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Holomorphic reduction of N=2 gauge theories, Wilson-'t Hooft operators,
and S-duality: We study twisted N=2 superconformal gauge theory on a product of two Riemann
surfaces Sigma and C. The twisted theory is topological along C and holomorphic
along Sigma and does not depend on the gauge coupling or theta-angle. Upon
Kaluza-Klein reduction along Sigma, it becomes equivalent to a topological
B-model on C whose target is the moduli space MV of nonabelian vortex equations
on Sigma. The N=2 S-duality conjecture implies that the duality group acts by
autoequivalences on the derived category of MV. This statement can be regarded
as an N=2 counterpart of the geometric Langlands duality. We show that the
twisted theory admits Wilson-'t Hooft loop operators labelled by both electric
and magnetic weights. Correlators of these loop operators depend
holomorphically on coordinates and are independent of the gauge coupling. Thus
the twisted theory provides a convenient framework for studying the Operator
Product Expansion of general Wilson-'t Hooft loop operators.
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Wigner Particle Theory and Local Quantum Physics: Wigner's irreducible positive energy representations of the Poincare group
are often used to give additional justifications for the Lagrangian
quantization formalism of standard QFT. Here we study another more recent
aspect. We explain in this paper modular concepts by which we are able to
construct the local operator algebras for all standard positive energy
representations directly i.e. without going through field coordinatizations. In
this way the artificial emphasis on Lagrangian field coordinates is avoided
from the very beginning. These new concepts allow to treat also those cases of
``exceptional'' Wigner representations associated with anyons and the famous
Wigner ``spin tower''which have remained inaccessible to Lagrangian
quantization. Together with the d=1+1 factorizing models (whose modular
construction has been studied previously), they form an interesting family of
theories with a rich vacuum-polarization structure (but no on shell real
particle creation) to which the modular methods can be applied for their
explicit construction. We explain and illustrate the algebraic strategy of this
construction. We also comment on possibilities of formulating the Wigner theory
in a setting of a noncommutative spacetime substrate. This is potentially
interesting in connection with recent unitarity- and Lorentz invariance-
preserving results of the special nonlocality caused by this kind of
noncommutativity.
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PP-wave string interactions from n-point correlators of BMN operators: BMN operators are characterized by the fact that they have infinite R-charge
and finite anomalous dimension in the BMN double scaling limit. Using this
fact, we show that the BMN operators close under operator product expansion and
form a sector in the N=4 supersymmetric Yang-Mills theory. We then identify
short-distance limits of general BMN n-point correlators, and show how they
correspond to the pp-wave string interactions. We also discuss instantons in
the light of the pp-wave/SYM correspondence.
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Dynamical Symmetry Breaking in Flat Space with Non-trivial Topology: We consider a four-fermion theory as a simple model of dynamical symmetry
breaking in flat space with non-trivial topology, motivated from recent studies
in similar considerations in curved space. The phase structure is investigated,
by developing a useful formalism to evaluate the effective potential in
arbitrary compactified flat space in 3- and 4-dimensional spacetime. The phase
structure is significantly altered due to the finite volume effect in the
compactified space. Interestingly, the effect works in different way depending
on the boundary condition of the fermion fields. The physical interpretation of
the results and its implication on the dynamical symmetry breaking phenomenon
in curved space are discussed.
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Celestial superamplitude in $\mathcal N=4$ SYM theory: Celestial amplitude is a new reformulation of momentum space scattering
amplitude and offers a promising way for flat holography. In this paper, we
study the celestial amplitude in $\mathcal N=4$ Super-Yang-Mills (SYM) theory
aiming at understanding the role of superconformal symmetry in celestial
holography. We first construct the superconformal generators acting on the
celestial superfield which assembles all the on-shell fields in the multiplet
together in terms of celestial variables and Grassmann parameters. These
generators satisfy the superconformal algebra of $\mathcal N=4$ SYM theory. We
also compute the three-point and four-point celestial super-amplitude
explicitly. They can be identified as the correlation functions of the
celestial superfields living at the celestial sphere. We further study the soft
and collinear limits which give rise to the super-Ward identity and super-OPE
on the celestial sphere, respectively. Our results initiate a new perspective
of understanding the well-studied $\mathcal N=4$ SYM amplitude via 2D celestial
conformal field theory.
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Compact and Noncompact Gauged Maximal Supergravities in Three Dimensions: We present the maximally supersymmetric three-dimensional gauged
supergravities. Owing to the special properties of three dimensions --
especially the on-shell duality between vector and scalar fields, and the
purely topological character of (super)gravity -- they exhibit an even richer
structure than the gauged supergravities in higher dimensions. The allowed
gauge groups are subgroups of the global E_8 symmetry of ungauged N=16
supergravity. They include the regular series SO(p,8-p) x SO(p,8-p) for all
p=0,1,...,4, the group E_8 itself, as well as various noncompact forms of the
exceptional groups E_7, E_6 and F_4 x G_2. We show that all these theories
admit maximally supersymmetric ground states, and determine their background
isometries, which are superextensions of the anti-de Sitter group SO(2,2). The
very existence of these theories is argued to point to a new supergravity
beyond the standard D=11 supergravity.
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Time-Like Extra Dimension and Cosmological Constant in Brane Models: We discuss the general models with one time-like extra dimension and parallel
3-branes on the space-time $M^4 \times M^1$. We also construct the general
brane models or networks with $n$ space-like and $m$ time-like extra dimensions
and with constant bulk cosmological constant on the space-time $M^4\times
(M^1)^{n+m}$, and point out that there exist two kinds of models with zero bulk
cosmological constant: for static solutions, we have to introduce time-like and
space-like extra dimensions, and for non-static solutions, we can obtain the
models with only space-like extra dimension(s). In addition, we give two
simplest models explicitly, and comment on the 4-dimensional effective
cosmological constant.
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The Generalized Uncertainty Principle and Corrections to the
Cardy-Verlinde Formula in $SAdS_5$ Black Holes: In this letter, we investigate a possible modification to the temperature and
entropy of $5-$dimensional Schwarzschild anti de Sitter black holes due to
incorporating stringy corrections to the modified uncertainty principle. Then
we subsequently argue for corrections to the Cardy-Verlinde formula in order to
account for the corrected entropy. Then we show, one can taking into account
the generalized uncertainty principle corrections of the Cardy-Verlinde entropy
formula by just redefining the Virasoro operator $L_0$ and the central charge
$c$.
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Effects of the generalized uncertainty principle on the thermal
properties of Kemmer oscillator: A series of aspects of the quantum gravity predict a modification in the
Heisenberg uncertainty principle to the generalized uncertainty principle
(GUP). In the present work, using the momentum space representation, we study
the behavior of the Kemmer oscillator in the context of the GUP. The wave
function, the probability densities, and the energy spectrum are obtained
analytically. Furthermore, the thermodynamic properties of the system are
investigated via numerical method and the influence of GUP on thermodynamic
functions is also discussed.
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Feasibility of finite renormalization of particle mass in quantum
electrodynamics: The paper proposes an algorithm for regularization of the self-energy
expressions for a Dirac particle that meets the relativistic and gauge
invariance requirements.
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Shear Modes, Criticality and Extremal Black Holes: We consider a (2+1)-dimensional field theory, assumed to be holographically
dual to the extremal Reissner-Nordstrom AdS(4) black hole background, and
calculate the retarded correlators of charge (vector) current and
energy-momentum (tensor) operators at finite momentum and frequency. We show
that, similar to what was observed previously for the correlators of scalar and
spinor operators, these correlators exhibit emergent scaling behavior at low
frequency. We numerically compute the electromagnetic and gravitational
quasinormal frequencies (in the shear channel) of the extremal
Reissner-Nordstrom AdS(4) black hole corresponding to the spectrum of poles in
the retarded correlators. The picture that emerges is quite simple: there is a
branch cut along the negative imaginary frequency axis, and a series of
isolated poles corresponding to damped excitations. All of these poles are
always in the lower half complex frequency plane, indicating stability. We show
that this analytic structure can be understood as the proper limit of finite
temperature results as T is taken to zero holding the chemical potential fixed.
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Zero modes, beta functions and IR/UV interplay in higher-loop QED: We analyze the relation between the short-distance behavior of quantum field
theory and the strong-field limit of the background field formalism, for QED
effective Lagrangians in self-dual backgrounds, at both one and two loop. The
self-duality of the background leads to zero modes in the case of spinor QED,
and these zero modes must be taken into account before comparing the
perturbative beta function coefficients and the coefficients of the
strong-field limit of the effective Lagrangian. At one-loop this is familiar
from instanton physics, but we find that at two-loop the role of the zero
modes, and the interplay between IR and UV effects in the renormalization, is
quite different. Our analysis is motivated in part by the remarkable simplicity
of the two-loop QED effective Lagrangians for a self-dual constant background,
and we also present here a new independent derivation of these two-loop
results.
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Flux compactifications in string theory: a comprehensive review: We present a pedagogical overview of flux compactifications in string theory,
from the basic ideas to the most recent developments. We concentrate on closed
string fluxes in type II theories. We start by reviewing the supersymmetric
flux configurations with maximally symmetric four-dimensional spaces. We then
discuss the no-go theorems (and their evasion) for compactifications with
fluxes. We analyze the resulting four-dimensional effective theories, as well
as some of its perturbative and non-perturbative corrections, focusing on
moduli stabilization. Finally, we briefly review statistical studies of flux
backgrounds.
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Homological mirror symmetry on noncommutative two-tori: Homological mirror symmetry is a conjecture that a category constructed in
the A-model and a category constructed in the B-model are equivalent in some
sense. We construct a cyclic differential graded (DG) category of holomorphic
vector bundles on noncommutative two-tori as a category in the B-model side. We
define the corresponding Fukaya's category in the A-model side, and prove the
equivalence of the two categories at the level of cyclic categories. We further
write down explicitly Feynman rules for higher Massey products derived from the
cyclic DG category. As a background of these arguments, a physical explanation
of the mirror symmetry for noncommutative two-tori is also given.
