebra Osp(3|4) with maximal spin content s_{max}>=2. |
Some exact Bradlow vortex solutions: We consider the Bradlow equation for vortices which was recently found by
Manton and find a two-parameter class of analytic solutions in closed form on
nontrivial geometries with non-constant curvature. The general solution to our
class of metrics is given by a hypergeometric function and the area of the
vortex domain by the Gaussian hypergeometric function. | Generalized Kerr-NUT-de Sitter metrics in all dimensions: We classify all spacetimes with a closed rank-2 conformal Killing-Yano
tensor. They give a generalization of Kerr-NUT-de Sitter spacetimes. The
Einstein condition is explicitly solved and written as an indefinite integral.
It is characterized by a polynomial in the integrand. We briefly discuss the
smoothness conditions of the Einstein metrics over compact Riemannian
manifolds. |
Heterotic NS5-branes from closed string tachyon condensation: We show how to construct the familiar heterotic NS5 brane as a topological
soliton in a supercritical version of heterotic string theory. Closed string
tachyon condensation removes the extra dimensions, leaving the NS5 in 10d, in a
process highly reminiscent of the K-theoretical description of type II
D-branes, but linking non-trivial gauge bundles and geometry. The construction
requires a modification of the anomalous Bianchi identity for $H_3$ in
supercritical heterotic string theory. We give various proofs for the existence
of this modification. | Renormalization of supersymmetric chiral theories in rational spacetime
dimensions: We renormalize models with scalar chiral superfields with an odd
superpotential to several orders in perturbation theory. These extensions of
the cubic Wess-Zumino model are renormalizable in spacetime dimensions which
are rational. When endowed with an $O(N)$ symmetry it is shown that they share
the same property as their non-supersymmetric counterparts in that at a
particular fixed point there is an emergent $OSp(1|n-1)$ symmetry, where $n$ is
the power of the superpotential. This is shown at a loop order beyond that for
which it was established in the parallel non-supersymmetric theory. |
Quasinormal modes around the BTZ black hole at the tricritical
generalized massive gravity: Employing the operator method, we obtain log-square quasinormal modes and
frequencies of a graviton around the BTZ black hole at the tricritical point of
the generalized massive gravity. The log-square quasinormal frequencies are
also obtained by considering a finite temperature conformal field theory. This
shows the AdS/LCFT correspondence at the tricritical point approximately. We
discuss a truncation process to the unitary theory on the BTZ black hole
background. | Supersymmetry, Variational Method and Hulthén Potential: The formalism of Supersymmetric Quantum Mechanics provides us the
eigenfunctions to be used in the variational mathod to obtain the eigenvalues
for the Hulth\'en Potential. |
Synchrotron Radiation in the Standard Model Extension: We obtain a system of exact solutions of the Dirac equation for an electron
moving in a constant homogeneous external magnetic field with account of its
vacuum magnetic moment and assumed Lorentz invariance violation in the minimal
CPT-odd form in the framework of the Standard Model Extension. Using these
solutions, characteristics of the particle synchrotron radiation are
calculated, and possible observable effects caused by the Lorentz non-invariant
interaction are described. We demonstrate that the angular distribution of the
radiation has specific asymmetry, which can be explained as a consequence of
non-conservation of transversal electron polarization in the presence of a
background Lorentz non-invariant condensate field. | Sphalerons, knots, and dynamical compactification in
Yang-Mills-Chern-Simon theories: Euclidean d=3 SU(2) Yang-Mills-Chern-Simons (YMCS) theory, including
Georgi-Glashow (GGCS) theory, may have solitons in the presence of appropriate
mass terms. For integral CS level k and for solitons carrying integral CS
number, YMCS is gauge-invariant and consistent. However, individual solitons
such as sphalerons and linked center vortices with CS number of 1/2 and
writhing center vortices with arbitrary CS number are non-compact; a condensate
of them threatens compactness of the theory. We study various forms of the
non-compact theory in the dilute-gas approximation, treating the parameters of
non-compact large gauge transformations as collective coordinates. We conclude:
1) YMCS theory dynamically compactifies; non-compact YMCS have infinitely
higher vacuum energy than compact YMCS. 2) An odd number of sphalerons is
associated with a domain- wall sphaleron, a pure-gauge configuration on a
closed surface enclosing them and with a half-integral CS number. 3) We
interpret the domain-wall sphaleron in terms of fictitious closed Abelian
magnetic field lines that express the links of the Hopf fibration. Sphalerons
are over- and under-crossings of knots in the field lines; the domain-wall
sphaleron is a superconducting wall confining these knots to a compact domain.
4) Analogous results hold for center vortices and nexuses. 5) For a CS term
induced with an odd number of fermion doublets, domain-wall sphalerons are
related to non-normalizable fermion modes. 6) GGCS with monopoles is
compactified with center-vortex-like strings. |
Chiral string theories as an interpolation between strings and particles: A new set of boundary conditions for string propagators is proposed in this
paper. The boundary conditions are parametrized by a complex number $\lambda$.
Under these new boundary conditions, the left-moving and right-moving modes are
treated unequally. Thus, we called them chiral string theories. If $\lambda =
-1$, the spectrum of such theory truncates to a finite number, and therefore it
becomes a different description of supergravity. We found the spectrum of
chiral string theories by requiring that the vertex operators are conformally
invariant. In addition, we also calculate the amplitudes for arbitrary
$\lambda$. The amplitudes are expressed as a product of open string amplitudes
which are similar to the KLT relation. The unitarity of these theories are
investigated. However, we found out that except for $\lambda = \pm 1$, all
other theories are not unitary; i.e., only the supergravity and ordinary
strings are unitary. Although most of the chiral strings are not physical, they
still serve as a valuable tool in studying the relation between particle
theories and string theories. | Two-dimensional models: Proposal for contribution to the quantum field theory section in
"Encyclopedia of Mathematical Physics". |
Geometry of Higher-Dimensional Black Hole Thermodynamics: We investigate thermodynamic curvatures of the Kerr and Reissner-Nordstr\"om
(RN) black holes in spacetime dimensions higher than four. These black holes
possess thermodynamic geometries similar to those in four dimensional
spacetime. The thermodynamic geometries are the Ruppeiner geometry and the
conformally related Weinhold geometry. The Ruppeiner geometry for $d=5$ Kerr
black hole is curved and divergent in the extremal limit. For $d \geq 6$ Kerr
black hole there is no extremality but the Ruppeiner curvature diverges where
one suspects that the black hole becomes unstable. The Weinhold geometry of the
Kerr black hole in arbitrary dimension is a flat geometry. For RN black hole
the Ruppeiner geometry is flat in all spacetime dimensions, whereas its
Weinhold geometry is curved. In $d \geq 5$ the Kerr black hole can possess more
than one angular momentum. Finally we discuss the Ruppeiner geometry for the
Kerr black hole in $d=5$ with double angular momenta. | Propagation peculiarities of mean field massive gravity: Massive gravity (mGR) describes a dynamical "metric" on a fiducial,
background one. We investigate fluctuations of the dynamics about mGR
solutions, that is about its "mean field theory". Analyzing mean field massive
gravity propagation characteristics is not only equivalent to studying those of
the full non-linear theory, but also in direct correspondence with earlier
analyses of charged higher spin systems, the oldest example being the charged,
massive spin 3/2 Rarita--Schwinger (RS) theory. The fiducial and mGR mean field
background metrics in the mean field mGR model correspond to the RS Minkowski
metric and external EM field. The common implications in both systems are that
hyperbolicity holds only in a weak background-mean-field limit, immediately
ruling both theories out as fundamental theories. Although both can still be
considered as predictive effective models in the weak regime, their lower
helicities exhibit superluminal behavior: lower helicity gravitons are
superluminal as compared to photons propagating on either the fiducial or
background metric. This "crystal-like" phenomenon of differing helicities
having differing propagation speeds in both mean field mGR and mGR is a
peculiar feature of these models. |
Fermion states localized on a self-gravitating Skyrmion: We investigate self-gravitating solutions of the Einstein-Skyrme theory
coupled to spin-isospin Dirac fermions and consider the dependence of the
spectral flow on the effective gravitational coupling constant and on the
Yukawa coupling. It is shown that the effects of the backreaction of the
fermionic mode may strongly deform the configuration. In particular, the energy
conditions may be violated, and regular anti-gravitating asymptotically flat
solutions with negative ADM mass may emerge. | Hyperscaling violation, quasinormal modes and shear diffusion: We study quasinormal modes of shear gravitational perturbations for
hyperscaling violating Lifshitz theories, with Lifshitz and hyperscaling
violating exponents $z$ and $\theta$. The lowest quasinormal mode frequency
yields a shear diffusion constant which is in agreement with that obtained in
previous work by other methods. In particular for theories with $z<
d_i+2-\theta$ where $d_i$ is the boundary spatial dimension, the shear
diffusion constant exhibits power-law scaling with temperature, while for
$z=d_i+2-\theta$, it exhibits logarithmic scaling. We then calculate certain
2-point functions of the dual energy-momentum tensor holographically for $z\leq
d_i+2-\theta$, identifying the diffusive poles with the quasinormal modes
above. This reveals universal behaviour $\eta/s=1/4\pi$ for the
viscosity-to-entropy-density ratio for all $z\leq d_i+2-\theta$. |
Holographic RG and Exact RG in O(N) Model: In this paper an Exact Renormalization Group (ERG) equation is written for
the the critical $O(N)$ model in $D$-dimensions (with $D\approx 3$) at the
Wilson-Fisher fixed point perturbed by a scalar composite operator. The action
is written in terms of an auxiliary scalar field and reproduces correlation
functions of a scalar composite operator. The equation is derived starting from
the Polchinski ERG equation for the fundamental scalar field. As described in
arXiv:1706.03371 an evolution operator for the Polchinski ERG equation can be
written in the form of a functional integral, with a $D+1$ dimensional scalar
field theory action. In the case of the fundamental scalar field this action
only has a kinetic term and therefore looks quite different from Holographic RG
where there are potential terms. But in the composite operator case discussed
in this paper, the ERG equation and consequently the $D+1$ dimensional action
contains higher order potential terms for the scalar field and is therefore
very similar to the case of Holographic RG. Furthermore this action can be
mapped to a scalar field action in $AdS_{D+1}$ using the techniques of
arXiv:1706.03371. The leading cubic term of the potential is computed in this
paper for $D \approx 3$ and expectedly vanishes in $D=3$ in agreement with
results in the AdS/CFT literature. | New Massive JT Multi-Gravity and N-Replica of SYK Models: We study a series of powerful correspondences among new multi-gravity
extensions of the Jackiw-Teitelboim model, multi-SYK models and
multi-Schwarzian quantum mechanics, in the $\rm{(A)dS_{2}/CFT}$ arena.
Deploying a $BF$-like formulation of the model, we discuss the counting of the
degrees of freedom for some specific classes of multi-gravity potentials, and
unveil connections among a variety of apparently different models. Quantization
of multi-gravity models can be then achieved from both the Hartle-Hawking
no-boundary proposal, the SYK partition function and the spin-foam approaches.
We comment on the SYK quantization procedure, and deepen in the appendix the
quantization scheme naturally achieved in the $BF$ framework. The new
multi-gravity theory hence recovered presents intriguing applications for
analogue gravitational models developed for condensed matter physics, including
graphene, endowed with defects and high intensity magnetic fields. |
On two-loop divergences of effective action in $6D$, ${\cal N}=(1,1)$
SYM theory: We study the off-shell structure of the two-loop effective action in $6D,
{\cal N}=(1,1)$ supersymmetric gauge theories formulated in ${\cal N}=(1,0)$
harmonic superspace. The off-shell effective action involving all fields of
$6D, {\cal N}=(1,1)$ supermultiplet is constructed by the harmonic superfield
background field method, which ensures both manifest gauge covariance and
manifest ${\cal N}=(1,0)$ supersymmetry. We analyze the off-shell divergences
dependent on both gauge and hypermultiplet superfields and argue that the gauge
invariance of the divergences is consistent with the non-locality in harmonics.
The two-loop contributions to the effective action are given by harmonic
supergraphs with the background gauge and hypermultiplet superfields. The
procedure is developed to operate with the harmonic-dependent superpropagators
in the two-loop supergraphs within the superfield dimensional regularization.
We explicitly calculate the gauge and the hypermultiplet-mixed divergences as
the coefficients of $\frac{1}{{\varepsilon}^2}$ and demonstrate that the
corresponding expressions are non-local in harmonics. | From Seiberg-Witten invariants to topological Green-Schwarz string: In this note we describe the physics of equivalence of the Seiberg-Witten
invariants of 4-manifolds and certain Gromov-Witten invariants defined by
pseudo-holomorphic curves. We show that physics of the pseudo-holomorphic
curves should be governed by the N=2 Green-Schwarz string. |
Kappa-Minkowski space-time and the star product realizations: We investigate a Lie algebra-type $ \kappa$-deformed Minkowski space-time
with undeformed Lorentz algebra and mutually commutative vector-like Dirac
derivatives. There are infinitely many realizations of $ \kappa$-Minkowski
space. The coproduct and the star product corresponding to each of them are
found. Utilizing the properties of the {\em{natural}} realization, we construct
a scalar field theory on $ \kappa$-deformed Minkowski space and show that it is
equivalent to the scalar, nonlocal, relativistically invariant field theory on
the ordinary Minkowski space. | On the structure of symmetric self-dual Lie algebras: A finite-dimensional Lie algebra is called (symmetric) self-dual, if it
possesses an invariant nondegenerate (symmetric) bilinear form. Symmetric
self-dual Lie algebras have been studied by Medina and Revoy, who have proven a
very useful theorem about their structure. In this paper we prove a refinement
of their theorem which has wide applicability in Conformal Field Theory, where
symmetric self-dual Lie algebras start to play an important role due to the
fact that they are precisely the Lie algebras which admit a Sugawara
construction. We also prove a few corollaries which are important in Conformal
Field Theory. (This paper provides mathematical details of results used, but
only sketched, in the companion paper hep-th/9506151.) |
The Stoyanovsky-Ribault-Teschner Map and String Scattering Amplitudes: Recently, Ribault and Teschner pointed out the existence of a one-to-one
correspondence between N-point correlation functions for the SL(2,C)_k/SU(2)
WZNW model on the sphere and certain set of 2N-2-point correlation functions in
Liouville field theory. This result is based on a seminal work by Stoyanovsky.
Here, we discuss the implications of this correspondence focusing on its
application to string theory on curved backgrounds. For instance, we analyze
how the divergences corresponding to worldsheet instantons in AdS_3 can be
understood as arising from the insertion of the dual screening operator in the
Liouville theory side. We also study the pole structure of N-point functions in
the 2D Euclidean black hole and its holographic meaning in terms of the Little
String Theory. This enables us to interpret the correspondence between CFTs as
encoding a LSZ-type reduction procedure. Furthermore, we discuss the scattering
amplitudes violating the winding number conservation in those backgrounds and
provide a formula connecting such amplitudes with observables in Liouville
field theory. Finally, we study the WZNW correlation functions in the limit k
-> 0 and show that, at the point k=0, the Stoyanovsky-Ribault-Teschner
dictionary turns out to be in agreement with the FZZ conjecture at a particular
point of the space of parameters where the Liouville central charge becomes
c=-2. This result makes contact with recent studies on the dynamical tachyon
condensation in closed string theory. | False vacuum decay in kink scattering: In this work we consider kink-antikink and antikink-kink collisions in a
modified $\phi^4$ model with a false vacuum characterized by a dimensionless
parameter $\epsilon$. The usual $\phi^4$ model is recovered for $\epsilon=0$.
We investigate the $\epsilon<<1$ regime where the kink in the presence of false
vacuum can be understood as a small deformation of the standard kink for the
$\phi^4$ model. We show that the attractive interaction between the
kink-antikink pair leads to a rich scattering pattern, in some cases delaying
considerably the false vacuum decay. |
Swampland Conjectures and Cosmological Expansion: Swampland conjectures (SCs) of string theory require that a constant
cosmological constant $\Lambda$ be replaced by a time-dependent scalar-field
quintessence with constrained parameters. The constraints limit the duration of
the present expansion era because, although the SCs may be fulfilled at the
present time, they will be violated at a finite time in the future allowing
only an order-one number of e-foldings. In contrast, cyclic cosmology requires
$\sim94$ e-foldings of the present universe before turnaround from expansion to
contraction. This presents a dilemma to the original SCs. One possibility is
that one of the SCs, the range conjecture, be significantly weakened. A second
possibility, difficult to believe, is that cyclic cosmology vastly
overestimates the number of e-foldings. A third possibility, which is the least
disfavoured, is that string theory is not the correct theory of quantum
gravity. | Entanglement Entropy of Two Black Holes and Entanglement Entropic Force: We study the entanglement entropy, $S_C$, of a massless free scalar field on
the outside region $C$ of two black holes $A$ and $B$ whose radii are $R_1$ and
$R_2$ and how it depends on the distance, $r(\gg R_1,R_2)$, between two black
holes. If we can consider the entanglement entropy as thermodynamic entropy, we
can see the entropic force acting on the two black holes from the $r$
dependence of $S_C$. We develop the computational method based on that of
Bombelli et al to obtain the $r$ dependence of $S_C$ of scalar fields whose
Lagrangian is quadratic with respect to the scalar fields. First we study $S_C$
in $d+1$ dimensional Minkowski spacetime. In this case the state of the
massless free scalar field is the Minkowski vacuum state and we replace two
black holes by two imaginary spheres, and we take the trace over the degrees of
freedom residing in the imaginary spheres. We obtain the leading term of $S_C$
with respect to $1/r$. The result is $S_C=S_A+S_B+\tfrac{1}{r^{2d-2}}
G(R_1,R_2)$, where $S_A$ and $S_B$ are the entanglement entropy on the inside
region of $A$ and $B$, and $G(R_1,R_2) \leq 0$. We do not calculate
$G(R_1,R_2)$ in detail, but we show how to calculate it. In the black hole case
we use the method used in the Minkowski spacetime case with some modifications.
We show that $S_C$ can be expected to be the same form as that in the Minkowski
spacetime case. But in the black hole case, $S_A$ and $S_B$ depend on $r$, so
we do not fully obtain the $r$ dependence of $S_C$. Finally we assume that the
entanglement entropy can be regarded as thermodynamic entropy, and consider the
entropic force acting on two black holes. We argue how to separate the
entanglement entropic force from other force and how to cancel $S_A$ and $S_B$
whose $r$ dependence are not obtained. Then we obtain the physical prediction
which can be tested experimentally in principle. |
Hook variables: cut-and-join operators and $τ$-functions: Young diagrams can be parameterized with the help of hook variables, which is
well known but never studied in big detail. We demonstrate that this is the
most adequate parameterization for many physical applications: from the Schur
functions, conventional, skew and shifted, which all satisfy their own kinds of
determinant formulas in these coordinates, to KP/Toda integrability and related
basis of cut-and-join $\hat W$-operators, which are both actually expressed
through the single-hook diagrams. In particular, we discuss a new type of
multi-component KP $\tau$-functions, Matisse $\tau$-functions. We also
demonstrate that the Casimir operators, which are responsible for
integrability, are single-hook, with the popular basis of "completed cycles"
being distinguished by especially simple coefficients in the corresponding
expansion. The Casimir operators also generate the $q=t$ Ruijsenaars
Hamiltonians. However, these properties are broken by the naive Macdonald
deformation, which is the reason for the loss of KP/Toda integrability and
related structures in $q$-$t$ matrix models. | N=4 Topological Amplitudes and Black Hole Entropy: We study the effects of N=4 topological string amplitudes on the entropy of
black holes. We analyse the leading contribution associated to six-derivative
terms and find one particular operator which can correct the entropy of N=4
black holes. This operator is BPS-like and appears in the effective action of
type II string theory on K3 x T^2 or equivalently its heterotic dual on T^6. In
both descriptions the leading contribution arises at one-loop, which we
calculate explicitly on the heterotic side. We then consider whether this term
has any consequences for the entropy of (large) N=4 black holes and find that
it makes indeed a contribution at subleading order. Repeating the computation
for small black holes with vanishing horizon area at the classical level, we
prove that this coupling lifts certain flat directions in the entropy function
thereby being responsible for the attractor equations of some moduli fields. |
On the String Pair Creation in Dp-Dp' Brane System: We address the bosonic string pair creation in a system of parallel Dp-Dp'
(p<p') branes by applying the path integral formalism. We drive the string pair
creation rate by calculating the one loop vacuum amplitude of the setup in
presence of the background electric field defined over the Dp'-brane. It is
pointed out that just the components of the electric field defined over the $p$
spatial directions (the common directions along which the both D-branes are
extended) give rise to the pair creation | Holographic Jets in an Expanding Plasma: We use the holographic principle to study quark jets with trailing strings in
an expanding plasma that asymptotes Bjorken hydrodynamics. We make use of the
fact that the trailing string is the locus of the light delay in bulk to obtain
the explicit form for quark jets in the expanding plasma. From the trailing
string solution we calculate the drag coefficient of a heavy quark in the
strongly coupled expanding plasma. The energy scaling of the maximum
penetration length of an ultrarelativistic light quark jet using light rays in
bulk is estimated. |
Deformation of the Cubic Open String Field Theory: We study a consistent deformation of the cubic open bosonic string theory in
such a way that the non-planar world sheet diagrams of the perturbative string
theory are mapped onto their equivalent planar diagrams of the light-cone
string field theory with some length parameters fixed. An explicit evaluation
of the cubic string vertex in the zero-slope limit yields the correct
relationship between the string coupling constant and the Yang-Mills coupling
constant. The deformed cubic open string field theory is shown to produce the
non-Abelian Yang-Mills action in the zero-slope limit if it is defined on
multiple D-branes. Applying the consistent deformation systematically to
multi-string world sheet diagrams, we may be able to calculate scattering
amplitudes with an arbitrary number of external open strings. | A new method for directly computing reduced density matrices: We demonstrate the power of a first principle-based and practicable method
that allows for the perturbative computation of reduced density matrix elements
of an open quantum system without making use of any master equations. The
approach is based on techniques from non-equilibrium quantum field theory like
thermo field dynamics, the Schwinger-Keldsyh formalism, and the Feynman-Vernon
influence functional. It does not require the Markov approximation and is
essentially a Lehmann-Szymanzik-Zimmermann-like reduction. In order to
illustrate this method, we consider a real scalar field as an open quantum
system interacting with an environment comprising another real scalar field. We
give a general formula that allows for the perturbative computation of density
matrix elements for any number of particles in a momentum basis. Finally, we
consider a simple toy model and use this formula to obtain expressions for some
of the system's reduced density matrix elements. |
Violation of vacuum stability by inverse square electric fields: In the framework of QED with a strong background, we study particle creation
(the Schwinger effect) by a time-dependent inverse square electric field. To
this end corresponding exact in- and out-solutions of the Dirac and
Klein-Gordon equations are found. We calculate the vacuum-to-vacuum probability
and differential and total mean numbers of pairs created from the vacuum. For
electric fields varying slowly in time, we present detailed calculations of the
Schwinger effect and discuss possible asymptotic regimes. The obtained results
are consistent with universal estimates of the particle creation effect by
electric fields in the locally constant field approximation. Differential and
total quantities corresponding to asymmetrical configurations are also
discussed in detail. Finally, the inverse square electric field is used to
imitate switching on and off processes. Then the case under consideration is
compared with the one where an exponential electric field is used to imitate
switching on and off processes. | Infinite-dimensional representations of the rotation group and Dirac's
monopole problem: Within the context of infinite-dimensional representations of the rotation
group the Dirac monopole problem is studied in details. Irreducible
infinite-dimensional representations, being realized in the indefinite metric
Hilbert space, are given by linear unbounded operators in infinite-dimensional
topological spaces, supplied with a weak topology and associated weak
convergence. We argue that an arbitrary magnetic charge is allowed, and the
Dirac quantization condition can be replaced by a generalized quantization rule
yielding a new quantum number, the so-called topological spin, which is related
to the weight of the Dirac string. |
Accelerated Cosmological Models in First-Order Non-Linear Gravity: The evidence of the acceleration of universe at present time has lead to
investigate modified theories of gravity and alternative theories of gravity,
which are able to explain acceleration from a theoretical viewpoint without the
need of introducing dark energy. In this paper we study alternative
gravitational theories defined by Lagrangians which depend on general functions
of the Ricci scalar invariant in minimal interaction with matter, in view of
their possible cosmological applications. Structural equations for the
spacetimes described by such theories are solved and the corresponding field
equations are investigated in the Palatini formalism, which prevents
instability problems. Particular examples of these theories are also shown to
provide, under suitable hypotheses, a coherent theoretical explanation of
earlier results concerning the present acceleration of the universe and
cosmological inflation. We suggest moreover a new possible Lagrangian,
depending on the inverse of sinh(R), which gives an explanation to the present
acceleration of the universe. | Unitarity Violation in Field Theories of Lee-Wick's Complex Ghost: Theories with fourth-order derivatives, including the Lee-Wick finite QED
model and Quadratic Gravity, have a better UV behaviour, but the presence of
negative metric ghost modes endanger unitarity. Noticing that the ghost
acquires a complex mass by radiative corrections, Lee and Wick, in particular,
claimed that such complex ghosts would never be created by collisions of
physical particles because of energy conservation, so that the physical
S-matrix unitarity must hold.
We investigate the unitarity problem faithfully working in the operator
formalism of quantum field theory. When complex ghosts participate, a complex
delta function (generalization of Dirac delta function) appears at each
interaction vertex, which enforces a specific conservation law of complex
energy. Its particular property implies that the naive Feynman rule is wrong if
the four-momenta are assigned to the internal lines after taking account of the
conservation law in advance. We show that the complex ghosts are actually
created and unitarity is violated in such fourth-order derivative theories. We
also find a definite energy threshold below which the ghosts cannot be created:
The theories are unitary and renormalizable below the threshold. |
Magnetic Vortex Line Configuration of Faddeev-Niemi Knot: This paper has been withdrawn by the author due to the inaccurate result. | Hidden Symmetries of the Principal Chiral Model Unveiled: By relating the two-dimensional U(N) Principal Chiral Model to a simple
linear system we obtain a free-field parametrisation of solutions. Obvious
symmetry transformations on the free-field data give symmetries of the model.