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Perturbative dynamics of fuzzy spheres at large N: We clarify some peculiar aspects of the perturbative expansion around a
classical fuzzy-sphere solution in matrix models with a cubic term. While the
effective action in the large-N limit is saturated at the one-loop level, we
find that the ``one-loop dominance'' does not hold for generic observables due
to one-particle reducible diagrams. However, we may exploit the one-loop
dominance for the effective action and obtain various observables to all orders
from one-loop calculation by simply shifting the center of expansion to the
``quantum solution'', which extremizes the effective action. We confirm the
validity of this method by comparison with the direct two-loop calculation and
with Monte Carlo results in the 3d Yang-Mills-Chern-Simons matrix model. From
the all order result we find that the perturbative expansion has a finite
radius of convergence.
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Induced fermionic current in toroidally compactified spacetimes with
applications to cylindrical and toroidal nanotubes: The vacuum expectation value of the fermionic current is evaluated for a
massive spinor field in spacetimes with an arbitrary number of toroidally
compactified spatial dimensions in presence of a constant gauge field. By using
the Abel-Plana type summation formula and the zeta function technique we
present the fermionic current in two different forms. Non-trivial topology of
the background spacetime leads to the Aharonov-Bohm effect on the fermionic
current induced by the gauge field. The current is a periodic function of the
magnetic flux with the period equal to the flux quantum. In the absence of the
gauge field it vanishes for special cases of untwisted and twisted fields.
Applications of the general formulae to Kaluz-Klein type models and to
cylindrical and toroidal carbon nanotubes are given. In the absence of magnetic
flux the total fermionic current in carbon nanotubes vanishes, due to the
cancellation of contributions from two different sublattices of the graphene
hexagonal lattice.
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On Fractional Instanton Numbers in Six Dimensional Heterotic E_8 x E_8
Orbifolds: We show how the level matching condition in six dimensional, abelian and
supersymmetric orbifolds of the E_8 x E_8 heterotic string can be given
equivalently in terms of fractional gauge and gravitational instanton numbers.
This relation is used to restate the classification of the orbifolds in terms
of flat bundles away from the orbifold singularities under the constraint of
the level matching condition. In an outlook these results are applied to
Kaluza-Klein monopoles of the heterotic string on S^1 in Wilson line
backgrounds.
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Supergravity couplings: a geometric formulation: This report provides a pedagogical introduction to the description of the
general Poincare supergravity/matter/Yang-Mills couplings using methods of
Kahler superspace geometry. At a more advanced level this approach is
generalized to include tensor field and Chern-Simons couplings in supersymmetry
and supergravity, relevant in the context of weakly and strongly coupled string
theories.
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Gravitational Bound Waveforms from Amplitudes: With the aim of computing bound waveforms from scattering amplitudes, we
explore gravitational two-body dynamics using the Schwinger-Dyson equations and
Bethe-Salpeter recursion. We show that the tree-level scattering waveform
admits a natural analytic continuation, in rapidity, to the bound waveform,
which we confirm from an independent calculation, in the Post-Newtonian
expansion, of the time-domain multipoles at large eccentricity. We demonstrate
consistency of this scattering-to-bound map with the Damour-Deruelle
prescription for orbital elements in the quasi-Keplerian parametrization (which
enters into the evaluation of the multipoles) and with the analytic
continuation, in the binding energy, of radiated energy and angular momentum at
3PM.
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Fuzzy Scalar Field Theory as a Multitrace Matrix Model: We develop an analytical approach to scalar field theory on the fuzzy sphere
based on considering a perturbative expansion of the kinetic term. This
expansion allows us to integrate out the angular degrees of freedom in the
hermitian matrices encoding the scalar field. The remaining model depends only
on the eigenvalues of the matrices and corresponds to a multitrace hermitian
matrix model. Such a model can be solved by standard techniques as e.g. the
saddle-point approximation. We evaluate the perturbative expansion up to second
order and present the one-cut solution of the saddle-point approximation in the
large N limit. We apply our approach to a model which has been proposed as an
appropriate regularization of scalar field theory on the plane within the
framework of fuzzy geometry.
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Twelve-Dimensional Aspects of Four-Dimensional N=1 Type I Vacua: Four-dimensional supergravity theories are reinterpreted in a 12-dimensional
F-theory framework. The O(8) symmetry of N=8 supergravity is related to a
reduction of F-theory on T_8, with the seventy scalars formally associated, by
O(8) triality, to a fully compactified four-form A_4. For the N=1 type I model
recently obtained from the type IIB string on the Z orbifold, we identify the
K\"ahler manifold of the untwisted scalars in the unoriented closed sector with
the generalized Siegel upper-half plane Sp(8,R)/(SU(4) \times U(1)). The SU(4)
factor reflects the holonomy group of Calabi-Yau fourfolds.
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Anomalies in orbifold field theories: We study the constraints on models with extra dimensions arising from local
anomaly cancellation. We consider a five-dimensional field theory with a U(1)
gauge field and a charged fermion, compactified on the orbifold S^1/(Z_2 x
Z_2'). We show that, even if the orbifold projections remove both fermionic
zero modes, there are gauge anomalies localized at the fixed points. Anomalies
naively cancel after integration over the fifth dimension, but gauge invariance
is broken, spoiling the consistency of the theory. We discuss the implications
for realistic supersymmetric models with a single Higgs hypermultiplet in the
bulk, and possible cancellation mechanisms in non-minimal models.
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Topics in vacuum decay (Ph.D Thesis): If a theory has more than one classically stable vacuum, quantum tunneling
and thermal jumps make the transition between the vacua possible. The
transition happens through a first order phase transition started by nucleation
of a bubble of the new vacuum. The outward pressure of the truer vacuum makes
the bubble expand and consequently eat away more of the old phase. In the
presence of gravity this phenomenon gets more complicated and meanwhile more
interesting. It can potentially have important cosmological consequences. Some
aspects of this decay are studied in this thesis. Solutions with different
symmetry than the generically used O(4) symmetry are studied and their actions
calculated. Vacuum decay in a spatial vector field is studied and novel
features like kinky domain walls are presented. The question of stability of
vacua in a landscape of potentials is studied and the possible instability in
large dimension of fields is shown. Finally a compactification of the
Einstein-Maxwell theory is studied which can be a good lab to understand the
decay rates in compactification models of arbitrary dimensions.
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Tinkertoys for the E7 Theory: We classify the class $S$ theories of type $E_7$. These are four-dimensional
$\mathcal{N}=2$ superconformal field theories arising from the compactification
of the $E_7$ $(2,0)$ theory on a punctured Riemann surface, $C$. The
classification is given by listing all 3-punctured spheres ("fixtures"), and
connecting cylinders, which can arise in a pants-decomposition of $C$. We find
exactly 11,000 fixtures with three regular punctures, and an additional 48 with
one "irregular puncture" (in the sense used in our previous works). To organize
this large number of theories, we have created a web application at
https://golem.ph.utexas.edu/class-S/E7/ . Among these theories, we find 10 new
ones with a simple exceptional global symmetry group, as well as a new rank-2
SCFT and several new rank-3 SCFTs. As an application, we study the
strong-coupling limit of the $E_7$ gauge theory with 3 hypermultiplets in the
$56$. Using our results, we also verify recent conjectures that the $T^2$
compactification of certain $6d$ $(1,0)$ theories can alternatively be realized
in class $S$ as fixtures in the $E_7$ or $E_8$ theories.
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Transport properties of a holographic model with novel gauge-axion
coupling: We investigate the transport properties within a holographic model
characterized by a novel gauge-axion coupling. A key innovation is the
introduction of the direct coupling between axion fields, the antisymmetric
tensor, and the gauge field in our bulk theory. This novel coupling term leads
to the emergence of nondiagonal components in the conductivity tensor. An
important characteristic is that the off-diagonal elements manifest
antisymmetry. Remarkably, the conductivity behavior in this model akin to that
of Hall conductivity. Additionally, this model can also achieve metal-insulator
transition.
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Self-force on an electric dipole in the spacetime of a cosmic string: We calculate the electrostatic self-force on an electric dipole in the
spacetime generated by a static, thin, infinite and straight cosmic string. The
electric dipole is held fixed in different configurations, namely, parallel,
perpendicular to the cosmic string and oriented along the azimuthal direction
around this topological defect, which is stretched along the z axis. We show
that the self-force is equivalent to an interaction of the electric dipole with
an effective dipole moment which depends on the linear mass density of the
cosmic string and on the configuration. The plots of the self-forces as
functions of the parameter which determines the angular deficit of the cosmic
string are shown for those different configurations.
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Borcherds Algebras and N=4 Topological Amplitudes: The perturbative spectrum of BPS-states in the E_8 x E_8 heterotic string
theory compactified on T^2 is analysed. We show that the space of BPS-states
forms a representation of a certain Borcherds algebra G which we construct
explicitly using an auxiliary conformal field theory. The denominator formula
of an extension G_{ext} \supset G of this algebra is then found to appear in a
certain heterotic one-loop N=4 topological string amplitude. Our construction
thus gives an N=4 realisation of the idea envisioned by Harvey and Moore,
namely that the `algebra of BPS-states' controls the threshold corrections in
the heterotic string.
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Renormalization constants from string theory: We review some recent results on the calculation of renormalization constants
in Yang-Mills theory using open bosonic strings. The technology of string
amplitudes, supplemented with an appropriate continuation off the mass shell,
can be used to compute the ultraviolet divergences of dimensionally regularized
gauge theories. The results show that the infinite tension limit of string
amplitudes corresponds to the background field method in field theory.
(Proceedings of the Workshop ``Strings, Gravity and Physics at the Planck
scale'', Erice (Italy), September 1995. Preprint DFTT 82/95)
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Elementary Quantum Geometry: These Lecture Notes provide an elementary introduction to the quantization of
two-dimensional quantum gravity. Nothing beyond undergratuate physics and
mathematic is required. Explicit formulas for the partition functions for
universes with n boundaries are derived, as well as for the so-called two-point
function. The latter shows explicitly that the fractal dimension of a typical
two-dimensional quantum universe is four.