In this way all known `hidden symmetries' and B\"acklund transformations, as
well as a host of new symmetries, arise. |
Large mass expansion of the one-loop effective action induced by a
scalar field on the two-dimensional Minkowski background with non-trivial
$(1+1)$ splitting: A large mass expansion of the one-loop effective action of a scalar field on
the two-dimensional Minkowski spacetime is found in the system of coordinates,
where the metric $g_{\mu\nu}(t,x)\neq\eta_{\mu\nu}=diag(1,-1)$, and
$g_{\mu\nu}(t,x)$ tends to $\eta_{\mu\nu}$ at the spatial and temporal
infinities. It is shown that, apart from the Coleman-Weinberg potential, this
expansion contains the terms both analytic and non-analytic in $m^{-2}$, where
$m$ is the mass of a scalar field. A general unambiguous expression for the
one-loop correction to the effective action on non-stationary backgrounds is
derived. | Nonspherical Giant Gravitons and Matrix Theory: We consider the plane wave limit of the nonspherical giant gravitons. We
compute the Poisson brackets of the coordinate functions and find a nonlinear
algebra. We show that this algebra solves the supersymmetry conditions of the
matrix model. This is the generalization of the algebraic realization of the
spherical membrane as the ``fuzzy sphere''. We describe finite dimensional
representations of the algebra corresponding to the fuzzy torus. |
Conserved charges in timelike Warped-AdS$_3$ spaces: We consider the timelike version of Warped Anti-de Sitter space (WAdS), which
corresponds to the three-dimensional section of the G\"{o}del solution of
four-dimensional cosmological Einstein equations. This geometry presents closed
timelike curves (CTCs), which are inherited from its four-dimensional
embedding. In three dimensions, this type of solutions can be supported without
matter provided the graviton acquires mass. Here, among the different ways to
consistenly give mass to the graviton in three dimensions, we consider the
parity-even model known as New Massive Gravity (NMG). In the bulk of timelike
WAdS$_{3}$ space, we introduce defects that, from the three-dimensional point
of view, represent spinning massive particle-like objects. For this type of
sources, we investigate the definition of quasi-local gravitational energy as
seen from infinity, far beyond the region where the CTCs appear. We also
consider the covariant formalism applied to NMG to compute the mass and the
angular momentum of spinning particle-like defects, and compare the result with
the one obtained by means of the quasi-local stress-tensor. We apply these
methods to special limits in which the WAdS$_3$ solutions coincide with locally
AdS$_3$ and locally AdS$_{2}\times \mathbb{R}$ spaces. Finally, we make some
comments about the asymptotic symmetry algebra of asymptotically WAdS$_3$
spaces in NMG. | Self-Gravitating Strings and String/Black Hole Correspondence: In a recent essay, we discussed the possibility of using polymer sizing to
model the collapse of a single, long excited string to a black hole. In this
letter, we apply this idea to bring further support to string/black hole
correspondence. In particular, we reproduce Horowitz and Polchinki's results
for self-gravitating fundamental strings and speculate on the nature of the
quantum degrees of freedom of black holes in string theory. |
Holographic Floquet states II: Floquet condensation of vector mesons in
nonequilibrium phase diagram: With the aim to reveal universal features of hadronic matter and correlated
Dirac insulators in strong AC-electric fields, we study the $\mathcal{N}=2$
supersymmetric QCD with a finite quark mass driven by a rotating electric field
$\mathcal{E}_x+i\mathcal{E}_y= E e^{i\Omega t}$. The analysis is done in the
holographically dual D3/D7 system in the co-rotating frame, effectively. The
nonequilibrium phase diagram is determined from the threshold electric field at
which the insulator phase breaks down to a conductive phase due to the AC
version of the Schwinger mechanism. The external field induces a rotating
current $\mathcal{J}_x + i \mathcal{J}_y = J e^{i\Omega t}$ originating from
vacuum polarization and dissipative current in the insulating and conductive
phases respectively. Intriguing features are observed as the frequency $\Omega$
approaches resonance with the meson excitation energy $\Omega_{\rm meson}$.
There, the threshold minimizes and a condensate of vector mesons with
oscillating current exists even in the zero driving field limit. This state,
which we call Floquet condensate of vector mesons, is expected to be
dynamically stable realizing a non-thermal fixed point that breaks time
translational and reversal symmetries. Our finding has many similarities with
exciton BEC discussed in solid state systems, where the semiconductor is to be
replaced by materials hosting gapped Dirac electrons, e.g. 3D topological
insulators or bismuth. Vector meson Floquet condensate may also have
implications in the pre-thermalized dynamics in heavy ion collision
experiments. | Isolated vacua in supersymmetric Yang-Mills theories: An explicit proof of the existence of nontrivial vacua in the pure
supersymmetric Yang-Mills theories with higher orthogonal SO(N), N>=7 or the
G_2 gauge group defined on a 3-torus with periodic boundary conditions is
given. Extra vacuum states are separated by an energy barrier from the
perturbative vacuum A_i=0 and its gauge copies. |
Towards a Swampland Global Symmetry Conjecture using Weak Gravity: It is widely believed and in part established that exact global symmetries
are inconsistent with quantum gravity. One then expects that approximate global
symmetries can be quantitatively constrained by quantum gravity or swampland
arguments. We provide such a bound for an important class of global symmetries:
Those arising from a gauged $U(1)$ with the vector made massive via Higgsing
with an axion. The latter necessarily couples to instantons, and their action
can be constrained, using both the electric and magnetic version of the axionic
weak gravity conjecture, in terms of the cutoff of the theory. As a result,
instanton-induced symmetry breaking operators with a suppression factor not
smaller than $\exp(-M_{\rm P}^2/\Lambda^2)$ are present, where $\Lambda$ is a
cutoff of the 4d effective theory. We provide a general argument and clarify
the meaning of $\Lambda$. Simple 4d and 5d models are presented to illustrate
this, and we recall that this is the standard way in which things work out in
string compactifications with brane instantons. The relation of our constraint
to bounds that can be derived from wormholes or gravitational instantons and to
those motivated by black-hole effects at finite temperature are discussed, and
we present a generalization of the Giddings-Strominger wormhole solution to the
case of a gauge-derived $U(1)$ global symmetry. Finally, we discuss potential
loopholes to our arguments. | Problems with False Vacua in Supersymmetric Theories: It has been suggested recently that in a consistent theory any Minkowski
vacuum must be exactly stable. As a result, a large class of theories that in
ordinary treatment would appear sufficiently long-lived, in reality make no
sense. In particular, this applies to supersymmetric models in which global
supersymmetry is broken in a false vacuum. We show that in any such theory the
dynamics of supersymmetry breaking cannot be decoupled from the Planck scale
physics. This finding poses an obvious challenge for the idea of low-scale
metastable (for example gauge) mediation. |
World-Volume Potentials on D-branes: By evaluating string scattering amplitudes, we investigate various low energy
interactions for the massless scalars on a nonabelian Dirichlet brane. We
confirm the existence of couplings of closed string fields to the world-volume
scalars, involving commutators of the latter. Our results are consistent with
the recently proposed nonabelian world-volume actions for Dp-branes. | Integrability As Duality: The Gauge/YBE Correspondence: The Gauge/YBE correspondence states a surprising connection between solutions
to the Yang-Baxter equation with spectral parameters and partition functions of
supersymmetric quiver gauge theories. This correspondence has lead to
systematic discoveries of new integrable models based on quantum-field-theory
methods. We provide pedagogical introduction to the subject and summarizes many
recent developments. This is a write-up of the lecture at the String-Math 2018
conference. |
Deformed supersymmetric gauge theories from the fluxtrap background: The fluxtrap background of string theory provides a transparent and
algorithmic way of constructing supersymmetric gauge theories with both mass
and Omega-type deformations in various dimensions. In this article, we review a
number of deformed supersymmetric gauge theories in two and four dimensions
which can be obtained via the fluxtrap background from string or M-theory. Such
theories, the most well-known being Omega-deformed super Yang-Mills theory in
four dimensions, have met with a lot of interest in the recent literature. The
string theory treatment offers many new avenues of analysis and applications,
such as for example the study of the gravity duals for deformed N=4 gauge
theories. | Left-right symmetric gauge model in a noncommutative geometry on
$M_4\times Z_4$: The left-right symmetric gauge model with the symmetry of $SU(3)_c\times
SU(2)_L\times SU(2)_R\times U(1)$ is reconstructed in a new scheme of the
noncommutative differential geometry (NCG) on the discrete space $M_4\times
Z_4$ which is a product space of Minkowski space and four points space. The
characteristic point of this new scheme is to take the fermion field to be a
vector in a 24-dimensional space which contains all leptons and quarks.
Corresponding to this specification, all gauge and Higgs boson fields are
represented in $24\times 24$ matrix forms. We incorporate two Higgs doublet
bosons $h$ and $SU(2)_R$ adjoint Higgs $\xi_R$ which are as usual transformed
as $(2,2^\ast,0)$ and $(1,3,-2)$ under $SU(2)_L\times SU(2)_R\times U(1)$,
respectively. Owing to the revise of the algebraic rules in a new NCG, we can
obtain the necessary potential and interacting terms between these Higgs bosons
which are responsible for giving masses to the particles included. Among the
Higgs doublet bosons, one CP-even scalar boson survives in the weak energy
scale and other four scalar bosons acquire the mass of the $SU(2)_R\times U(1)$
breaking scale, which is similar to the situation in the standard model.
$\xi_R$ is responsible to spontaneously break $SU(2)\ma{R} \times U(1)$ down to
$U(1)\ma{Y}$ and so well explains the seesaw mechanism. Up and down quarks have
the different masses through the vacuum expectation value of $h$. |
Noncommutative cosmological models coupled to a perfect fluid and a
cosmological constant: In this work we carry out a noncommutative analysis of several
Friedmann-Robert-Walker models, coupled to different types of perfect fluids
and in the presence of a cosmological constant. The classical field equations
are modified, by the introduction of a shift operator, in order to introduce
noncommutativity in these models. We notice that the noncommutative versions of
these models show several relevant differences with respect to the
correspondent commutative ones. | Non-ladder Extended Renormalization Group Analysis of the Dynamical
Chiral Symmetry Breaking: The order parameters of dynamical chiral symmetry breaking in QCD, the
dynamical mass of quarks and the chiral condensates, are evaluated by
numerically solving the Non-Perturbative Renormalization Group (NPRG)
equations. We employ an approximation scheme beyond ``the ladder'', that is,
beyond the (improved) ladder Schwinger-Dyson equations. The chiral condensates
are enhanced compared with the ladder ones, which is phenomenologically
favorable. The gauge dependence of the order parameters is fairly reduced in
this scheme. |
Dp-branes, NS5-branes and U-duality from nonabelian (2,0) theory with
Lie 3-algebra: We derive the super Yang-Mills action of Dp-branes on a torus T^{p-4} from
the nonabelian (2,0) theory with Lie 3-algebra. Our realization is based on Lie
3-algebra with pairs of Lorentzian metric generators. The resultant theory then
has negative norm modes, but it results in a unitary theory by setting VEV's of
these modes. This procedure corresponds to the torus compactification,
therefore by taking a transformation which is equivalent to T-duality, the
Dp-brane action is obtained. We also study type IIA/IIB NS5-brane and
Kaluza-Klein monopole systems by taking other VEV assignments. Such various
compactifications can be realized in the nonabelian (2,0) theory, since both
longitudinal and transverse directions can be compactified, which is different
from the BLG theory. We finally discuss U-duality among these branes, and show
that most of the moduli parameters in U-duality group are recovered. Especially
in D5-brane case, the whole U-duality relation is properly reproduced. | Search of scaling solutions in scalar-tensor gravity: We write new functional renormalization group equations for a scalar
nonminimally coupled to gravity. Thanks to the choice of the parametrization
and of the gauge fixing they are simpler than older equations and avoid some of
the difficulties that were previously present. In three dimensions these
equations admit, at least for sufficiently small fields, a solution that may be
interpreted as a gravitationally dressed Wilson-Fisher fixed point. We also
find for any dimension d>2 two analytic scaling solutions which we study for
d=3 and d=4. One of them corresponds to the fixed point of the Einstein-Hilbert
truncation, the others involve a nonvanishing minimal coupling. |
Alday-Maldacena duality and AdS Plateau problem: A short summary of approximate approach to the study of minimal surfaces in
AdS, based on solving Nambu-Goto equations iteratively. Today, after partial
denunciation of the BDS conjecture, this looks like the only constructive
approach to understanding the ways of its possible modification and thus to
saving the Alday-Maldacena duality. Numerous open technical problems are
explicitly formulated throughout the text. | Duality Between the Webs of Heterotic and Type II Vacua: We discuss how transitions in the space of heterotic K3*T^2 compactifications
are mapped by duality into transitions in the space of Type II
compactifications on Calabi-Yau manifolds. We observe that perturbative
symmetry restoration, as well as non-perturbative processes such as changes in
the number of tensor multiplets, have at least in many cases a simple
description in terms of the reflexive polyhedra of the Calabi-Yau manifolds.
Our results suggest that to many, perhaps all, four-dimensional N=2 heterotic
vacua there are corresponding type II vacua. |
Exophobic Quasi-Realistic Heterotic String Vacua: We demonstrate the existence of heterotic-string vacua that are free of
massless exotic fields. The need to break the non-Abelian GUT symmetries in k=1
heterotic-string models by Wilson lines, while preserving the GUT embedding of
the weak-hypercharge and the GUT prediction sin^2\theta_w(M(GUT))=3/8,
necessarily implies that the models contain states with fractional electric
charge. Such states are severely restricted by observations, and must be
confined or sufficiently massive and diluted. We construct the first
quasi-realistic heterotic-string models in which the exotic states do not
appear in the massless spectrum, and only exist, as they must, in the massive
spectrum. The SO(10) GUT symmetry is broken to the Pati-Salam subgroup. Our PS
heterotic-string models contain adequate Higgs representations to break the GUT
and electroweak symmetry, as well as colour Higgs triplets that can be used for
the missing partner mechanism. By statistically sampling the space of
Pati-Salam vacua we demonstrate the abundance of quasi--realistic three
generation models that are completely free of massless exotics, rendering it
plausible that obtaining realistic Yukawa couplings may be possible in this
space of models. | Allowable complex metrics in minisuperspace quantum cosmology: Kontsevich and Segal (K-S) have proposed a criterion to determine which
complex metrics should be allowed, based on the requirement that quantum field
theories may consistently be defined on these metrics, and Witten has recently
suggested that their proposal should also apply to gravity. We explore this
criterion in the context of gravitational path integrals, in simple
minisuperspace models, specifically considering de Sitter (dS), no-boundary and
Anti-de Sitter (AdS) examples. These simple examples allow us to gain some
understanding of the off-shell structure of gravitational path integrals. In
all cases, we find that the saddle points of the integral lie right at the edge
of the allowable domain of metrics, even when the saddle points are complex or
Euclidean. Moreover the Lefschetz thimbles, in particular the steepest descent
contours for the lapse integral, are cut off as they intrude into the domain of
non-allowable metrics. In the AdS case, the implied restriction on the
integration contour is found to have a simple physical interpretation. In the
dS case, the lapse integral is forced to become asymptotically Euclidean. We
also point out that the K-S criterion provides a reason, in the context of the
no-boundary proposal, for why scalar fields would start their evolution at
local extrema of their potential. |
Electromagnetic signatures of a strongly coupled anisotropic plasma: In heavy-ion collisions, quark-gluon plasma is likely to be produced with
sizable initial pressure anisotropy, which may leave an imprint on
electromagnetic observables. In order to model a strongly coupled anisotropic
plasma, we use the AdS/CFT correspondence to calculate the current-current
correlator of a weakly gauged U(1) subgroup of R symmetry in an N=4
super-Yang-Mills plasma with a (temporarily) fixed anisotropy. The dual
geometry, obtained previously by Janik and Witaszczyk, contains a naked
singularity which however permits purely infalling boundary conditions and
therefore the usual definition of a retarded correlator. We obtain numerical
results for the cases of wave vector parallel and orthogonal to the direction
of anisotropy, and we compare with previous isotropic results. In the
(unphysical) limit of vanishing frequency (infinite time) we obtain a vanishing
DC conductivity for any amount of anisotropy, but the anisotropic AC
conductivities smoothly approach the isotropic case in the limit of high
frequencies. We also discuss hard photon production from an anisotropic plasma
and compare with existing hard-loop resummed calculations. | On hypersymmetry in three dimensioons: In this work we presented a number of explicit examples for the cubic
vertices describing an interaction of massless spin-5/2 field with massive
boson and fermion including all hypertransformations necessary for the vertices
to be gauge invariant. Here we restrict ourselves with the massive bosons with
spins s=2,1,0 and massive fermions with spins s=3/2,1/2. Our general analysis
predicted that the vertex must exist for any boson and fermion with the spin
difference 3/2 or 1/2. And indeed it appeared that the vertex exists for all
six possible pairs (2,1,0) X (3/2,1/2). As in the case of massive
supermultiplets, our construction is based on the gauge invariant description
for the massive fields with spins s >= 1. Moreover, we have explicitly checked
that all the vertices are invariant also under the gauge symmetries of these
massive fields. |
Semi-Chiral Operators in 4d ${\cal N}=1$ Gauge Theories: We discuss the properties of quarter-BPS local operators in four dimensional
${\cal N}=1$ supersymmetric Yang-Mills theory using the formalism of
holomorphic twists. We study loop corrections both to the space of local
operators and to algebraic operations which endow the twisted theory with an
infinite symmetry algebra. We classify all single-trace quarter-BPS operators
in the planar approximation for $SU(N)$ gauge theory and propose a holographic
dual description for the twisted theory. We classify perturbative quarter-BPS
operators in $SU(2)$ and $SU(3)$ gauge theories with sufficiently small quantum
numbers and discuss possible non-perturbative corrections to the answer. We set
up analogous calculations for some theories with matter. | Hydrodynamic fluctuations and long-time tails in a fluid on an
anisotropic background: The effective low-energy late-time description of many body systems near
thermal equilibrium provided by classical hydrodynamics in terms of dissipative
transport phenomena receives important corrections once the effects of
stochastic fluctuations are taken into account. One such physical effect is the
occurrence of long-time power law tails in correlation functions of conserved
currents. In the hydrodynamic regime $\vec{k} \rightarrow 0$ this amounts to
non-analytic dependence of the correlation functions on the frequency $\omega$.
In this article, we consider a relativistic fluid with a conserved global
$U(1)$ charge in the presence of a strong background magnetic field, and
compute the long-time tails in correlation functions of the stress tensor. The
presence of the magnetic field renders the system anisotropic. In the absence
of the magnetic field, there are three out-of-equilibrium transport parameters
that arise at the first order in the hydrodynamic derivative expansion, all of
which are dissipative. In the presence of a background magnetic field, there
are ten independent out-of-equilibrium transport parameters at the first order,
three of which are non-dissipative and the rest are dissipative. We provide the
most general linearized equations about a given state of thermal equilibrium
involving the various transport parameters in the presence of a magnetic field,
and use them to compute the long-time tails for the fluid. |
Superstring loop amplitudes from the field theory limit: We propose a procedure to determine the moduli-space integrands of loop-level
superstring amplitudes for massless external states in terms of the field
theory limit. We focus on the type II superstring. The procedure is to: (i)
take a supergravity loop integrand written in a BCJ double-copy representation,
(ii) use the loop-level scattering equations to translate that integrand into
the ambitwistor string moduli-space integrand, localised on the nodal Riemann
sphere, and (iii) uplift that formula to one on the higher-genus surface valid
for the superstring, guided by modular invariance. We show how this works for
the four-point amplitude at two loops, where we reproduce the known answer, and
at three loops, where we present a conjecture that is consistent with a
previous proposal for the chiral measure. Useful supergravity results are
currently known up to five loops. | Crunches, Hats, and a Conjecture: Our purpose in this paper is to discuss criteria for the existence of a
precise dual description of a cosmology. A number of exact descriptions exist
for flat and anti de Sitter backgrounds and possibly for open FRW universes
that nucleate in an eternally inflating background. In addition duals have been
proposed for de Sitter space, and for crunching FRW bubbles with negative
cosmological constant. In the latter cases there is reason to think the
dualities are at best approximate. One of our primary purposes is to analyze
the quality of these descriptions, i.e., how exact they can be made.
Maldacena's recent discussion of dualities involving crunching FRW cosmologies
provides an opportunity for exploring some of these question. |
Branes wrapped on orbifolds and their gravitational blocks: We construct new supersymmetric $\mathrm{AdS}_2\times \mathbb{M}_4$ solutions
of $D=6$ gauged supergravity, where $\mathbb{M}_4$ are certain four-dimensional
orbifolds. After uplifting to massive type IIA supergravity these correspond to
the near-horizon limit of a system of $N$ D4-branes and $N_f$ D8-branes wrapped
on $\mathbb{M}_4$. In one class of solutions $\mathbb{M}_4 =
\Sigma_{\mathrm{g}}\ltimes\Sigma$ is a spindle fibred over a smooth Riemann
surface of genus $\mathrm{g}>1$, while in another class $\mathbb{M}_4 =
\Sigma\ltimes\Sigma$ is a spindle fibred over another spindle. Both classes can
be thought of as orbifold generalizations of Hirzebruch surfaces and, in the
second case, we describe the solutions in terms of toric geometry. We show that
the entropy associated with these solutions is reproduced by extremizing an
entropy function obtained by gluing gravitational blocks, using a general
recipe for orbifolds that we propose. We also discuss how our prescription can
be used to define an off-shell central charge whose extremization reproduces
the gravitational central charge of analogous $\mathrm{AdS}_3\times
\mathbb{M}_4$ solutions of $D=7$ gauged supergravity, arising from wrapping
M5-branes on $\mathbb{M}_4$. | Noncommutativity and the Aharonov-Bohm Effect: The possibility of detecting noncommutive space relics is analyzed by using
the Aharonov-Bohm effect. If space is non-commutative, it turns out that the
holonomy receives kinematical corrections that tend to diffuse the fringe
pattern. This fringe pattern has a non-trivial energy dependence and,
therefore, one could observe noncommutative effects by modifying the energy of
the incident electrons beam in the Tonomura experimental arrangement |
Possible alternative mechanism to SUSY: conservative extensions of the
Poincaré group: A group theoretical mechanism is outlined, which can indecomposably extend
the Poincar\'e group by the compact internal (gauge) symmetries at the price of
allowing some nilpotent (or, more precisely: solvable) internal symmetries in
addition. Due to the presence of this nilpotent part, the prohibitive argument
of the well known Coleman-Mandula and McGlinn no-go theorems do not go through.
In contrast to SUSY or extended SUSY, in our construction the symmetries
extending the Poincar\'e group will be all internal, i.e. they do not act on
the spacetime, merely on some internal degrees of freedom -- hence the name:
conservative extensions of the Poincar\'e group. Using the Levi decomposition
and O'Raifeartaigh theorem, the general structure of all possible conservative
extensions of the Poincar\'e group is outlined, and a concrete example group is
presented with U(1) being the compact gauge group component. It is argued that
such nilpotent internal symmetries may be inapparent symmetries of some more
fundamental field variables, and therefore do not carry an ab initio
contradiction with the present experimental understanding in particle physics.
The construction is compared to (extended) SUSY, since SUSY is somewhat
analogous to the proposed mechanism. It is pointed out, however, that the
proposed mechanism is less irregular in comparison to SUSY, in certain aspects.
The only exoticity needed in comparison to a traditional gauge theory setting
is that the full group of internal symmetries is not purely compact, but is a
semi-direct product of a nilpotent and of a compact part. | Relativistic Landau problem at finite temperature: We study the zero temperature Casimir energy and fermion number for Dirac
fields in a 2+1-dimensional Minkowski space-time, in the presence of a uniform
magnetic field perpendicular to the spatial manifold. Then, we go to the
finite-temperature problem with a chemical potential, introduced as a uniform
zero component of the gauge potential. By performing a Lorentz boost, we obtain
Hall's conductivity in the case of crossed electric and magnetic fields. |
The 2-Dimensional Quantum Euclidean Algebra: The algebra dual to Woronowicz's deformation of the 2-\-di\-men\-sion\-al
Euclidean group is constructed. The same algebra is obtained from $SU_{q}(2)$
via contraction on both the group and algebra levels. | A supersymmetric version of the quark model, and supersymmetry breaking
for the Leptons, Baryons and Hadronic Mesons: Cybersusy V: Cybersusy is a new mechanism for supersymmetry breaking in the standard
supersymmetric model (SSM). Here we note that the superpotential for the SSM
has a set of thirteen invariances, five of which are well known, and eight of
which are new. The eight new invariances generate a sort of supersymmetric
quark and lepton model, together with supersymmetry breaking that makes the
squarks and sleptons very heavy. This breaking regenerates the standard model
out of the supersymmetric standard model, except that the gauge particles are
not yet included in this reduction. In this paper, it is shown that, with some
continued effort, cybersusy will make some predictions for hadron masses that
may actually be wrong, so that it is a supersymmetry breaking theory that can
be proved wrong! This is the fifth paper in what was intended to be a series of
four papers on cybersusy. |
A covariant regulator for entanglement entropy: proofs of the Bekenstein
bound and QNEC: While von Neumann entropies for subregions in quantum field theory
universally contain ultraviolet divergences, differences between von Neumann
entropies are finite and well-defined in many physically relevant scenarios. We
demonstrate that such a notion of entropy differences can be rigorously defined
in quantum field theory in a general curved spacetime by introducing a novel,
covariant regulator for the entropy based on the modular crossed product. This
regulator associates a type II von Neumann algebra to each spacetime subregion,
resulting in well-defined renormalized entropies. This prescription reproduces
formulas for entropy differences that coincide with heuristic formulas widely
used in the literature, and we prove that it satisfies desirable properties
such as unitary invariance and concavity. As an application, we provide proofs
of the Bekenstein bound and the quantum null energy condition, formulated
directly in terms of vacuum-subtracted von Neumann entropies. | Strings on Calabi--Yau spaces and Toric Geometry: After a brief introduction into the use of Calabi--Yau varieties in string
dualities, and the role of toric geometry in that context, we review the
classification of toric Calabi-Yau hypersurfaces and present some results on
complete intersections. While no proof of the existence of a finite bound on
the Hodge numbers is known, all new data stay inside the familiar range
$h_{11}+h_{12}\le 502$. |
Holographic relationships in Lovelock type brane gravity: We show that the Lovelock type brane gravity is naturally holographic by
providing a correspondence between bulk and surface terms that appear in the
Lovelock-type brane gravity action functional. We prove the existence of
relationships between the $\mathcal{L}_{\mbox{\tiny bulk}}$ and
$\mathcal{L}_{\mbox{\tiny surf}}$ allowing $\mathcal{L}_{\mbox{\tiny surf}}$ to
be determined completely by $\mathcal{L}_{\mbox{\tiny bulk}}$. In the same
spirit, we provide relationships among the various conserved tensors that this
theory possesses. We further comment briefly on the correspondence between
geometric degrees of freedom in both bulk and surface space. | Colour-kinematics duality, double copy, and homotopy algebras: Colour-kinematics duality is a remarkable property of Yang-Mills theory. Its
validity implies a relation between gauge theory and gravity scattering
amplitudes, known as double copy. Albeit fully established at the tree level,
its extension to the loop level is conjectural. Lifting the on-shell,
scattering amplitudes-based description to the level of action functionals, we
argue that a theory that exhibits tree-level colour-kinematics duality can be
reformulated in a way such that its loop integrands manifest a generalised form
of colour-kinematics duality. Moreover, we show how the structures of higher
homotopy theory naturally describe this off-shell reformulation of
colour-kinematics duality. |
Gauge symmetry breaking in ten-dimensional Yang-Mills theory dynamically
compactified on S^6: We study fluctuation modes in ten-dimensional Yang-Mills theory with a higher
derivative term for the gauge field. We consider the ten-dimensional space-time
to be a product of a four-dimensional space-time and six-dimensional sphere
which exhibits dynamical compactification. Because of the isometry on S^6,
there are flat directions corresponding to the