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Non-linear Realizations and Higher Curvature Supergravity: We focus on non-linear realizations of local supersymmetry as obtained by
using constrained superfields in supergravity. New constraints, beyond those of
rigid supersymmetry, are obtained whenever curvature multiplets are affected as
well as higher derivative interactions are introduced. In particular, a new
constraint, which removes a very massive gravitino is introduced, and in the
rigid limit it merely reduces to an explicit supersymmetry breaking. Higher
curvature supergravities free of ghosts and instabilities are also obtained in
this way. Finally, we consider direct coupling of the goldstino multiplet to
the super Gauss--Bonnet multiplet and discuss the emergence of a new scalar
degree of freedom.
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Ground-state isolation and discrete flows in a rationally extended
quantum harmonic oscillator: Ladder operators for the simplest version of a rationally extended quantum
harmonic oscillator (REQHO) are constructed by applying a Darboux
transformation to the quantum harmonic oscillator system. It is shown that the
physical spectrum of the REQHO carries a direct sum of a trivial and an
infinite-dimensional irreducible representation of the polynomially deformed
bosonized osp(1|2) superalgebra. In correspondence with this the ground state
of the system is isolated from other physical states but can be reached by
ladder operators via non-physical energy eigenstates, which belong to either an
infinite chain of similar eigenstates or to the chains with generalized Jordan
states. We show that the discrete chains of the states generated by ladder
operators and associated with physical energy levels include six basic
generalized Jordan states, in comparison with the two basic Jordan states
entering in analogous discrete chains for the quantum harmonic oscillator.
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Instanton solution for Schwinger production of 't Hooft-Polyakov
monopoles: We present the results of an explicit numerical computation of a novel
instanton in Georgi-Glashow SU(2) theory. The instanton is physically relevant
as a mediator of Schwinger production of 't Hooft-Polyakov magnetic monopoles
from strong magnetic fields. In weak fields, the pair production rate has
previously been computed using the worldline approximation, which breaks down
in strong fields due to the effects of finite monopole size. Using lattice
field theory we have overcome this limit, including finite monopole size
effects to all orders. We demonstrate that a full consideration of the internal
monopole structure results in an enhancement to the pair production rate, and
confirm earlier results that monopole production becomes classical at the
Ambjorn-Olesen critical field strength.
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Moving Interfaces and two-dimensional Black Holes: Conformal field theories can exchange energy through a boundary interface.
Imposing conformal boundary conditions for static interfaces implies energy
conservation at the interface. Recently, the reflective and transmitive
properties of such static conformal interfaces have been studied in two
dimensions by scattering matter at the interface impurity. In this note, we
generalize this to the case of dynamic interfaces. Motivated by the connections
between the moving mirror and the black hole, we choose a particular profile
for the dynamical interface. We show that a part of the total energy of each
side will be lost in the interface. In other words, a time-dependent interface
can accumulate or absorb energy. While, in general, the interface follows a
time-like trajectory, one can take a particular limit of a profile
parameter($\beta$), such that the interface approaches a null line
asymptotically$(\beta\rightarrow 0)$. In this limit, we show that for a class
of boundary conditions, the interface behaves like a `semipermeable membrane'.
We also consider another set of conformal boundary conditions for which, in the
null line limit, the interface mimics the properties expected of a horizon. In
this case, we devise a scattering experiment, where (zero-point subtracted)
energy from one CFT is fully transmitted to the other CFT, while from the other
CFT, energy can neither be transmitted nor reflected, i.e., it gets lost in the
interface. This boundary condition is also responsible for the thermal energy
spectrum which mimics Hawking radiation. This is analogous to the black hole
where the horizon plays the role of a one-sided `membrane', which accumulates
all the interior degrees of freedom and radiates thermally in the presence of
quantum fluctuation. Stimulated by this observation, we comment on some
plausible construction of wormhole analogues.
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An Operator Product Expansion for Form Factors II. Born level: Form factors in planar N=4 Super-Yang-Mills theory admit a type of
non-perturbative operator product expansion (OPE), as we have recently shown in
arXiv:2009.11297. This expansion is based on a decomposition of the dual
periodic Wilson loop into elementary building blocks: the known pentagon
transitions and a new object that we call form factor transition, which encodes
the information about the local operator. In this paper, we compute the
two-particle form factor transitions for the chiral part of the stress-tensor
supermultiplet at Born level; they yield the leading contribution to the OPE.
To achieve this, we explicitly construct the Gubser-Klebanov-Polyakov
two-particle singlet states. The resulting transitions are then used to test
the OPE against known perturbative data and to make higher-loop predictions.
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A Massive S-duality in 4 dimensions: We reduce the Type IIA supergravity theory with a generalized Scherk-Schwarz
ansatz that exploits the scaling symmetry of the dilaton, the metric and the NS
2-form field. The resulting theory is a new massive, gauged supergravity theory
in four dimensions with a massive 2-form field and a massive 1-form field. We
show that this theory is S-dual to a theory with a massive vector field and a
massive 2-form field, which are dual to the massive 2-form and 1-form fields in
the original theory, respectively. The S-dual theory is shown to arise from a
Scherk-Schwarz reduction of the heterotic theory. Hence we establish a massive,
S-duality type relation between the IIA theory and the heterotic theory in four
dimensions. We also show that the Lagrangian for the new four dimensional
theory can be put in the most general form of a D=4, N=4 gauged Lagrangian
found by Schon and Weidner, in which (part of) the SL(2) group has been gauged.
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Turbulence without pressure in d dimensions: The randomly driven Navier-Stokes equation without pressure in d-dimensional
space is considered as a model of strong turbulence in a compressible fluid. We
derive a closed equation for the velocity-gradient probability density
function. We find the asymptotics of this function for the case of the gradient
velocity field (Burgers turbulence), and provide a numerical solution for the
two-dimensional case. Application of these results to the velocity-difference
probability density function is discussed.
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Fermions in Gödel-type background space-times with torsion and the
Landau quantization: In this paper, we analyze Dirac fermions in G\"odel-type background
space-times with torsion. We also consider the G\"odel-type spacetimes embedded
in a topological defect background. We show that relativistic bound states
solutions to the Dirac equation can be obtained by dealing with three cases of
the G\"odel-type solutions with torsion, where a cosmic string passes through
these three cases of the space-time. We obtain the relativistic energy levels
for all cases of the G\"odel-type solutions with torsion with a cosmic string,
where we show that there exists an analogy with the Landau levels for Dirac
particles. We also show that the presence of torsion in the space-time yields
new contributions to the relativistic spectrum of energies and that the
presence of the topological defect modifies the degeneracy of the relativistic
energy levels.
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The generalised scaling function: a note: A method for determining the generalised scaling function(s) arising in the
high spin behaviour of long operator anomalous dimensions in the planar $sl(2)$
sector of ${\cal N}=4$ SYM is proposed. The all-order perturbative expansion
around the strong coupling is detailed for the prototypical third and fourth
scaling functions, showing the emergence of the O(6) Non-Linear Sigma Model
mass-gap from different SYM 'mass' functions. Remarkably, only the fourth one
gains contribution from the non-BES reducible densities and also shows up, as
first, NLSM interaction and specific model dependence. Finally, the computation
of the $n$-th generalised function is sketched and might be easily finalised
for checks versus the computations in the sigma model or the complete string
theory.
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Analysis of resonance production using relativistic Gamow vectors: The calculation of an amplitude involving resonance production is presented.
This calculation employs for the resonance state a relativistic Gamow vector.
It is used for investigating the question of compatibility of the relativistic
Gamow vectors kinematics, defined by real 4-velocities and complex mass, with
the stable particle kinematics; or in other words, the integration of the Gamow
vectors with the conventional Dirac bra-ket formalism. The calculation
demonstrates a consistent framework comprising stable and Gamow vectors.
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High-temperature asymptotics of the 4d superconformal index: The superconformal index of a typical Lagrangian 4d SCFT is given by a
special function known as an elliptic hypergeometric integral (EHI). The
high-temperature limit of the index corresponds to the hyperbolic limit of the
EHI. The hyperbolic limit of certain special EHIs has been analyzed by Eric
Rains around 2006; extending Rains's techniques, we discover a surprisingly
rich structure in the high-temperature limit of a (rather large) class of EHIs
that arise as the superconformal index of unitary Lagrangian 4d SCFTs with
non-chiral matter content. Our result has implications for $\mathcal{N}=1$
dualities, the AdS/CFT correspondence, and supersymmetric gauge dynamics on
$R^3\times S^1$.
We also investigate the high-temperature asymptotics of the large-N limit of
the superconformal index of a class of holographic 4d SCFTs (described by toric
quiver gauge theories with SU(N) nodes). We show that from this study a rather
general solution to the problem of holographic Weyl anomaly in AdS$_5$/CFT$_4$
at the subleading order (in the 1/N expansion) emerges.
Most of this dissertation is based on published works by Jim Liu, Phil
Szepietowski, and the author. We include here a few previously unpublished
results as well, one of which is the high-temperature asymptotics of the
superconformal index of puncture-less SU(2) class-$\mathcal{S}$ theories.
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F-theory and the Witten Index: We connect the fermionic fields, localized on the intersection curve $\Sigma$
of two D7-branes with zero background flux, to a N=2 supersymmetric quantum
mechanics algebra, within the theoretical framework of F-theory.
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Estimating Calabi-Yau Hypersurface and Triangulation Counts with
Equation Learners: We provide the first estimate of the number of fine, regular, star
triangulations of the four-dimensional reflexive polytopes, as classified by
Kreuzer and Skarke (KS). This provides an upper bound on the number of
Calabi-Yau threefold hypersurfaces in toric varieties. The estimate is
performed with deep learning, specifically the novel equation learner (EQL)
architecture. We demonstrate that EQL networks accurately predict numbers of
triangulations far beyond the $h^{1,1}$ training region, allowing for reliable
extrapolation. We estimate that number of triangulations in the KS dataset is
$10^{10,505}$, dominated by the polytope with the highest $h^{1,1}$ value.
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Parametric Representation of Rank d Tensorial Group Field Theory:
Abelian Models with Kinetic Term $\sum_{s}|p_s| + μ$: We consider the parametric representation of the amplitudes of Abelian models
in the so-called framework of rank $d$ Tensorial Group Field Theory. These
models are called Abelian because their fields live on $U(1)^D$. We concentrate
on the case when these models are endowed with particular kinetic terms
involving a linear power in momenta. New dimensional regularization and
renormalization schemes are introduced for particular models in this class: a
rank 3 tensor model, an infinite tower of matrix models $\phi^{2n}$ over
$U(1)$, and a matrix model over $U(1)^2$. For all divergent amplitudes, we
identify a domain of meromorphicity in a strip determined by the real part of
the group dimension $D$. From this point, the ordinary subtraction program is
applied and leads to convergent and analytic renormalized integrals.
Furthermore, we identify and study in depth the Symanzik polynomials provided
by the parametric amplitudes of generic rank $d$ Abelian models. We find that
these polynomials do not satisfy the ordinary Tutte's rules
(contraction/deletion). By scrutinizing the "face"-structure of these
polynomials, we find a generalized polynomial which turns out to be stable only
under contraction.
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Finite-size effect for four-loop Konishi of the beta-deformed N=4 SYM: We propose that certain twists of the su(2|2) S-matrix elements describe the
beta-deformation of N=4 supersymmetric Yang-Mills theory. We compute the
perturbative four-loop anomalous dimension of the Konishi operator of the
deformed gauge theory from the Luscher formula based on these twisted S-matrix
elements. The result agrees exactly with the perturbative gauge theory
computations.
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Remarks on E11 approach: We consider a few topics in $E_{11}$ approach to superstring/M-theory: even
subgroups ($Z_2$ orbifolds) of $E_{n}$, n=11,10,9 and their connection to
Kac-Moody algebras; $EE_{11}$ subgroup of $E_{11}$ and coincidence of one of
its weights with the $l_1$ weight of $E_{11}$, known to contain brane charges;
possible form of supersymmetry relation in $E_{11}$; decomposition of $l_1$
w.r.t. the $SO(10,10)$ and its square root at first few levels; particle orbit
of $l_1 \ltimes E_{11}$. Possible relevance of coadjoint orbits method is
noticed, based on a self-duality form of equations of motion in $E_{11}$.
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Spinor Helicity and Dual Conformal Symmetry in Ten Dimensions: The spinor helicity formalism in four dimensions has become a very useful
tool both for understanding the structure of amplitudes and also for practical
numerical computation of amplitudes. Recently, there has been some discussion
of an extension of this formalism to higher dimensions. We describe a
particular implementation of the spinor-helicity method in ten dimensions.
Using this tool, we study the tree-level S-matrix of ten dimensional super
Yang-Mills theory, and prove that the theory enjoys a dual conformal symmetry.
Implications for four-dimensional computations are discussed.
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Color-kinematics duality and Sudakov form factor at five loops for N=4
supersymmetric Yang-Mills theory: Using color-kinematics duality, we construct for the first time the full
integrand of the five-loop Sudakov form factor in N=4 super-Yang-Mills theory,
including non-planar contributions. This result also provides a first
manifestation of the color-kinematics duality at five loops. The integrand is
explicitly ultraviolet finite when D<26/5, coincident with the known finiteness
bound for amplitudes. If the double-copy method could be applied to the form
factor, this would indicate an interesting ultraviolet finiteness bound for N=8
supergravity at five loops. The result is also expected to provide an essential
input for computing the five-loop non-planar cusp anomalous dimension.
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Review of AdS/CFT Integrability, Chapter III.4: Twist states and the
cusp anomalous dimension: We review the computation of the anomalous dimension of twist operators in
the planar limit of N=4 SYM using the asymptotic Bethe ansatz and demonstrate
how this quantity is obtained at weak, strong and intermediate values of the
coupling constant. The anomalous dimension of twist operators in the limit of
large Lorentz spin played a major role in the construction as well as in many
tests of the asymptotic Bethe equations, this aspect of the story is
emphasised.
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Majorana neutrino and the vacuum of Bogoliubov quasiparticle: The Lagrangian of the seesaw mechanism is C violating but the same Lagrangian
when re-written in terms of Majorana neutrinos is manifestly C invariant. To
resolve this puzzling feature, a relativistic analogue of Bogoliubov
transformation, which preserves CP but explicitly breaks C and P separately,
was introduced together with the notions of a Bogoliubov quasiparticle and an
analogue of the energy gap in BCS theory. The idea of Majorana neutrino as
Bogoliubov quasiparticle was then suggested. In this paper, we study the vacuum
structure of the Bogoliubov quasiparticle which becomes heavy by absorbing the
C-breaking. By treating an infinitesimally small C violating term as an
analogue of the chiral symmetry breaking nucleon mass in the model of Nambu and
Jona-Lasinio, we construct an explicit form of the vacuum of the Bogoliubov
quasiparticle which defines Majorana neutrinos in seesaw mechanism. The vacuum
of the Bogoliubov quasiparticle thus constructed has an analogous condensate
structure as the vacuum of the quasiparticle (nucleon) in the
Nambu--Jona-Lasinio model.
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Non-equilibrium dynamics in Holography: We investigate aspects of non-equilibrium dynamics of strongly coupled field
theories within holography. We establish a hydrodynamic description for
anomalous quantum field theories subject to a strong external field for the
first time in the literature. Within holography, we explicitly demonstrate
which transport coefficients are non-zero due to the chiral anomaly and thus
important for the transport. We show that the standard treatment of the
hydrodynamics for spontaneously broken translational invariance is more subtle
and has to be revised since the description is missing a novel thermodynamic
coefficient. Within holographic massive gravity, we lay out a road map for
extensions of hydrodynamics to momentum dissipation. Furthermore, we study the
imprint of spontaneously broken translations beyond linear response theory in
terms of periodically driven strongly coupled quantum field theories. Another
important non-equilibrium scenario specially important for the understanding of
our universe is quantum gravity in de-Sitter. Recently, the bold claim of the
so-called swampland conjectures has attracted great interest since it banishes
all stable theories of quantum gravity on de-Sitter with matter into swampland.
Within the well-defined framework of the DS/dS correspondence, we set out to
derive consistency conditions on the matter content in de-Sitter. Surprisingly,
our proposed bound is violated by any reasonable form of matter. In our
discussion, we find a novel one-parameter family of entangling surfaces. The
last chapter is dedicated to solvable irrelevant deformations in quantum field
theory -- the $T\bar T$ deformation. Within holography, we derive the
entanglement entropies for generic subintervals on a sphere. We also resolve
the confusion in the literature about a seeming mismatch between the
holographic field theory results for the entanglement entropy in general
dimensions.
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Differential Renormalization of a Yukawa Model with $γ_5$: We present a two-loop computation of the beta functions and the anomalous
dimensions of a $\gamma_5$-Yukawa model using differential renormalization. The
calculation is carried out in coordinate space without modifying the space-time
dimension and no ad-hoc prescription for $\gamma_5$ is needed.
It is shown that this procedure is specially suited for theories involving
$\gamma_5$, and it should be considered in analyzing chiral gauge theories.
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Intersecting branes, Higgs sector, and chirality from $\mathcal{N}=4$
SYM with soft SUSY breaking: We consider $SU(N)$ $\mathcal{N}=4$ super Yang-Mills with cubic and quadratic
soft SUSY breaking potential, such that the global $SU(4)_R$ is broken to
$SU(3)$ or further. As shown recently, this set-up supports a rich set of
non-trivial vacua with the geometry of self-intersecting $SU(3)$ branes in 6
extra dimensions. The zero modes on these branes can be interpreted as 3
generations of bosonic and chiral fermionic strings connecting the branes at
their intersections. Here, we uncover a large class of exact solutions
consisting of branes connected by Higgs condensates, leading to Yukawa
couplings between the chiral fermionic zero modes. Under certain decoupling
conditions, the backreaction of the Higgs on the branes vanishes exactly. The
resulting physics is that of a spontaneously broken chiral gauge theory on
branes with fluxes. In particular, we identify combined brane plus Higgs
configurations which lead to gauge fields that couple to chiral fermions at low
energy. This turns out to be quite close to the Standard Model and its
constructions via branes in string theory. As a by-product, we construct a
$G_2$-brane solution corresponding to a squashed fuzzy coadjoint orbit of
$G_2$.
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Supersymmetry Breaking with Zero Vacuum Energy in M-Theory Flux
Compactifications: An attractive mechanism to break supersymmetry in vacua with zero vacuum
energy arose in E_8 x E_8 heterotic models with hidden sector gaugino
condensate. An H-flux balances the exponentially small condensate on shell and
fixes the complex structure moduli. At quantum level this balancing is,
however, obstructed by the quantization of the H-flux. We show that the warped
flux compactification background in heterotic M-theory can solve this problem
through a warp-factor suppression of the integer flux relative to the
condensate. We discuss the suppression mechanism both in the M-theory and the
4-dimensional effective theory and provide a derivation of the condensate's
superpotential which is free of delta-function squared ambiguities.
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Charges of Monopole Operators in $\widehat{ADE}$ Chern-Simons Quiver
Gauge Theories: We compute R-charges of the BPS-monopole operators in $\mathcal{N} = 3$
$\widehat{ADE}$ Chern-Simons quiver gauge theories, along the lines of the work
of Benna, Klebanov and Klose in \cite{bkk}. These theories have a weakly
coupled UV completion in terms of $\mathcal{N}=3$ supersymmetric Chern-Simons
Yang-Mills theories. In the UV limit the monopole operators are well
approximated by classical solutions. We construct classical BPS and anti-BPS
monopole solutions to these theories which preserve $\frac{1}{3}$ supersymmetry
all along the RG flow. We compute the $SU(2)_R$ charges in these backgrounds
and show that the smallest possible value of quantised $SU(2)_R$ charge is zero
in each quiver theory.