Nambu-Goldstone zero modes in the effective theory on the solution. The zero
modes are absorbed into gauge fields and form massive vector fields as a
consequence of the Higgs-Kibble mechanism. The mass of the vector fields is
proportional to the inverse of the radius of the sphere and larger than the
mass scale set by the radius because of the higher derivative term. | On the equivalence between Starobinsky and Higgs inflationary models in
gravity and supergravity: Starobinsky inflation and Higgs inflation in gravity, and their equivalence
based on the common inflationary potential are extended to supergravity in the
proper framework, where the Starobinsky and Higgs descriptions of inflation
arise in two different gauges of the same supergravity model. |
Doubled Geometry and T-Folds: The doubled formulation of string theory, which is T-duality covariant and
enlarges spacetime with extra coordinates conjugate to winding number, is
reformulated and its geometric and topological features examined. It is used to
formulate string theory in T-fold backgrounds with T-duality transition
functions and a quantum implementation of the constraints of the doubled
formalism is presented. This establishes the quantum equivalence to the usual
sigma-model formalism for world-sheets of arbitrary genus, provided a
topological term is added to the action. The quantisation involves a local
choice of polarisation, but the results are independent of this. The natural
dilaton of the doubled formalism is duality-invariant and so T-duality is a
perturbative symmetry for the perturbation theory in the corresponding coupling
constant. It is shown how this dilaton is related to the dilaton of the
conventional sigma-model which does transform under T-duality. The
generalisation of the doubled formalism to the superstring is given and shown
to be equivalent to the usual formulation. Finally, the formalism is
generalised to one in which the whole spacetime is doubled. | Four-dimensional gravity on supersymmetric dilatonic domain walls: We investigate the localization of four-dimensional metastable gravity in
supersymmetric dilatonic domain walls through massive modes by considering
several scenarios in the model. We compute corrections to the Newtonian
potential for small and long distances compared with a crossover scale given in
terms of the dilatonic coupling. 4D gravity behavior is developed on the brane
for distance very much below the crossover scale, while for distance much
larger, the 5D gravity is recovered. Whereas in the former regime gravity is
always attractive, in the latter regime due to non-normalizable unstable
massive graviton modes present on the spectrum, in some special cases, gravity
appears to be repulsive and signalizes a gravitational confining phase which is
able to produce an inflationary phase of the Universe. |
Conformal Foliations and Constraint Quantization: We show that the Classical Constraint Algebra of a Parametrized Relativistic
Gauge System induces a natural structure of Conformal Foliation on a
Transversal Gauge. Using the theory of Conformal Foliations, we provide a
natural Factor Ordering for the Quantum Operators associated to the Canonical
Quantization of such Gauge System. | Anomalous dimensions of twist 2 operators and $\mathcal{N}=4$ SYM
quantum spectral curve: We present algorithmic perturbative solution of $\mathcal{N}=4$ SYM quantum
spectral curve in the case of twist 2 operators, valid to in principle
arbitrary order in coupling constant. The latter treats operator spins as
arbitrary integer values and is written in terms of special class of functions
-- products of rational functions in spectral parameter with sums of Baxter
polynomials and Hurwitz functions. It is shown that this class of functions is
closed under elementary operations, such as shifts, partial fractions,
multiplication by spectral parameter and differentiation. Also, it is fully
sufficient to solve arising non-homogeneous multiloop Baxter and first order
difference equations. As an application of the proposed method we present the
computation of anomalous dimensions of twist 2 operators up to four loop order. |
Dark Radiation Dynamics on the Brane: We investigate the dynamics of a spherically symmetric vaccum on a Randall
and Sundrum 3-brane world. Under certain natural conditions, the effective
Einstein equations on the brane form a closed system for spherically symmetric
dark radiation. We determine exact dynamical and inhomogeneous solutions, which
are shown to depend on the brane cosmological constant, on the dark radiation
tidal charge and on its initial energy configuration. We identify the
conditions defining these solutions as singular or as globally regular.
Finally, we discuss the confinement of gravity to the vicinity of the brane and
show that a phase transition to a regime where gravity is not bound to the
brane may occur at short distances during the collapse of positive dark energy
density on a realistic de Sitter brane. | Screening fifth forces in k-essence and DBI models: New fifth forces have not yet been detected in the laboratory or in the solar
system, hence it is typically difficult to introduce new light scalar fields
that would mediate such forces. In recent years it has been shown that a number
of non-linear scalar field theories allow for a dynamical mechanism, such as
the Vainshtein and chameleon ones, that suppresses the strength of the scalar
fifth force in experimental environments. This is known as screening, however
it is unclear how common screening is within non-linear scalar field theories.
k-essence models are commonly studied examples of non-linear models, with DBI
as the best motivated example, and so we ask whether these non-linearities are
able to screen a scalar fifth force. We find that a Vainshtein-like screening
mechanism exists for such models although with limited applicability. For
instance, we cannot find a screening mechanism for DBI models. On the other
hand, we construct a large class of k-essence models which lead to the
acceleration of the Universe in the recent past for which the fifth force
mediated by the scalar can be screened. |
Microscopic Spectrum of the QCD Dirac Operator in Three Dimensions: The microscopic spectral correlators of the Dirac operator in
three-dimensional Yang-Mills theory coupled to fundamental fermions and with
three or more colours are derived from the supersymmetric formulation of
partially quenched effective Lagrangians. The flavour supersymmetry breaking
patterns are appropriately identified and used to calculate the corresponding
finite volume partition functions from Itzykson-Zuber type integrals over
supersymmetric cosets. New and simple determinant expressions for the spectral
correlators in the mesoscopic scaling region are thereby found. The microscopic
spectrum derived from the effective finite volume partition function of
three-dimensional QCD agrees with earlier results based on the unitary ensemble
of random matrix theory and extends the corresponding calculations for QCD in
four dimensions. | Different realizations of kappa-momentum space and relative-locality
effect: We consider different realizations for the momentum sector of kappa-Poincare
Hopf algebra, which is associated with a curved momentum space. We show that
the notion of the particle mass as introduced recently by Amelino-Camelia et
al. in the context of relative-locality is realization independent for a wide
class of realizations, up to linear order in deformation parameter l. On the
other hand, the time delay formula clearly shows a dependence on the choice of
realization. |
On Graviton non-Gaussianities in the Effective Field Theory of Inflation: We derive parity-even graviton bispectra in the Effective Field Theory of
Inflation (EFToI) to all orders in derivatives. Working in perturbation theory,
we construct all cubic interactions that can contribute to tree-level graviton
bispectra, showing that they all come from EFToI operators containing two or
three powers of the extrinsic curvature and its covariant derivatives: all
other operators can be removed by field redefinitions or start at higher-order
in perturbations. For operators cubic in the extrinsic curvature, where the
single-clock consistency relations are satisfied without a correction to the
graviton two-point function, we use the Manifestly Local Test (MLT) to
efficiently extract the effects of evolving graviton fluctuations to the end of
inflation. Despite the somewhat complicated nature of the bulk interactions,
the final boundary correlators take a very compact form. For operators
quadratic in the extrinsic curvature, the leading order bispectra are a sum of
contact and single exchange diagrams, which are tied together by spatial
diffeomorphisms, and to all orders in derivatives we derive these bispectra by
computing the necessary bulk time integrals. For single exchange diagrams we
exploit factorisation properties of the bulk-bulk propagator for massless
gravitons and write the result as a finite sum over residues. Perhaps
surprisingly, we show these single exchange contributions have only
total-energy poles and also satisfy the MLT. | Induced Magnetic Field in a Finite Fermion Density Maxwell QED$_{2+1}$: We are studying finite fermion density states in Maxwell QED$_{2+1}$ with
external magnetic field. It is shown that at any fermion density the energy of
some magnetized states may be less than that of the state with the same
density, but no magnetic field. Magnetized states are described by the
effective Maxwell-Chern-Simons QED$_{2+1}$ Lagrangian with gauge field mass
proportional to the number of filled Landau levels. |
Cosmological Breaking of Supersymmetry?: It is conjectured that M-theory in asymptotically flat spacetime must be
supersymmetric, and that the observed SUSY breaking in the low energy world
must be attributed to the existence of a nonzero cosmological constant. This
would be consistent with experiment, if the {\it critical exponent} $\alpha$ in
the relation $M_{SUSY} \sim M_P (\Lambda /M_P^4)^{\alpha}$ took on the value
1/8, rather than its classical value 1/4. We attribute this large
renormalization to the effect of large virtual black holes via the UV/IR
correspondence. | Nonlocal Electrodynamics of Rotating Systems: The nonlocal electrodynamics of uniformly rotating systems is presented and
its predictions are discussed. In this case, due to paucity of experimental
data, the nonlocal theory cannot be directly confronted with observation at
present. The approach adopted here is therefore based on the correspondence
principle: the nonrelativistic quantum physics of electrons in circular
"orbits" is studied. The helicity dependence of the photoeffect from the
circular states of atomic hydrogen is explored as well as the resonant
absorption of a photon by an electron in a circular "orbit" about a uniform
magnetic field. Qualitative agreement of the predictions of the classical
nonlocal electrodynamics with quantum-mechanical results is demonstrated in the
correspondence regime. |
Symmetric Vacua in Heterotic M-Theory: Symmetric vacua of heterotic M-theory, characterized by vanishing cohomology
classes of individual sources in the three-form Bianchi identity, are analyzed
on smooth Calabi-Yau three-folds. We show that such vacua do not exist for
elliptically fibered Calabi-Yau spaces. However, explicit examples are found
for Calabi-Yau three-folds arising as intersections in both unweighted and
weighted projective space. We show that such symmetric vacua can be combined
with attractive phenomenological features such as three generations of quarks
and leptons. Properties of the low energy effective actions associated with
symmetric vacua are discussed. In particular, the gauge kinetic functions
receive no perturbative threshold corrections, there are no corrections to the
matter field Kahler metric and the associated five-dimensional effective theory
admits flat space as its vacuum. | A Brief Summary Of Global Anomaly Cancellation In Six-Dimensional
Supergravity: This is a short summary of a talk at Strings 2018. See also arXiv:1808.01334. |
Branes, quivers and wave-functions: We consider a large class of branes in toric strip geometries, both
non-periodic and periodic ones. For a fixed background geometry we show that
partition functions for such branes can be reinterpreted, on one hand, as
quiver generating series, and on the other hand as wave-functions in various
polarizations. We determine operations on quivers, as well as
$SL(2,\mathbb{Z})$ transformations, which correspond to changing positions of
these branes. Our results prove integrality of BPS multiplicities associated to
this class of branes, reveal how they transform under changes of polarization,
and imply all other properties of brane amplitudes that follow from the
relation to quivers. | Once again about quantum deformations of D=4 Lorentz algebra: twistings
of q-deformation: This paper together with the previous one (arXiv:hep-th/0604146) presents the
detailed description of all quantum deformations of D=4 Lorentz algebra as Hopf
algebra in terms of complex and real generators. We describe here in detail two
quantum deformations of the D=4 Lorentz algebra o(3,1) obtained by twisting of
the standard q-deformation U_{q}(o(3,1)). For the first twisted q-deformation
an Abelian twist depending on Cartan generators of o(3,1) is used. The second
example of twisting provides a quantum deformation of Cremmer-Gervais type for
the Lorentz algebra. For completeness we describe also twisting of the Lorentz
algebra by standard Jordanian twist. By twist quantization techniques we obtain
for these deformations new explicit formulae for the deformed coproducts and
antipodes of the o(3,1)-generators. |
The boundary dual of the bulk symplectic form: In this paper, we study the overlaps of wavefunctionals prepared by turning
on sources in the Euclidean path integral. For nearby states, these overlaps
give rise to a Kahler structure on the space of sources, which is naturally
induced by the Fubini-Study metric. The Kahler form obtained this way can also
be thought of as a Berry curvature and, for holographic field theories, we show
that it is identical to the gravitational symplectic form in the bulk. We
discuss some possible applications of this observation, in particular a
boundary prescription to calculate the variation of the volume of a maximal
slice. | The evolution of conifolds: We simulate the gravitational dynamics of the conifold geometries (resolved
and deformed) involved in the description of certain compact spacetimes. As the
cycles of the conifold collapse towards a singular geometry we find that a
horizon develops, shielding the external spacetime from the curvature
singularity of the newly formed black hole. The structure of the black hole is
examined for a range of initial conditions, and we find a candidate black-hole
solution for the final state of the collapse. |
The vacuum as a Lagrangian subspace: We unify and generalize the notions of vacuum and amplitude in linear quantum
field theory in curved spacetime. Crucially, the generalized notion admits a
localization in spacetime regions and on hypersurfaces. The underlying concept
is that of a Lagrangian subspace of the space of complexified germs of
solutions of the equations of motion on hypersurfaces. Traditional vacua and
traditional amplitudes correspond to the special cases of definite and real
Lagrangian subspaces respectively. Further, we introduce both infinitesimal and
asymptotic methods for vacuum selection that involve a localized version of
Wick rotation. We provide examples from Klein-Gordon theory in settings
involving different types of regions and hypersurfaces to showcase generalized
vacua and the application of the proposed vacuum selection methods. A recurrent
theme is the occurrence of mixed vacua, where propagating solutions yield
definite Lagrangian subspaces and evanescent solutions yield real Lagrangian
subspaces. The examples cover Minkowski space, Rindler space, Euclidean space
and de Sitter space. A simple formula allows for the calculation of expectation
values for observables in the generalized vacua. | Toward a Nonlocal Theory of Gravitation: The nonlocal theory of accelerated systems is extended to linear
gravitational waves as measured by accelerated observers in Minkowski
spacetime. The implications of this approach are discussed. In particular, the
nonlocal modifications of helicity-rotation coupling are pointed out and a
nonlocal wave equation is presented for a special class of uniformly rotating
observers. The results of this study, via Einstein's heuristic principle of
equivalence, provide the incentive for a nonlocal classical theory of the
gravitational field. |
Symmetries of fundamental interactions in quantum phase space: Quantum operators of coordinates and momentum components of a particle in
Minkowski space-time belong to a noncommutative algebra and give rise to a
quantum phase space. Under some constraints, in particular, the Lorentz
invariance condition, the algebra of observables, including Lorentz group
generators, depends on additional fundamental physical constants with the
dimensions of mass, length and action. Generalized symmetries in a quantum
phase space and some consequences for fundamental interactions of particles are
considered. | Imprints of phase transitions on Kasner singularities: Under the AdS/CFT correspondence, asymptotically AdS geometries with
backreaction can be viewed as CFT states subject to a renormalization group
(RG) flow from an ultraviolet (UV) description towards an infrared (IR) sector.