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Holographic entanglement entropy and complexity in St$\ddot{u}$ckelberg
superconductor: The holographic superconductors, as one of the most important application of
gauge/gravity duality, promote the study of strongly coupled superconductors
via classical general relativity living in one higher dimension. One of the
interesting properties in holographic superconductor is the appearance of first
and second order phase transitions. Recently, another active studies in
holographic framework is the holographic entanglement entropy and complexity
evaluated from gravity side. In this note, we study the properties of the
holographic entanglement entropy and complexity crossing both first and second
order phase transitions in St$\ddot{u}$ckelberg superconductor. We find that
they behave differently in two types of phase transitions. We argue that
holographic entanglement entropy and complexity conjectured with the volume can
also be a possible probe to the type of superconducting phase transition.
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Instantons on noncommutative R^4, and (2,0) superconformal six
dimensional theory: We show that the resolution of moduli space of ideal instantons parameterizes
the instantons on non-commutative $\IR^{4}$. This moduli space appears as a
Higgs branch of the theory of $k$ $D0$-branes bound to $N$ $D4$-branes by the
expectation value of the $B$ field. It also appears as a regularized version of
the target space of supersymmetric quantum mechanics arising in the light cone
description of $(2,0)$ superconformal theories in six dimensions.
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Non-Commutative (Softly Broken) Supersymmetric Yang-Mills-Chern-Simons: We study d=2+1 non-commutative U(1) YMCS, concentrating on the one-loop
corrections to the propagator and to the dispersion relations. Unlike its
commutative counterpart, this model presents divergences and hence an IR/UV
mechanism, which we regularize by adding a Majorana gaugino of mass m_f, that
provides (softly broken) supersymmetry. The perturbative vacuum becomes stable
for a wide range of coupling and mass values, and tachyonic modes are generated
only in two regions of the parameters space. One such region corresponds to
removing the supersymmetric regulator (m_f >> m_g), restoring the well-known
IR/UV mixing phenomenon. The other one (for m_f ~ m_g/2 and large \theta) is
novel and peculiar of this model. The two tachyonic regions turn out to be very
different in nature. We conclude with some remarks on the theory's off-shell
unitarity.
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Emergent geometry through quantum entanglement in Matrix theories: In the setting of the Berenstein-Maldacena-Nastase Matrix theory, dual to
light-cone M-theory in a PP-wave background, we compute the Von Neumann
entanglement entropy between a probe giant graviton and a source. We
demonstrate that this entanglement entropy is directly and generally related to
the local tidal acceleration experienced by the probe. This establishes a new
map between local spacetime geometry and quantum entanglement, suggesting a
mechanism through which geometry emerges from Matrix quantum mechanics. We
extend this setting to light-cone M-theory in flat space, or the
Banks-Fischler-Shenker-Susskind Matrix model, and we conjecture a new general
relation between a certain measure of entanglement in Matrix theories and local
spacetime geometry. The relation involves a `c-tensor' that measures the
evolution of local transverse area and relates to the local energy-momentum
tensor measured by a probe.
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No resonant tunneling in standard scalar quantum field theory: We investigate the nature of resonant tunneling in Quantum Field Theory.
Following the pioneering work of Banks, Bender and Wu, we describe quantum
field theory in terms of infinite dimensional quantum mechanics and utilize the
``Most probable escape path'' (MPEP) as the class of paths which dominate the
path integral in the classically forbidden region. Considering a 1+1
dimensional field theory example we show that there are five conditions that
any associated bound state in the classically allowed region must satisfy if
resonant tunnelling is to occur, and we then proceed to show that it is
impossible to satisfy all five conditions simultaneously.
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A Skyrme Model with Novel Chiral Symmetry Breaking: An extension of the Skyrme model is presented in which derivative terms are
added that break chiral symmetry to isospin symmetry. The theory contains just
one new parameter and it reduces to the standard Skyrme model when this
symmetry breaking parameter vanishes. The same Faddeev-Bogomolny energy bound
applies for all parameter values, but the parameter can be tuned so that the
energy of the single Skyrmion is much closer to the bound than in the standard
Skyrme model. Applying the rational map approximation to multi-Skyrmions
suggests that, for a suitable value of the symmetry breaking parameter, binding
energies in this theory may be significantly more realistic than in the
standard Skyrme model.
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Excited states in the twisted XXZ spin chain: We compute the finite size spectrum for the spin 1/2 XXZ chain with twisted
boundary conditions, for anisotropy in the regime $0< \gamma <\pi/2$, and
arbitrary twist $\theta$. The string hypothesis is employed for treating
complex excitations. The Bethe Ansatz equtions are solved within a coupled
non-linear integral equation approach, with one equation for each type of
string. The root-of-unity quantum group invariant periodic chain reduces to the
XXZ_1/2 chain with a set of twist boundary conditions ($\pi/\gamma\in Z$,
$\theta$ an integer multiple of $\gamma$). For this model, the restricted
Hilbert space corresponds to an unitary conformal field theory, and we recover
all primary states in the Kac table in terms of states with specific twist and
strings.
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$\mathcal{A}$-theory: A brane world-volume theory with manifest
U-duality: In this paper, the ${\cal A}$-theory, an extension of F-theory, is described
as a fully U-duality covariant brane theory. This theory has some
distinguishing features not known from world-sheet models. In particular, seen
as a sigma model, both world-volume and target space coordinates are specific
representations of the same group (the U-duality group). The U-duality group in
question is an exceptional group (a split form of the $E_d$ series). The
structure of this group allows it to encompass both the T-duality group of
string theory as well as the general linear symmetry group of ${\cal
M}$-theory. ${\cal A}$-theory is defined by the current algebras in Hamiltonian
formalism, or by world-volume actions in Lagrangian formalism. The spacetime
coordinates are selfdual gauge fields on the world-volume, requiring the Gauss
law constraints tying the world-volume to spacetime. Solving the Gauss law
constraints/the Virasoro constraints gives the world-volume/spacetime
sectioning from ${\cal A}$-theory to ${\cal T}$-theory/ ${\cal M}$-theory
respectively. The ${\cal A}$-theory Lagrangian admits extended symmetry which
has not been observed previously in the literature, where the background fields
include both the spacetime and the world-volume gravitational fields. We also
constructed the four-point amplitude of ${\cal A}$-theory in the low energy
limit. The amplitude is written in a way that the U-duality symmetry is
manifest, but after solving the section condition, it reduces to the usual
four-graviton amplitude. In the previous papers, we have referred to this model
as F-theory, however, F-theory initiated by Vafa is now a big branch of string
theory as the study of elliptic fibrations, so we refer to these constructions
as generalized models of theory for all dimensions with all duality symmetries
as ${\cal A}$-theory.
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Holographic thermalization from non relativistic branes: In this paper, based on the fundamental principles of Gauge/gravity duality
and considering a \textit{global quench}, we probe the physics of
thermalization for a special class of strongly coupled non relativistic QFTs by
computing the entanglement entropy of the plasma. The isometry group of such
QFTs is comprised of the generators of the Schr\"odinger algebra which could be
precisely realized as an isometry group of the killing generators of an
asymptotically Schr\"odinger $ Dp $ brane space time. In our analysis, we note
that during the pre local stages of the thermal equilibrium the entanglement
entropy has a faster growth in time compared to its relativistic cousin.
However, it shows a linear growth during the post local stages of thermal
equilibrium where the so called tsunami velocity associated with the linear
growth of the entanglement entropy saturates to that of its value corresponding
to the relativistic scenario. Finally, we explore the saturation region and it
turns out that one must constraint certain parameters of the theory in a
specific way in order to have a discontinuous transitions at the point of
saturation.
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Holomorphic Classical Limit for Spin Effects in Gravitational and
Electromagnetic Scattering: We provide universal expressions for the classical piece of the amplitude
given by the graviton/photon exchange between massive particles of arbitrary
spin, at both tree and one loop level. In the gravitational case this leads to
higher order terms in the post-Newtonian expansion, which have been previously
used in the binary inspiral problem. The expressions are obtained in terms of a
contour integral that computes the Leading Singularity, which was recently
shown to encode the relevant information up to one loop. The classical limit is
performed along a holomorphic trajectory in the space of kinematics, such that
the leading order is enough to extract arbitrarily high multipole corrections.
These multipole interactions are given in terms of a recently proposed
representation for massive particles of any spin by Arkani-Hamed et al. This
explicitly shows universality of the multipole interactions in the effective
potential with respect to the spin of the scattered particles. We perform the
explicit match to standard EFT operators for $S=\frac{1}{2}$ and $S=1$. As a
natural byproduct we obtain the classical pieces up to one loop for the bending
of light.
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Stability and Symmetry Breaking for Closed String with Massive Point: The closed relativistic string carrying a point-like mass in the space with
nontrivial geometry is considered. For rotational states of this system
(resulting in non-trivial Regge trajectories) the stability problem is solved.
It was shown that rotations of the folded string with the massive point placed
at the rotational center are stable (with respect to small disturbances) if the
mass exceeds some critical value: $m>m_{cr}$. But these rotational states are
unstable in the opposite case $m<m_{cr}$. We can treat this effect as the
spontaneous symmetry breaking for the string state. Other classes of rotational
motions of this system have appeared to be stable. These results were obtained
both in numerical experiments and the analytical investigation of small
disturbances for the rotational states.
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Non-Cartan Mordell-Weil lattices of rational elliptic surfaces and
heterotic/F-theory compactifications: The Mordell-Weil lattices (MW lattices) associated to rational elliptic
surfaces are classified into 74 types. Among them, there are cases in which the
MW lattice is none of the weight lattices of simple Lie algebras or direct sums
thereof. We study how such "non-Cartan MW lattices" are realized in the
six-dimensional heterotic/F-theory compactifications. In this paper, we focus
on non-Cartan MW lattices that are torsion free and whose associated
singularity lattices are sublattices of $A_7$. For the heterotic string
compactification, a non-Cartan MW lattice yields an instanton gauge group $H$
with one or more $U(1)$ group(s). We give a method for computing massless
spectra via the index theorem and show that the $U(1)$ instanton number is
limited to be a multiple of some particular non-one integer. On the F-theory
side, we examine whether we can construct the corresponding threefold
geometries, i.e., rational elliptic surface fibrations over $P^1$. Except for
some cases, we obtain such geometries for specific distributions of instantons.
All the spectrum derived from those geometries completely match with the
heterotic results.