For black holes however, the IR point is the horizon, so one way to interpret
the interior is as an analytic continuation to a "trans-IR" imaginary-energy
regime. In this paper, we demonstrate that this analytic continuation preserves
some imprints of the UV physics, particularly near its "endpoint" at the
classical singularity. We focus on holographic phase transitions of geometric
objects in round black holes. We first assert the consistency of interpreting
such black holes, including their interiors, as RG flows by constructing a
monotonic $a$-function. We then explore how UV phase transitions of
entanglement entropy and scalar two-point functions, each of which are encoded
by bulk geometry under the holographic mapping, are connected to the structure
of the near-singularity geometry, which is characterized by Kasner exponents.
Using 2d holographic flows triggered by relevant scalar deformations as test
beds, we find that the 3d bulk's near-singularity Kasner exponents can be
viewed as functions of the UV physics precisely when the deformation is
nonzero. |
Gauge Symmetries on $θ$-Deformed Spaces: A Hamiltonian formulation of gauge symmetries on noncommutative ($\theta$
deformed) spaces is discussed. Both cases- star deformed gauge transformation
with normal coproduct and undeformed gauge transformation with twisted
coproduct- are considered. While the structure of the gauge generator is
identical in either case, there is a difference in the computation of the
graded Poisson brackets that yield the gauge transformations. Our analysis
provides a novel interpretation of the twisted coproduct for gauge
transformations. | Konishi Anomalies and N=1 Curves: We present a brief summary of exact results on the non-perturbative effective
superpotential of N=1 supersymmetric gauge theories based on generalized
Konishi anomaly equations. In particular we consider theories with classical
gauge groups and chiral matter in two-index tensor representations. All these
theories can be embedded into theories with unitary gauge group and adjoint
matter. This embedding can be used to derive expressions for the exact
non-perturbative superpotential in terms of the 1/N expansion of the free
energy of the related matrix models. |
Phase Transition in (2+1)d Quantum Gravity: (2+1) dimensional gravity is equivalent to an exactly soluble non-Abelian
Chern-Simons gauge field theory (E Witten 1988). Regarding this as the
topological phase of quantum gravity in (2+1)d, we suggest a topological
symmetry breaking by introducing a mass term for the gauge fields, which
carries a space-time metric and local dynamical degrees of freedom. We consider
the finite temperature behavior of the symmetry broken phase, and claim a
restoration of the topological invariance at some critical temperature. The
phase transition is shown of the zeroth order. | Gauged AdS-Maxwell algebra and gravity: We deform the anti-de Sitter algebra by adding additional generators
$\mathcal{Z}_{ab}$, forming in this way the negative cosmological constant
counterpart of the Maxwell algebra. We gauge this algebra and construct a
dynamical model with the help of a constrained the BF theory. It turns out that
the resulting theory is described by the Einstein-Cartan action with Holst
term, and the gauge fields associated with the Maxwell generators
$\mathcal{Z}_{ab}$ appear only in topological terms that do not influence
dynamical field equations. We briefly comment on the extension of this
construction, which would lead to a nontrivial Maxwell fields dynamics. |
Integrable structure in supersymmetric gauge theories with massive
hypermultiplets: We study the quantum moduli space of vacua of $N=2$ supersymmetric $SU(N_c)$
gauge theories coupled to $N_f$ flavors of quarks in the fundamental
representation. We identify the moduli space of the $N_c = 3$ and $N_f=2$
massless case with the full spectral curve obtained from the Lax representation
of the Goryachev-Chaplygin top. For the case with {\it massive} quarks, we
present an integrable system where the corresponding hyperelliptic curve
parametrizing the Laurent solution coincides with that of the moduli space of
$N_{c}=3$ with $N_{f}=0, 1, 2$. We discuss possible generalizations of the
integrable systems relevant to gauge theories with $N_c \neq 3 $ and general
$N_f$. | The effect of dark strings on semilocal strings: Dark strings have recently been suggested to exist in new models of dark
matter that explain the excessive electronic production in the galaxy. We study
the interaction of these dark strings with semilocal strings which are
solutions of the bosonic sector of the Standard Model in the limit
$\sin^2\theta_{\rm w}=1$, where $\theta_{\rm w}$ is the Weinberg angle. While
embedded Abelian-Higgs strings exist for generic values of the coupling
constants, we show that semilocal solutions with non-vanishing condensate
inside the string core exist only above a critical value of the Higgs to gauge
boson mass ratio when interacting with dark strings. Above this critical value,
which is greater than unity, the energy per unit length of the semilocal-dark
string solutions is always smaller than that of the embedded Abelian-Higgs-dark
string solutions and we show that Abelian-Higgs-dark strings become unstable
above this critical value. Different from the non-interacting case, we would
thus expect semilocal strings to be stable for values of the Higgs to gauge
boson mass ratio larger than unity. Moreover, the one-parameter family of
solutions present in the non-interacting case ceases to exist when semilocal
strings interact with dark strings. |
Euler numbers of four-dimensional rotating black holes with the
Euclidean signature: For a black hole's spacetime manifold in the Euclidean signature, its metric
is positive definite and therefore a Riemannian manifold. It can be regarded as
a gravitational instanton and a topological characteristic which is the Euler
number is associated. In this paper we derive a formula for the Euler numbers
of four-dimensional rotating black holes by the integral of the Euler density
on the spacetime manifolds of black holes. Using this formula, we obtain that
the Euler numbers of Kerr and Kerr-Newman black holes are 2. We also obtain
that the Euler number of the Kerr-Sen metric in the heterotic string theory
with one boost angle nonzero is 2 that is in accordence with its topology. | M-theory on Elliptic Calabi-Yau Threefolds and 6d Anomalies: We consider the 8-supercharge 5d su(N) gauge theories from M-theory
compactified on elliptic Calabi-Yau threefolds. By matching the triple
intersection numbers in the elliptic Calabi-Yau with the 5d Chern-Simons
levels, we determine the charged matter contents for these theories. We show
that all these 5d theories can be lifted to 6d N = (1, 0) theories while
satisfying the anomaly cancellation equations. This suggests that the 5d
theories obtained from M-theory compactified on elliptic Calabi-Yau threefolds
have a natural 12d description, which as we know is F-theory. Furthermore, we
compute the Euler characteristics of the elliptic Calabi-Yau threefolds. |
Effects related to spacetime foam in particle physics: It is found that the existence of spacetime foam leads to a situation in
which the number of fundamental quantum bosonic fields is a variable quantity.
The general aspects of an exact theory that allows for a variable number of
fields are discussed, and the simplest observable effects generated by the foam
are estimated. It is shown that in the absence of processes related to
variations in the topology of space, the concept of an effective field can be
reintroduced and standard field theory can be restored. However, in the
complete theory the ground state is characterized by a nonvanishing particle
number density. From the effective-field standpoint, such particles are "dark".
It is assumed that they comprise dark matter of the universe. The properties of
this dark matter are discussed, and so is the possibility of measuring the
quantum fluctuation in the field potentials. | The Bekenstein Bound: Bekenstein's conjectured entropy bound for a system of linear size $R$ and
energy $E$, namely $S \leq 2 \pi E R$, has counterexamples for many of the ways
in which the "system," $R$, $E$, and $S$ may be defined. One consistent set of
definitions for these quantities in flat Minkowski spacetime is that $S$ is the
total von Neumann entropy and $E$ is the expectation value of the energy in a
"vacuum-outside-$R$" quantum state that has the the vacuum expectation values
for all operators entirely outside a sphere of radius $R$. However, there are
counterexamples to the Bekenstein bound for this set of definitions.
Nevertheless, an alternative formulation ten years ago by Horacio Casini for
the definitions of $S$ and of $2 \pi E R$ have finally enabled a proof for this
particular formulation of the Bekenstein bound. |
Dirac electron in a Coulomb Field in 2+1 Dimensions: Exact solutions of Dirac equation in two spatial dimensions in the Coulomb
field are obtained. Equation which determines the so-called critical charge of
the Coulomb field is derived and solved for a simple model. | Physics of crypto-Hermitian and/or cryptosupersymmetric field theories: We discuss non-Hermitian field theories where the spectrum of the Hamiltonian
involves only real energies. We make three observations. (i) The theories
obtained from supersymmetric theories by nonanticommutative deformations belong
in many cases to this class. (ii) When the deformation parameter is small, the
deformed theory enjoys the same supersymmetry algebra as the undeformed one.
Half of the supersymmetries are manifest and the existence of another half can
be deduced from the structure of the spectrum. (iii) Generically, the
conventionally defined S--matrix is not unitary for such theories. |
Higher-derivative N=4 superparticle in three-dimensional spacetime: Using the coset approach (nonlinear realization) we construct component
actions for a superparticle in three-dimensional spacetime with N=4
supersymmetry partially broken to N=2. These actions may contain an anyonic
term and the square of the first extrinsic worldline curvature. We present the
supercharges for the unbroken and broken supersymmetries as well as the
Hamiltonian for the supersymmetric anyon. In terms of the nonlinear realization
superfields, the superspace actions take a simple form in all cases. | Perturbed N=(2,2) supersymmetric sigma models on Lie groups: We perturbed N=(2,2) supersymmetric WZW and sigma models on Lie groups by
adding a term to their actions. Then by using non-coordinate basis we obtain
conditions, from the algebraic point of view, under which the N=(2,2)
supersymmetry is preserved. By applying this method, we have obtained
conditions on the existence of N=(2,2) supersymmetry on the Drinfeld action
(master action for the Poisson-Lie T-dual sigma models). |
Sphalerons and resonance phenomenon in kink-antikink collisions: We show that in some kink-antikink (KAK) collisions sphalerons, i.e.,
unstable static solutions - rather than the asymptotic free soliton states -
can be the source of the internal degrees of freedom (normal modes) which
trigger the resonance phenomenon responsible for the fractal structure in the
final state formation. | Probability Distributions for Space and Time Averaged Quantum Stress
Tensors: We extend previous work on quantum stress tensor operators which have been
averaged over finite time intervals to include averaging over finite regions of
space as well. The space and time averaging can be viewed as describing a
measurement process for a stress tensor component, such as the energy density
of a quantized field in its vacuum state. Although spatial averaging reduces
the probability of large vacuum fluctuations compared to time averaging alone,
we find that the probability distribution decreases more slowly than
exponentially as the magnitude of the measured energy density increases. This
implies that vacuum fluctuations can sometimes dominate over thermal
fluctuations and potentially have observable effects. |
Holography, Fractionalization and Magnetic Fields: Four dimensional gravity with a U(1) gauge field, coupled to various fields
in asymptotically anti-de Sitter spacetime, provides a rich arena for the
holographic study of the strongly coupled (2+1)-dimensional dynamics of finite
density matter charged under a global U(1). As a first step in furthering the
study of the properties of fractionalized and partially fractionalized degrees
of freedom in the strongly coupled theory, we construct electron star solutions
at zero temperature in the presence of a background magnetic field. We work in
Einstein-Maxwell-dilaton theory. In all cases we construct, the magnetic source
is cloaked by an event horizon. A key ingredient of our solutions is our
observation that starting with the standard Landau level structure for the
density of states, the electron star limits reduce the charge density and
energy density to that of the free fermion result. Using this result we
construct three types of solution: One has a star in the infra-red with an
electrically neutral horizon, another has a star that begins at an electrically
charged event horizon, and another has the star begin a finite distance from an
electrically charged horizon. | Exact operator Hamiltonians and interactions in the droplet bosonization
method: We derive the exact form of the bosonized Hamiltonian for a many-body fermion
system in one spatial dimension with arbitrary dispersion relations, using the
droplet bosonization method. For a single-particle Hamiltonian polynomial in
the momentum, the bosonized Hamiltonian is a polynomial of one degree higher in
the bosonic "boundary" field and includes subleading lower-order and derivative
terms. This generalizes the known results for massless relativistic and
nonrelativistic fermions (quadratic and cubic bosonic Hamiltonians,
respectively). We also consider two-body interactions and demonstrate that they
lead to interesting collective behavior and phase transitions in the Fermi sea. |
On Duality in the Born-Infeld Theory: The $SL(2,R)$ duality symmetric action for the Born-Infeld theory in terms of
two potentials, coupled with non-trivial backgroud fields in four dimensions is
established. This construction is carried out in detail by analysing the
hamiltonian structure of the Born-Infeld theory. The equivalence with the usual
Born-Infeld theory is shown. | Multi-matrix models without continuum limit: We derive the discrete linear systems associated to multi--matrix models, the
corresponding discrete hierarchies and the appropriate coupling conditions. We
also obtain the $W_{1+\infty}$ constraints on the partition function. We then
apply to multi--matrix models the technique, developed in previous papers, of
extracting hierarchies of differential equations from lattice ones without
passing through a continuum limit. In a q--matrix model we find 2q coupled
differential systems. The corresponding differential hierarchies are particular
versions of the KP hierarchy. We show that the multi--matrix partition function
is a $\tau$--function of these hierarchies. We discuss a few examples in the
dispersionless limit. |
Comment on Operator Algebra in Chern-Simons Theory on a Torus: It is shown that "nonintegrable phases of Wilson line integrals" are not true
dynamical variables in Chern-Simons field theory. | Tachyonic Instability and Dynamics of Spontaneous Symmetry Breaking: Spontaneous symmetry breaking usually occurs due to the tachyonic (spinodal)
instability of a scalar field near the top of its effective potential at $\phi
= 0$. Naively, one might expect the field $\phi$ to fall from the top of the
effective potential and then experience a long stage of oscillations with
amplitude O(v) near the minimum of the effective potential at $\phi = v$ until
it gives its energy to particles produced during these oscillations. However,
it was recently found that the tachyonic instability rapidly converts most of
the potential energy V(0) into the energy of colliding classical waves of the
scalar field. This conversion, which was called "tachyonic preheating," is so
efficient that symmetry breaking typically completes within a single
oscillation of the field distribution as it rolls towards the minimum of its
effective potential. In this paper we give a detailed description of tachyonic
preheating and show that the dynamics of this process crucially depend on the
shape of the effective potential near its maximum. In the simplest models where
$V(\phi) \sim -m^2\phi^2$ near the maximum, the process occurs solely due to
the tachyonic instability, whereas in the theories $-\lambda\phi^n$ with n > 2
one encounters a combination of the effects of tunneling, tachyonic instability
and bubble wall collisions. |
Bootstrapping pentagon functions: In PRL 116 (2016) no.6, 062001, the space of planar pentagon functions that
describes all two-loop on-shell five-particle scattering amplitudes was
introduced. In the present paper we present a natural extension of this space
to non-planar pentagon functions. This provides the basis for our pentagon
bootstrap program. We classify the relevant functions up to weight four, which
is relevant for two-loop scattering amplitudes. We constrain the first entry of
the symbol of the functions using information on branch cuts. Drawing on an
analogy from the planar case, we introduce a conjectural second-entry condition
on the symbol. We then show that the information on the function space, when
complemented with some additional insights, can be used to efficiently
bootstrap individual Feynman integrals. The extra information is read off of
Mellin-Barnes representations of the integrals, either by evaluating simple
asymptotic limits, or by taking discontinuities in the kinematic variables. We
use this method to evaluate the symbols of two non-trivial non-planar
five-particle integrals, up to and including the finite part. | Supersymmetry from a braided point of view: We show that one-dimensional superspace is isomorphic to a non-trivial but
consistent limit as $q\to-1$ of the braided line. Supersymmetry is identified
as translational invariance along this line. The supertranslation generator and
covariant derivative are obtained in the limit in question as the left and
right derivatives of the calculus on the braided line. |
Fermion Localization and Resonances on A de Sitter Thick Brane: In arXiv:0901.3543, the simplest Yukawa coupling $\eta\bar{\Psi}\phi\chi\Psi$
was considered for a two-scalar-generated Bloch brane model. Fermionic
resonances for both chiralities were obtained, and their appearance is related
to branes with internal structure. Inspired on this result, we investigate the
localization and resonance spectrum of fermions on a one-scalar-generated $dS$
thick brane with a class of scalar-fermion couplings $\eta\bar{\Psi}\phi^k\Psi$
with positive odd integer $k$. A set of massive fermionic resonances for both
chiralities are obtained when provided large couple constant $\eta$. We find
that the masses and life-times of left and right chiral resonances are almost
the same, which demonstrates that it is possible to compose massive Dirac
fermions from the left and right chiral resonances. The resonance with lower
mass has longer life-time. For a same set of parameters, the number of
resonances increases with $k$ and the life-time of the lower level resonance
for larger $k$ is much longer than the one for smaller $k$. | 6D thick branes from interacting scalar fields: A thick brane in six dimensions is constructed using two scalar fields. The
field equations for 6D gravity plus the scalar fields are solved numerically.
This thick brane solution shares some features with a previously studied
analytic solutions, but has the advantage that the energy-momentum tensor which
forms the thick brane comes from the scalar fields rather than being put in by
hand. Additionally the scalar fields which form the brane also provide a
universal, non-gravitational trapping mechanism for test fields of various
spins. |
Facts of life with gamma(5): The increasing precision of many experiments in elementary particle physics
leads to continuing interest in perturbative higher order calculations in the
electroweak Standard Model or extensions of it. Such calculations are of
increasing complexity because more loops and/or more legs are considered.
Correspondingly efficient computational methods are mandatory for many
calculations. One problem which affects the feasibility of higher order
calculations is the problem with gamma(5) in dimensional regularization. Since
the subject thirty years after its invention is still controversial I advocate
here some ideas which seem not to be common knowledge but might shed some new
light on the problem. I present arguments in favor of utilizing an
anticommuting gamma(5) and a simple 4-dimensional treatment of the hard
anomalies. | Ghost conditions for Gauss-Bonnet cosmologies: We investigate the stability against inhomogeneous perturbations and the
appearance of ghost modes in Gauss-Bonnet gravitational theories with a
non-minimally coupled scalar field, which can be regarded as either the dilaton
or a compactification modulus in the context of string theory. Through
cosmological linear perturbations we extract four no-ghost and two sub-luminal
constraint equations, written in terms of background quantities, which must be
satisfied for consistency. We also argue that, for a general action with
quadratic Riemann invariants, homogeneous and inhomogeneous perturbations are,
in general, inequivalent, and that attractors in the phase space can have
ghosts. These results are then generalized to a two-field configuration.
Single-field models as candidates for dark energy are explored numerically and
severe bounds on the parameter space of initial conditions are placed. A number
of cases proposed in the literature are tested and most of them are found to be
unstable or observationally unviable. |
Multibrane Inflation and Dynamical Flattening of the Inflaton Potential: We investigate the problem of fine tuning of the potential in the KKLMMT
warped flux compactification scenario for brane-antibrane inflation in Type IIB
string theory. We argue for the importance of an additional parameter psi_0
(approximated as zero by KKLMMT), namely the position of the antibrane,
relative to the equilibrium position of the brane in the absence of the
antibrane. We show that for a range of values of a particular combination of
the Kahler modulus, warp factor, and psi_0, the inflaton potential can be
sufficiently flat. We point out a novel mechanism for dynamically achieving
flatness within this part of parameter space: the presence of multiple mobile
branes can lead to a potential which initially has a metastable local minimum,
but gradually becomes flat as some of the branes tunnel out. Eventually the
local minimum disappears and the remaining branes slowly roll together, with
assisted inflation further enhancing the effective flatness of the potential.
With the addition of Kahler and superpotential corrections, this mechanism can
completely remove the fine tuning problem of brane inflation, within large
regions of parameter space. The model can be falsified if future cosmic
microwave background observations confirm the hint of a large running spectral
index. | Effective Lagrangian for 3d N=4 SYM theories for any gauge group and
monopole moduli spaces: We construct low energy effective Lagrangians for 3d N=4 supersymmetric
Yang-Mills theory with any gauge group. They represent supersymmetric sigma
models at hyper-Kahlerian manifolds of dimension 4r (r is the rang of the
group). In the asymptotic region, perturbatively exact explicit expression for
the metric are written. We establish the relationship of this metric with the
TAUB-NUT metric describing the perturbatively exact effective Lagrangians for
unitary groups and monopole moduli spaces: the former is obtained out of the
latter by a proper hyper-Kahlerian reduction. We describe in details the
reduction procedure for SO/Sp/G_2 gauge groups, where it can also be given a
natural interpretation in D-brane language. We conjecture that the exact
nonperturbative metrics can be obtained by a similar hyper-Kahlerian reduction
from the corresponding multidimensional Atiyah-Hitchin metrics. |
Effects of wave propagation in canonical Poisson gauge theory under an
external magnetic field: The non-commutative electrodynamics based on the canonical Poisson gauge
theory is studied in this paper. For a pure spatial non-commutativity, we
investigate the plane wave solutions in the presence of a constant and uniform
magnetic background field for the classical electrodynamics in canonical
Poisson gauge theory. We obtain the properties of the medium ruled by the
permittivity and the permeability tensors in terms of the non-commutative
parameter, with the electrodynamics equations in the momentum space. Using the
plane wave solutions mentioned, the dispersion relations are modified by the
magnetic background, and the correspondent group velocity is affected by the
spatial non-commutative parameter. We construct the energy-momentum tensor and
discuss the conserved components of this tensor in the spatial non-commutative
case. The birefringence phenomenon is showed through the modified dispersion
relations, that depends directly on the non-commutative corrections and also on
the magnetic background field. Using the bound of the polarized vacuum with
laser (PVLAS) experiment for the vacuum magnetic birefringence, we estimate a
theoretical value for the spatial non-commutative parameter. | Colliding Waves on a Brane, the Big Bounce and Reconnection: We present a time-dependent solution of the Nambu-Goto action which
represents two colliding waves moving at the speed of light. This solution can
be decomposed into two distinct regions with different geometries corresponding
to shrinking or expanding brane universe and two colliding branes. The former
describes the Big Bounce without singularity while the latter describes that
two branes collide and reconnect to each other. The colliding brane region has
a signature change. Classical dynamics of a massive particle on the brane is
studied through the geodesics. |
Black hole entropy and thermodynamics from symmetries: Given a boundary of spacetime preserved by a Diff(S^{1}) sub-algebra, we
propose a systematic method to compute the zero mode and the central extension
of the associated Virasoro algebra of charges. Using these values in the Cardy
formula, we may derive an associated statistical entropy to be compared with
the Bekenstein-Hawking result.
To illustrate our method, we study in detail the BTZ and the rotating
Kerr-adS_{4} black holes (at spatial infinity and on the horizon). In both
cases, we are able to reproduce the area law with the correct factor of 1/4 for
the entropy. We also recover within our framework the first law of black hole
thermodynamics.
We compare our results with the analogous derivations proposed by Carlip and
others. Although similar, our method differs in the computation of the zero
mode. In particular, the normalization of the ground state is automatically
fixed by our construction. | Bilinear Functional Equations in 2D Quantum Gravity: The microscopic theories of quantum gravity related to integrable lattice
models can be constructed as special deformations of pure gravity. Each such
deformation is defined by a second order differential operator acting on the
coupling constants. As a consequence, the theories with matter fields satisfy a
set of constraints inherited from the integrable structure of pure gravity. In
particular, a set of bilinear functional equations for each theory with matter
fields follows from the Hirota equations defining the KP (KdV) structure of
pure gravity. |
Understanding Skyrmions using Rational Maps: We discuss an ansatz for Skyrme fields in three dimensions which uses
rational maps between Riemann spheres, and produces shell-like structures of
polyhedral form. Houghton, Manton and Sutcliffe showed that a single rational
map gives good approximations to the minimal energy Skyrmions up to baryon
number of order ten. We show how the method can be generalised by using two or
more rational maps to give a double-shell or multi-shell structure.