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Primordial Universe Inside the Black Hole and Inflation: We speculate that the early Universe was inside a primordial black hole. The
interior of the the black hole is a dS background and the two spacetimes are
separated on the surface of black hole's event horizon. We argue that this
picture provides a natural realization of inflation without invoking the
inflaton field. The black hole evaporation by Hawking radiation provides a
natural mechanism for terminating inflation so reheating and the hot big bang
cosmology starts from the evaporation of black hole to relativistic particles.
The quantum gravitational fluctuations at the boundary of black hole generate
the nearly scale invariant scalar and tensor perturbations with the ratio of
tensor to scalar power spectra at the order of $10^{-3}$. As the black hole
evaporates, the radius of its event horizon shrinks and the Hubble expansion
rate during inflation increases slowly so the quantum Hawking radiation
provides a novel mechanism for the violation of null energy condition in
cosmology.
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Circular orbit of a test particle and phase transition of a black hole: The radius of the circular orbit for the time-like or light-like test
particle in a background of general spherically symmetric spacetime is viewed
as a characterized quantity for the thermodynamic phase transition of the
corresponding black hole. We generally show that the phase transition
information of a black hole can be reflected by its surrounding particle's
circular orbit.
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Transformation of second-class into first-class constraints in
supersymmetric theories: We use the method due to Batalin, Fradkin, Fradkina, and Tyutin (BFFT) in
order to convert second-class into first-class constraints for some quantum
mechanics supersymmetric theories. The main point to be considered is that the
extended theory, where new auxiliary variables are introduced, has to be
supersymmetric too. This leads to some additional restrictions with respect the
conventional use of the BFFT formalism.
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Charged Dilaton Black Holes with a Cosmological Constant: The properties of static spherically symmetric black holes, which are either
electrically or magnetically charged, and which are coupled to the dilaton in
the presence of a cosmological constant, are considered. It is shown that such
solutions do not exist if the cosmological constant is positive (in arbitrary
spacetime dimension >= 4). However, asymptotically anti-de Sitter black hole
solutions with a single horizon do exist if the cosmological constant is
negative. These solutions are studied numerically in four dimensions and the
thermodynamic properties of the solutions are derived. The extreme solutions
are found to have zero entropy and infinite temperature for all non-zero values
of the dilaton coupling constant.
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Instanton Effects in ABJM Theory from Fermi Gas Approach: We study the instanton effects of the ABJM partition function using the Fermi
gas formalism. We compute the exact values of the partition function at the
Chern-Simons levels k=1,2,3,4,6 up to N=44,20,18,16,14 respectively, and
extract non-perturbative corrections from these exact results. Fitting the
resulting non-perturbative corrections by their expected forms from the Fermi
gas, we determine unknown parameters in them. After separating the oscillating
behavior of the grand potential, which originates in the periodicity of the
grand partition function, and the worldsheet instanton contribution, which is
computed from the topological string theory, we succeed in proposing an
analytical expression for the leading D2-instanton correction. Just as the
perturbative result, the instanton corrections to the partition function are
expressed in terms of the Airy function.
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More Pendants for Polya: Two loops in the SU(2) sector: We extend the methods of Spradlin and Volovich to compute the partition
function for a conformally-invariant gauge theory on R x S^3 in which the
dilatation operator is represented by a spin-chain Hamiltonian acting on pairs
of states, not necessarily nearest neighbors. A specific application of this is
the two-loop dilatation operator of the planar SU(2) subsector of the N=4 SU(N)
super Yang-Mills theory in the large-N limit. We compute the partition function
and Hagedorn temperature for this sector to second order in the gauge coupling.
The Hagedorn temperature is to be interpreted as giving the
exponentially-rising portion of the density of states of the SU(2) sector,
which may be a signal of stringy behavior in the dual theory.
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Radiative Corrections to the Aharonov-Bohm Scattering: We consider the scattering of relativistic electrons from a thin magnetic
flux tube and perturbatively calculate the order $\alpha$, radiative
correction, to the first order Born approximation. We show also that the second
order Born amplitude vanishes, and obtain a finite inclusive cross section for
the one-body scattering which incorporates soft photon bremsstrahlung effects.
Moreover, we determine the radiatively corrected Aharonov-Bohm potential and,
in particular, verify that an induced magnetic field is generated outside of
the flux tube.
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Rotating Attractors: We prove that, in a general higher derivative theory of gravity coupled to
abelian gauge fields and neutral scalar fields, the entropy and the near
horizon background of a rotating extremal black hole is obtained by extremizing
an entropy function which depends only on the parameters labeling the near
horizon background and the electric and magnetic charges and angular momentum
carried by the black hole. If the entropy function has a unique extremum then
this extremum must be independent of the asymptotic values of the moduli scalar
fields and the solution exhibits attractor behaviour. If the entropy function
has flat directions then the near horizon background is not uniquely determined
by the extremization equations and could depend on the asymptotic data on the
moduli fields, but the value of the entropy is still independent of this
asymptotic data. We illustrate these results in the context of two derivative
theories of gravity in several examples. These include Kerr black hole,
Kerr-Newman black hole, black holes in Kaluza-Klein theory, and black holes in
toroidally compactified heterotic string theory.
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Kinematical Reduction of Spatial Degrees of Freedom and Holographic
Relation in Yang's Quantized Space-Time Algebra: We try to find a possible origin of the holographic principle in the
Lorentz-covariant Yang's quantized space-time algebra (YSTA). YSTA, which is
intrinsically equipped with short- and long-scale parameters, $\lambda$ and
$R$, gives a finite number of spatial degrees of freedom for any bounded
spatial region, providing a basis for divergence-free quantum field theory.
Furthermore, it gives a definite kinematical reduction of spatial degrees of
freedom, compared with the ordinary lattice space. On account of the latter
fact, we find a certain kind of kinematical holographic relation in YSTA, which
may be regarded as a primordial form of the holographic principle suggested so
far in the framework of the present quantum theory that appears now in the
contraction limit of YSTA, $\lambda \to 0$ and $R \to \infty.$
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Dirichlet Topological Defects: We propose a class of field theories featuring solitonic solutions in which
topological defects can end when they intersect other defects of equal or
higher dimensionality. Such configurations may be termed ``Dirichlet
topological defects'', in analogy with the D-branes of string theory. Our
discussion focuses on defects in scalar field theories with either gauge or
global symmetries, in (3+1) dimensions; the types of defects considered include
walls ending on walls, strings on walls, and strings on strings.
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On the CFT Operator Spectrum at Large Global Charge: We calculate the anomalous dimensions of operators with large global charge
$J$ in certain strongly coupled conformal field theories in three dimensions,
such as the O(2) model and the supersymmetric fixed point with a single chiral
superfield and a $W = \Phi^3$ superpotential. Working in a $1/J$ expansion, we
find that the large-$J$ sector of both examples is controlled by a conformally
invariant effective Lagrangian for a Goldstone boson of the global symmetry.
For both these theories, we find that the lowest state with charge $J$ is
always a scalar operator whose dimension $\Delta_J$ satisfies the sum rule $
J^2 \Delta_J - \left( \tfrac{J^2}{2} + \tfrac{J}{4} + \tfrac{3}{16} \right)
\Delta_{J-1} - \left( \tfrac{J^2}{2} - \tfrac{J}{4} + \tfrac{3}{16} \right)
\Delta_{J+1} = 0.035147 $ up to corrections that vanish at large $J$. The
spectrum of low-lying excited states is also calculable explcitly: For example,
the second-lowest primary operator has spin two and dimension $\Delta\ll J +
\sqrt{3}$. In the supersymmetric case, the dimensions of all half-integer-spin
operators lie above the dimensions of the integer-spin operators by a gap of
order $J^{1/2}$. The propagation speeds of the Goldstone waves and heavy
fermions are $\frac{1}{\sqrt{2}}$ and $\pm \frac{1}{2}$ times the speed of
light, respectively. These values, including the negative one, are necessary
for the consistent realization of the superconformal symmetry at large $J$.
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Asymptotic Scalar Field Cosmology in String Theory: Asymptotic (late-time) cosmology depends on the asymptotic
(infinite-distance) limits of scalar field space in string theory. Such limits
feature an exponentially decaying potential $V \sim \exp(- c \phi)$ with
corresponding Hubble scale $H \sim \sqrt{\dot \phi^2 + 2 V} \sim \exp(-
\lambda_H \phi)$, and at least one tower of particles whose masses scale as $m
\sim \exp( - \lambda \phi)$, as required by the Distance Conjecture. In this
paper, we provide evidence that these coefficients satisfy the inequalities
$\sqrt{(d-1)/(d-2)} \geq \lambda_H \geq \lambda_{\text{lightest}} \geq
1/\sqrt{d-2}$ in $d$ spacetime dimensions, where $\lambda_{\text{lightest}}$ is
the $\lambda$ coefficient of the lightest tower. This means that at late times,
as the scalar field rolls to $\phi \rightarrow \infty$, the low-energy theory
remains a $d$-dimensional FRW cosmology with decelerated expansion, the light
towers of particles predicted by the Distance Conjecture remain at or above the
Hubble scale, and both the strong energy condition and the dominant energy
condition are satisfied.
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Acceleration-Enlarged Symmetries in Nonrelativistic Space-Time with a
Cosmological Constant: By considering the nonrelativistic limit of de-Sitter geometry one obtains
the nonrelativistic space-time with a cosmological constant and Newton-Hooke
(NH) symmetries. We show that the NH symmetry algebra can be enlarged by the
addition of the constant acceleration generators and endowed with central
extensions (one in any dimension (D) and three in D=(2+1)). We present a
classical Lagrangian and Hamiltonian framework for constructing models
quasi-invariant under enlarged NH symmetries which depend on three parameters
described by three nonvanishing central charges. The Hamiltonian dynamics then
splits into external and internal sectors with new non-commutative structures
of external and internal phase spaces. We show that in the limit of vanishing
cosmological constant the system reduces to the one presented in [1] which
possesses accelaration-enlarged Galilean symmetries.
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Aligned Natural Inflation and Moduli Stabilization from Anomalous $U(1)$
Gauge Symmetries: To obtain natural inflation with large tensor-to-scalar ratio in string
framework, we need a special moduli stabilization mechanism which can separate
the masses of real and imaginary components of K\"ahler moduli at different
scales, and achieve a trans-Planckian axion decay constant from sub-Planckian
axion decay constants. In this work, we stabilize the matter fields by F-terms
and the real components of K\"ahler moduli by D-terms of two anomalous
$U(1)_X\times U(1)_A$ symmetries strongly at high scales, while the
corresponding axions remain light due to their independence on the
Fayet-Iliopoulos (FI) term in moduli stabilization. The racetrack-type axion
superpotential is obtained from gaugino condensations of the hidden gauge
symmetries $SU(n)\times SU(m)$ with massive matter fields in the bi-fundamental
respresentations. The axion alignment via Kim-Nilles-Pelroso (KNP) mechanism
corresponds to an approximate $S_2$ exchange symmetry of two K\"ahler moduli in
our model, and a slightly $S_2$ symmetry breaking leads to the natural
inflation with super-Planckian decay constant.
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Inflationary Cosmology: I give a general review of the history of inflationary cosmology and of its
present status.
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Probe D-branes in Superconformal Field Theories: We overview the main configurations of D-brane probes in the AdS_5 x X^5
background of type IIB string theory (X^5 being a Sasaki-Einstein manifold),
and examine their most salient features from the point of view of the dual
quiver superconformal field theory.
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Coordinate-space singularities of massless gauge theories: The structure of singularities in perturbative massless gauge theories is
investigated in coordinate space. The pinch singularities in coordinate-space
integrals occur at configurations of vertices which have a direct
interpretation in terms of physical scattering of particles in real space-time
in the same way as for the loop momenta in the case of momentum-space
singularities. In the analysis of vertex functions in coordinate space, the
well-known factorization into hard, soft, and jet functions is found. By
power-counting arguments, it is found that coordinate-space integrals of vertex
functions have logarithmic divergences at worst.
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No interactions for a collection of spin-two fields intermediated by a
massive Rarita-Schwinger field: The cross-couplings among several massless spin-two fields (described in the
free limit by a sum of Pauli-Fierz actions) in the presence of a massive
Rarita-Schwinger field are investigated in the framework of the deformation
theory based on local BRST cohomology. Under the hypotheses of locality,
smoothness of the interactions in the coupling constant, Poincare invariance,
Lorentz covariance, and the preservation of the number of derivatives on each
field, we prove that there are no consistent cross-interactions among different
gravitons with a positively defined metric in internal space in the presence of
a massive Rarita-Schwinger field. The basic features of the couplings between a
single Pauli-Fierz field and a massive Rarita-Schwinger field are also
emphasized.
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Strong Coupling Problem with Time-Varying Sound Speed: For a single scalar field with unit sound speed minimally coupled to Einstein
gravity, there are exactly three distinct cosmological solutions which produce
a scale invariant spectrum of curvature perturbations in a dynamical attractor
background, assuming vacuum initial conditions: slow-roll inflation; a slowly
contracting adiabatic ekpyrotic phase, described by a rapidly-varying equation
of state; and an adiabatic ekpyrotic phase on a slowly expanding background. Of
these three, only inflation remains weakly coupled over a wide range of modes,
the other scenarios can produce at most 12 e-folds of scale invariant and
gaussian modes. In this paper, we investigate how allowing the speed of sound
of fluctuations to evolve in time affects this classification. While in the
presence of a variable sound speed there are many more scenarios which are
scale invariant at the level of the two-point function, they generically suffer
from strong coupling problems similar to those in the canonical case. There is,
however, an exceptional case with superluminal sound speed, which suppresses
non-gaussianities and somewhat alleviates strong coupling issues. We focus on a
particular realization of this limit and show these scenarios are constrained
and only able to produce at most 28 e-folds of scale invariant and gaussian
perturbations. A similar bound should hold more generally --- the condition
results from the combined requirements of matching the observed amplitude of
curvature perturbations, demanding that the Hubble parameter remain
sub-Planckian and keeping non-gaussianities under control. We therefore
conclude that inflation remains the unique scenario, assuming a single degree
of freedom on an attractor background, capable of producing arbitrarily many
scale invariant modes while remaining weakly coupled. Alternative mechanisms
must inevitably be unstable or rely on multiple degrees of freedom.
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Massless Thirring model in canonical quantization scheme: It is shown that the exact solvability of the massless Thirring model in the
canonical quantization scheme originates from the intrinsic linearizability of
its Heisenberg equations in the method of dynamical mappings. The corresponding
role of inequivalent representations of free massless Dirac field is
elucidated.
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Field Redefinitions in String Theory as a Solution Generating Technique: The purpose of this work is to show that there exists an additional
invariance of the $\beta$-function equations of string theory on
$d+1$-dimensional targets with $d$ toroidal isometries. It corresponds to a
shift of the dilaton field and a scaling of the lapse function, and is
reminiscent of string field redefinitions. While it preserves the form of the
$\beta$-function equations, it changes the effective action and the solutions.
Thus it can be used as a solution generating technique. It is particularly
interesting to note that there are field redefinitions which map solutions with
non-zero string cosmological constant to those with zero cosmological constant.
Several simple examples involving two- and three-dimensional black holes and
black strings are provided to illustrate the role of such field redefinitions.
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Deeper discussion of Schrödinger invariant and Logarithmic sectors of
higher-curvature gravity: The aim of this paper is to explore D-dimensional theories of pure gravity
whose space of solutions contains certain class of AdS-waves, including in
particular Schrodinger invariant spacetimes. This amounts to consider higher
order theories, and the natural case to start with is to analyze generic
square-curvature corrections to Einstein-Hilbert action. In this case, the
Schrodinger invariant sector in the space of solutions arises for a special
relation between the coupling constants appearing in the action. On the other
hand, besides the Schrodinger invariant configurations, logarithmic branches
similar to those of the so-called Log-gravity are also shown to emerge for
another special choice of the coupling constants. These Log solutions can be
interpreted as the superposition of the massless mode of General Relativity and
two scalar modes that saturate the Breitenlohner-Freedman bound (BF) of the AdS
space on which they propagate. These solutions are higher-dimensional analogues
of those appearing in three-dimensional massive gravities with relaxed AdS_3
asymptotic. Other sectors of the space of solutions of higher-curvature
theories correspond to oscillatory configurations, which happen to be below the
BF bound. Also, there is a fully degenerated sector, for which any wave profile
is admitted. We comment on the relation between this degeneracy and the
non-renormalization of the dynamical exponent of the Schrodinger spaces. Our
analysis also includes more general gravitational actions with non-polynomial
corrections consisting of arbitrary functions of the square-curvature
invariants. The same sectors of solutions are shown to exist for this more
general family of theories. We finally consider the Chern-Simons modified
gravity in four dimensions, for which we derive both the Schrodinger invariant
as well as the logarithmic sectors.
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On the Spontaneous Identity of Chiral and Super Symmetry Breaking in
Pure Super Yang Mills Theories: We show that in supersymmetric pure Yang Mills theories with arbitrary simple
gauge group, the spontaneous breaking of chiral fermionic and bosonic charge by
the associated gaugino and gauge boson condensates implies the spontaneous
breaking of supersymmetry by the condensate of the underlying Lagrangian
density. The explicit breaking of the restricted fermionic charge through the
chiral anomaly is deferred to a secondary stage in the elimination of infrared
singularities or long range forces.
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Holographic Lattices, Dimers, and Glasses: We holographically engineer a periodic lattice of localized fermionic
impurities within a plasma medium by putting an array of probe D5-branes in the
background produced by N D3-branes. Thermodynamic quantities are computed in
the large N limit via the holographic dictionary. We then dope the lattice by
replacing some of the D5-branes by anti-D5-branes. In the large N limit, we
determine the critical temperature below which the system dimerizes with bond
ordering. Finally, we argue that for the special case of a square lattice our
system is glassy at large but finite N, with the low temperature physics
dominated by a huge collection of metastable dimerized configurations without
long-range order, connected only through tunneling events.
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Chaos in the Mass-Deformed ABJM Model: Chaotic dynamics of the mass deformed ABJM model is explored. To do so, we
consider spatially uniform fields and obtain a family of reduced effective
Lagrangians by tracing over ansatz configurations involving fuzzy two-spheres
with collective time dependence. We examine how the largest Lyapunov exponent,
$\lambda_L$, changes as a function of $E/N^2$, where $N$ is the matrix size. In
particular, we inspect the temperature dependence of $\lambda_L$ and present
upper bounds on the temperature above which $\lambda_L$ values comply with the
MSS bound, $ \lambda_L \leq 2 \pi T $, and below which it will eventually be
not obeyed.
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Lectures on String Theory: This is a one semester course on bosonic string theory aimed at beginning
graduate students. The lectures assume a working knowledge of quantum field
theory and general relativity. Contents:
1. The Classical String
2. The Quantum String
3. Open Strings and D-Branes
4. Introducing Conformal Field Theory
5. The Polyakov Path Integral and Ghosts
6. String Interactions
7. The Low-Energy Effective Action
8. Compactification and T-Duality
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Exact Solutions of Kemmer Equation for Coulomb Potential: This article illustrates the bound states of Kemmer equation for spin-1
particles. The asymptotic, exact and Coulomb field solutions are obtained by
using action principle. In the conclusion the energy spectrum of spin-1
particles moving in a Coulomb potential compared with the energy spectrum of
spin-0 and spin-1/2 particles.
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Diffusion of Wilson Loops: A phenomenological analysis of the distribution of Wilson loops in SU(2)
Yang-Mills theory is presented in which Wilson loop distributions are described
as the result of a diffusion process on the group manifold. It is shown that,
in the absence of forces, diffusion implies Casimir scaling and, conversely,
exact Casimir scaling implies free diffusion. Screening processes occur if
diffusion takes place in a potential. The crucial distinction between screening
of fundamental and adjoint loops is formulated as a symmetry property related
to the center symmetry of the underlying gauge theory. The results are
expressed in terms of an effective Wilson loop action and compared with various
limits of SU(2) Yang-Mills theory.