Particularly interesting examples occur at baryon numbers twelve and fourteen. | N=2 Instanton Calculus In Closed String Background: In this contribution we describe how to obtain instanton effects in four
dimensional gauge theories by computing string scattering amplitudes in
D3/D(-1) brane systems. In particular we study a system of fractional D3/D(-1)
branes in a Z_2 orbifold and in a Ramond-Ramond closed string background, and
show that it describes the gauge instantons of N=2 super Yang-Mills theory and
their interactions with the graviphoton of N=2. Using string theory methods we
compute the prepotential of the effective gauge theory exploiting the
localization methods of the instanton calculus, showing that this leads to the
same information given by the topological string. |
Lattice Gauge Fields and Discrete Noncommutative Yang-Mills Theory: We present a lattice formulation of noncommutative Yang-Mills theory in
arbitrary even dimensionality. The UV/IR mixing characteristic of
noncommutative field theories is demonstrated at a completely nonperturbative
level. We prove a discrete Morita equivalence between ordinary Yang-Mills
theory with multi-valued gauge fields and noncommutative Yang-Mills theory with
periodic gauge fields. Using this equivalence, we show that generic
noncommutative gauge theories in the continuum can be regularized
nonperturbatively by means of {\it ordinary} lattice gauge theory with 't~Hooft
flux. In the case of irrational noncommutativity parameters, the rank of the
gauge group of the commutative lattice theory must be sent to infinity in the
continuum limit. As a special case, the construction includes the recent
description of noncommutative Yang-Mills theories using twisted large $N$
reduced models. We study the coupling of noncommutative gauge fields to matter
fields in the fundamental representation of the gauge group using the lattice
formalism. The large mass expansion is used to describe the physical meaning of
Wilson loops in noncommutative gauge theories. We also demonstrate Morita
equivalence in the presence of fundamental matter fields and use this property
to comment on the calculation of the beta-function in noncommutative quantum
electrodynamics. | Moduli Dependence of One--Loop Gauge Couplings in (0,2)
Compactifications: We derive the moduli dependence of the one--loop gauge couplings for
non--vanishing gauge background fields in a four--dimensional heterotic (0,2)
string compactification. Remarkably, these functions turn out to have a
representation as modular functions on an auxiliary Riemann surface on
appropriate truncations of the full moduli space. In particular, a certain kind
of one--loop functions is given by the free energy of two--dimensional solitons
on this surface. |
Renyi Entropy and Geometry: Entanglement entropy in even dimensional conformal field theories (CFTs)
contains well-known universal terms arising from the conformal anomaly. Renyi
entropies are natural generalizations of the entanglement entropy that are much
less understood. Above two spacetime dimensions, the universal terms in the
Renyi entropies are unknown for general entangling geometries. We conjecture a
new structure in the dependence of the four-dimensional Renyi entropies on the
intrinsic and extrinsic geometry of the entangling surface. We provide evidence
for this conjecture by direct numerical computations in the free scalar and
fermion field theories. The computation involves relating the four-dimensional
free massless Renyi entropies across cylindrical entangling surfaces to
corresponding three-dimensional massive Renyi entropies across circular
entangling surfaces. Our numerical technique also allows us to directly probe
other interesting aspects of three-dimensional Renyi entropy, including the
massless renormalized Renyi entropy and calculable contributions to the
perimeter law. | Geometric dualities in 4d field theories and their 5d interpretation: We study four-dimensional N=1 gauge theories arising on D3-branes probing
toric singularities. Toric dualities and flows between theories corresponding
to different singularities are analyzed by encoding the geometric information
into (p,q) webs. A new method for identifying global symmetries of the
four-dimensional theories using the brane webs is developed. Five-dimensional
theories are associated to the theories on the D3-branes by using (p,q) webs.
This leads to a novel interpretation of Seiberg duality, as crossing curves of
marginal stability in five dimensions. |
Thermodynamic curvature of charged black holes with $AdS_2$ horizons: Sign and magnitude of the thermodynamic curvature provides empirical
information about the nature of microstructures of a general thermodynamic
system. For charged black holes in AdS, thermodynamic curvature is positive for
large charge or chemical potential, and diverges for extremal black holes,
indicating strongly repulsive nature. We compute the thermodynamic curvature at
low temperatures, for charged black holes with AdS$_2$ near horizon geometry,
and containing a zero temperature horizon radius $r_h$, in a spacetime which
asymptotically approaches $AdS_D$ (for $D>3$). In the semi-classical analysis
at low temperatures, the curvature shows a novel crossover from negative to
positive side, indicating the shift from attraction to repulsion dominated
regime near $T=0$, before diverging as $1/(\gamma T)$, where $\gamma$ is the
coefficient of leading low temperature correction to entropy. Accounting for
quantum fluctuations, the curvature computed in the canonical ensemble is
positive, whereas the one in the grand canonical ensemble, continues to show a
crossover from negative to positive side. Moreover, the divergence of curvature
at $T=0$ is cured irrespective of the ensemble used, resulting in a universal
constant. | A stringy massive double copy: We derive a massive double copy construction within string theory. To this
end, we use massive vectors of the open string spectrum that appear in
compactifications to four dimensions and construct massive spin-2 tensors as
closed string states, thereby mimicking the structure of the massless graviton.
We then compute three-point amplitudes for the scattering of massless and
massive spin-2 closed string states and reveal the double copy structure of the
latter. With these results being finite in the string scale, we are further
able to reproduce the cubic Lagrangian of ghost-free bimetric theory around
flat spacetime for bulk massive spin-2 states originating in products of
vectors of extended brane supersymmetry. |
Contour gauges, canonical formalism and flux algebras: A broad class of contour gauges is shown to be determined by admissible
contractions of the geometrical region considered and a suitable equivalence
class of curves is defined. In the special case of magnetostatics, the relevant
electromagnetic potentials are directly related to the ponderomotive forces.
Schwinger's method of extracting a gauge invariant factor from the fermion
propagator could, it is argued, lead to incorrect results. Dirac brackets of
both Maxwell and Yang-Mills theories are given for arbitrary admissible
space-like paths. It is shown how to define a non-abelian flux and local
charges which obey a local charge algebra. Fields associated with the charges
differ from the electric fields of the theory by singular topological terms; to
avoid this obstruction to the Gauss law it is necessary to exclude a single,
gauge fixing curve from the region considered. | p-Brane Quantum Mechanical Wave Equations: Several quantum mechanical wave equations for $p$-branes are proposed based
on the role that the volume-preserving diffeomorphisms group has on the physics
of extended objects. The $p$-brane quantum mechanical wave equations determine
the quantum dynamics involving the creation/destruction of $p$-branes in a $D$
dimensional spacetime background with a given world-volume measure
configuration in a given quantum state $\Psi$. |
Boundaries in Free Higher Derivative Conformal Field Theories: We consider free higher derivative theories of scalars and Dirac fermions in
the presence of a boundary in general dimension. We establish a method for
finding consistent conformal boundary conditions in these theories by removing
certain boundary primaries from the spectrum. A rich set of renormalization
group flows between various conformal boundary conditions is revealed,
triggered by deformations quadratic in the boundary primaries. We compute the
free energy of these theories on a hemisphere, and show that the boundary
$a$-theorem is generally violated along boundary flows as a consequence of bulk
non-unitarity. We further characterize the boundary theory by computing the
two-point function of the displacement operator. | Supersymmetric Galilean Electrodynamics: In 2+1 dimensions, we propose a renormalizable non-linear sigma model action
which describes the $\mathcal{N}=2$ supersymmetric generalization of Galilean
Electrodynamics. We first start with the simplest model obtained by null
reduction of the relativistic Abelian $\mathcal{N}=1$ supersymmetric QED in 3+1
dimensions and study its renormalization properties directly in
non-relativistic superspace. Despite the existence of a non-renormalization
theorem induced by the causal structure of the non-relativistic dynamics, we
find that the theory is non-renormalizable. Infinite dimensionless,
supersymmetric and gauge-invariant terms, which combine into an analytic
function, are generated at quantum level. Renormalizability is then restored by
generalizing the theory to a non-linear sigma model where the usual minimal
coupling between gauge and matter is complemented by infinitely many marginal
couplings driven by a dimensionless gauge scalar and its fermionic
superpartner. Superconformal invariance is preserved in correspondence of a
non-trivial conformal manifold of fixed points where the theory is
gauge-invariant and interacting. |
Jets in strongly-coupled N = 4 super Yang-Mills theory: We study jets of massless particles in N=4 super Yang-Mills using the AdS/CFT
correspondence both at zero and finite temperature. We set up an initial state
corresponding to a highly energetic quark/anti-quark pair and follow its time
evolution into two jets. At finite temperature the jets stop after traveling a
finite distance, whereas at zero temperature they travel and spread forever. We
map out the corresponding baryon number charge density and identify the generic
late time behavior of the jets as well as features that depend crucially on the
initial conditions. | Belinfante Tensors Induced by Matter-Gravity Couplings: We show that any generally covariant coupling of matter fields to gravity
gives rise to a conserved, on-shell symmetric energy-momentum tensor equivalent
to the canonical energy-momentum tensor of the flat-space theory. For matter
fields minimally coupled to gravity our algorithm gives the conventional
Belinfante tensor. We establish that different matter-gravity couplings give
metric energy-momentum tensors differing by identically conserved tensors. We
prove that the metric energy-momentum tensor obtained from an arbitrary gravity
theory is on-shell equivalent to the canonical energy-momentum tensor of the
flat-space theory. |
Dynamical systems and nonlinear transient rheology of the
far-from-equilibrium Bjorken flow: In relativistic kinetic theory, the one-particle distribution function is
approximated by an asymptotic perturbative power series in Knudsen number which
is divergent. For the Bjorken flow, we expand the distribution function in
terms of its moments and study their nonlinear evolution equations. The
resulting coupled dynamical system can be solved for each moment consistently
using a multi-parameter transseries which makes the constitutive relations
inherit the same structure. A new non-perturbative dynamical renormalization
scheme is born out of this formalism that goes beyond the linear response
theory. We show that there is a Lyapunov function, aka dynamical potential,
which is, in general, a function of the moments and time satisfying Lyapunov
stability conditions along RG flows connected to the asymptotic hydrodynamic
fixed point. As a result, the transport coefficients get dynamically
renormalized at every order in the time-dependent perturbative expansion by
receiving non-perturbative corrections present in the transseries. The
connection between the integration constants and the UV data is discussed using
the language of dynamical systems. Furthermore, we show that the first
dissipative correction in the Knudsen number to the distribution function is
not only determined by the known effective shear viscous term but also a new
high energy non-hydrodynamic mode. It is demonstrated that the survival of this
new mode is intrinsically related to the nonlinear mode-to-mode coupling with
the shear viscous term. Finally, we comment on some possible phenomenological
applications of the proposed non-hydrodynamic transport theory. | Intersecting black branes in strong gravitational waves: We consider intersecting black branes with strong gravitational waves
propagating along their worldvolume in the context of supergravity theories.
Both near-horizon and space-filling gravitational wave modes are included in
our ansatz. The equations of motion (originally, partial differential
equations) are shown to reduce to ordinary differential equations, which
include a Toda-like system. For special arrangements of intersecting black
branes, the Toda-like system becomes integrable, permitting a more thorough
analysis of the gravitational equations of motion. |
Generalized Cardy conditions of topological defect lines: We propose a systematic procedure to work out systems of topological defect
lines (TDLs) in minimal models. The only input of this method is the modular
invariant partition function. For diagonal and permutation diagonal models, we
prove there is a bijection between simple TDLs and primary fields preserving
fusion rules. For block-diagonal models, we work out simple TDLs in the
$3$-state Potts model as an example. The results agree with those in $3D$
topological field theory methods. | Four-Dimensional Gravity on a Covariant Noncommutative Space (II): Based on the construction of the 4-dim noncommutative gravity model described
in our previous work, first, a more extended description of the covariant
noncommutative space (fuzzy 4-dim de Sitter space), which accommodates the
gravity model, is presented and then the corresponding field equations, which
are obtained after variation of the previously proposed action, are extracted.
Also, a spontaneous breaking of the initial symmetry is performed, this time
induced by the introduction of an auxiliary scalar field, and its implications
in the reduced theory, which is produced after considering the commutative
limit, are examined. |
The Recoils of a Dynamical Mirror and the Decoherence of its Fluxes: In order to address the problem of the validity of the "background field
approximation", we introduce a dynamical model for a mirror described by a
massive quantum field. We then analyze the properties of the scattering of a
massless field from this dynamical mirror and compare the results with the
corresponding quantities evaluated using the original Davies Fulling model in
which the mirror is represented by a boundary condition imposed on the massless
field at its surface. We show that in certain circumstances, the recoils of the
dynamical mirror induce decoherence effects which subsist even when the mass of
the mirror is sent to infinity. In particular we study the case of the
uniformly accelerated mirror and prove that, after a certain lapse of proper
time, the decoherence effects inevitably dominate the physics of the quanta
emitted forward. Then, the vanishing of the mean flux obtained in the Davies
Fulling model is no longer found but replaced by a positive incoherent flux. | A Note on the Symplectic Structure on the Dressing Group in the
sinh--Gordon Model: We analyze the symplectic structure on the dressing group in the \shG\, model
by calculating explicitly the Poisson bracket $\{g\x g\}$ where $g$ is the
\dg\, element which creates a generic one soliton solution from the vacuum. Our
result is that this bracket does not coincide with the Semenov--Tian--Shansky
one. The last induces a Lie--Poisson structure on the \dg . To get the bracket
obtained by us from the Semenov--Tian--Shansky bracket we apply the formalism
of the constrained Hamiltonian systems. The constraints on the \dg\, appear
since the element which generates one solitons from the vacuum has a specific
form. |
Conformal symmetry in non-local field theories: We have shown that a particular class of non-local free field theory has
conformal symmetry in arbitrary dimensions. Using the local field theory
counterpart of this class, we have found the Noether currents and Ward
identities of the translation, rotation and scale symmetries. The operator
product expansion of the energy-momentum tensor with quasi-primary fields is
also investigated. | Inflation with racetrack superpotential and matter field: Several models of inflation with the racetrack superpotential for the volume
modulus coupled to a matter field are investigated. In particular, it is shown
that two classes of racetrack inflation models, saddle point and inflection
point ones, can be constructed in a fully supersymmetric framework with the
matter field F-term as a source of supersymmetry breaking and uplifting. Two
models of F-term supersymmetry breaking are considered: the Polonyi model and
the quantum corrected O'Raifeartaigh model. In the former case, both classes of
racetrack inflation models differ significantly from the corresponding models
with non-supersymmetric uplifting. The main difference is a quite strong
dominance of the inflaton by the matter field. In addition, fine-tuning of the
parameters is relaxed as compared to the original racetrack models. In the case
of the racetrack inflation models coupled to the O'Raifeartaigh model, the
matter field is approximately decoupled from the inflationary dynamics. In all
of the above models the gravitino mass is larger than the Hubble scale during
inflation. The possibility of having the gravitino much lighter than the Hubble
scale is also investigated. It is very hard to construct models with light
gravitino in which the volume modulus dominates inflation. On the other hand,
models in which the inflationary dynamics is dominated by the matter field are
relatively simple and seem to be more natural. |
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