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Computation of the winding number diffusion rate due to the cosmological
sphaleron: A detailed quantitative analysis of the transition process mediated by a
sphaleron type non-Abelian gauge field configuration in a static Einstein
universe is carried out. By examining spectra of the fluctuation operators and
applying the zeta function regularization scheme, a closed analytical
expression for the transition rate at the one-loop level is derived. This is a
unique example of an exact solution for a sphaleron model in $3+1$ spacetime
dimensions.
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Gravitational Corner Conditions in Holography: Contrary to popular belief, asymptotically anti-de Sitter solutions of
gravitational theories cannot be obtained by taking initial data (satisfying
the constraints) on a spacelike surface, and choosing an arbitrary conformal
metric on the timelike boundary at infinity. There are an infinite number of
corner conditions that also must be satisfied where the initial data surface
hits the boundary. These are well known to mathematical relativists, but to
make them more widely known we give a simple explanation of why these
conditions exist and discuss some of their consequences. An example is given
which illustrates their power. Some implications for holography are also
mentioned.
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Entanglement entropy of asymptotically flat non-extremal and extremal
black holes with an island: The island rule for the entanglement entropy is applied to an eternal
Reissner-Nordstr\"om black hole. The key ingredient is that the black hole is
assumed to be in thermal equilibrium with a heat bath of an arbitrary
temperature and so the generalized entropy is treated as being off-shell.
Taking the on-shell condition to the off-shell generalized entropy, we find the
generalized entropy and then obtain the entanglement entropy following the
island rule. For the non-extremal black hole, the entanglement entropy grows
linearly in time and can be saturated after the Page time as expected. The
entanglement entropy also has a well-defined Schwarzschild limit. In the
extremal black hole, the island prescription provides a logarithmically growing
entanglement entropy in time and a constant entanglement entropy after the Page
time. In the extremal black hole, the boundary of the island hits the curvature
singularity where the semi-classical approximations appear invalid. To avoid
encountering the curvature singularity, we apply this procedure to the Hayward
black hole regular at the origin. Consequently, the presence of the island in
extremal black holes can provide a finite entanglement entropy, which might
imply non-trivial vacuum configurations of extremal black holes.
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Refinements of the Weyl pure geometrical thick branes from
information-entropic measure: This letter aims to analyse the so-called configurational entropy in the Weyl
pure geometrical thick brane model. The Weyl structure plays a prominent role
in the thickness of this model. We find a set of parameters associated to the
brane width where the configurational entropy exhibits critical points.
Furthermore, we show, by means of this information-theoretical measure, that a
stricter bound on the parameter of Weyl pure geometrical brane model arises
from the CE.
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Monopoles, Dyons and Theta Term in Dirac-Born-Infeld Theory: We present dyon solutions to an SU(2) Dirac-Born-Infeld (DBI) gauge theory
coupled to a Higgs triplet. We consider different non-Abelian extensions of the
DBI action and study the resulting solutions numerically, comparing them with
the standard Julia-Zee dyons. We discuss the existence of a critical value of
$\beta$, the Born-Infeld absolute field parameter, below which the solution
ceases to exist. We also analyse the effect of modifying the DBI action so as
to include the analogous of the $\theta$ term, showing that Witten formula for
the dyon charge also holds in DBI theories.
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Complex sine-Gordon Theory for Coherent Optical Pulse Propagation: It is shown that the McCall-Hahn theory of self-induced transparency in
coherent optical pulse propagation can be identified with the complex
sine-Gordon theory in the sharp line limit. We reformulate the theory in terms
of the deformed gauged Wess-Zumino-Witten sigma model and address various new
aspects of self-induced transparency.
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A note on the third way consistent deformation of Yang-Mills theory: Three-dimensional Yang-Mills theory allows for a deformation quadratic in the
field strengths which can not be integrated to a local action without auxiliary
fields. Yet, its covariant divergence consistently vanishes after iterating the
equation, realizing a spin-1 analogue of `minimal massive gravity', which has
been dubbed `third way consistent'. In this note, we show that after
dualization of the three-dimensional gauge fields, the model possesses a
natural action as a Chern-Simons coupled gauged sigma model. In this dual
formulation, coupling to matter and to gravity becomes straightforward. As a
direct application, we derive the coupling of the model to N=1 supergravity.
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An Update on Brane Supersymmetry Breaking: "Brane supersymmetry breaking" is a peculiar phenomenon that can occur in
perturbative orientifold vacua. It results from the simultaneous presence, in
the vacuum, of non-mutually BPS sets of BPS branes and orientifolds, which
leave behind a net tension and thus a runaway potential, but no tachyons. In
the simplest ten-dimensional realization, the low-lying modes combine the
closed sector of type-I supergravity with an open sector including USp(32)
gauge bosons, fermions in the antisymmetric 495 and an additional singlet
playing the role of a goldstino. We review some properties of this system and
of other non-tachyonic models in ten dimensions with broken supersymmetry, and
we illustrate some puzzles that their very existence raises, together with some
applications that they have stimulated.
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Utilizing Enumerative Methods in Quantum Electrodynamics: In this paper it is shown that many of the observables in QED-type theories
can be realized in terms of a combinatorial structure called chord diagrams.
One major advantage of this representation is that the asymptotic behaviour of
the corresponding Green functions can be captured completely without appealing
to the usual approach of singularity analysis. This relation also reveals the
unexplained correlation between the number of diagrams in Yukawa theory and the
diagrams in quenched QED.
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Resonance in Asymmetric Warped Geometry: We study the spectrum of an asymmetric warped braneworld model with different
AdS curvatures on either side of the brane. In addition to the RS-like modes we
find a resonance state. Its mass is proportional to the geometric mean of the
two AdS curvature scales, while the difference between them determines the
strength of the resonance peak. There is a complementarity between the RS
zero-mode and the resonance: making the asymmetry stronger weakens the
zero-mode but strengthens the resonance, and vice versa. We calculate
numerically the braneworld gravitational potential and discuss the holographic
correspondence for the asymmetric model.
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Spinors in non-relativistic Chern-Simons electrodynamics: It is shown that the non-relativistic `Dirac' equation of L\'evy-Leblond, we
used recently to describe a spin $1/2$ field interacting non-relativistically
with a Chern-Simons gauge field, can be obtained by lightlike reduction from
$3+1$ dimensions. This allows us to prove that the system is Schr\"odinger
symmetric. A spinor representation of the Schr\"odinger group is presented.
Static, self-dual solutions, describing spinor vortices are given and shown to
be the non-relativistic limits of the fermionic vortices found by Cho et al.
The construction is extended to external harmonic and uniform magnetic fields.
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Existence Theorem for Split Involution Constraint Algebra: Existence theorem is proven for the generating equations of the split
involution constraint algebra. The structure of the general solution is
established, and the characteristic arbitrariness in generating functions is
described.
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Symplectic critical models in $6+ε$ dimensions: We consider nontrivial critical models in $d=6+\epsilon$ spacetime dimensions
with anticommuting scalars transforming under the symplectic group
$\text{Sp}(N)$. These models are nonunitary, but the couplings are real and all
operator dimensions are positive. At large $N$ we can take $\epsilon\to1$
consistently with the loop expansion and thus provide evidence that these
theories may be used to define critical models in $d=7$. The relation of these
theories to critical $\text{Sp}(N)$ theories, defined similarly to the
well-known critical $\text{O}(N)$ theories, is examined, and some similarities
are pointed out.
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Wilson loops in SYM theory: from weak to strong coupling: We review Wilson loops in N=4 supersymmetric Yang-Mills theory with emphasis
on the exact results. The implications are discussed in the context of the
AdS/CFT correspondence.
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Uncovering Infinite Symmetries on [p,q] 7-branes: Kac-Moody Algebras and
Beyond: In a previous paper we explored how conjugacy classes of the modular group
classify the symmetry algebras that arise on type IIB [p,q] 7-branes. The
Kodaira list of finite Lie algebras completely fills the elliptic classes as
well as some parabolic classes. Loop algebras of E_N fill additional parabolic
classes, and exotic finite algebras, hyperbolic extensions of E_N and more
general indefinite Lie algebras fill the hyperbolic classes. Since they
correspond to brane configurations that cannot be made into strict
singularities, these non-Kodaira algebras are spectrum generating and organize
towers of massive BPS states into representations. The smallest brane
configuration with unit monodromy gives rise to the loop algebra \hat{E}_9
which plays a central role in the theory. We elucidate the patterns of
enhancement relating E_8, E_9, \hat{E}_9 and E_10. We examine configurations of
24 7-branes relevant to type IIB compactifications on a two-sphere, or F-theory
on K3. A particularly symmetric configuration separates the 7-branes into two
groups of twelve branes and the massive BPS spectrum is organized by E_10 +
E_10.
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Amplitude Relations in Non-linear Sigma Model: In this paper, we investigate tree-level scattering amplitude relations in
$U(N)$ non-linear sigma model. We use Cayley parametrization. As was shown in
the recent works [23,24] both on-shell amplitudes and off-shell currents with
odd points have to vanish under Cayley parametrization. We prove the off-shell
$U(1)$ identity and fundamental BCJ relation for even-point currents. By taking
the on-shell limits of the off-shell relations, we show that the color-ordered
tree amplitudes with even points satisfy $U(1)$-decoupling identity and
fundamental BCJ relation, which have the same formations within Yang-Mills
theory. We further state that all the on-shell general KK, BCJ relations as
well as the minimal-basis expansion are also satisfied by color-ordered tree
amplitudes. As a consequence of the relations among color-ordered amplitudes,
the total $2m$-point tree amplitudes satisfy DDM form of color decomposition as
well as KLT relation.
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D-brane States and Disk Amplitudes in OSp Invariant Closed String Field
Theory: We construct solitonic states in the OSp invariant string field theory, which
are BRST invariant in the leading order of regularization parameter $\epsilon$.
We calculate the disk amplitudes using these solitonic states and show that
they describe D-branes and ghost D-branes.
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BPS states of D=4 N=1 supersymmetry: We find the combinations of momentum and domain-wall charges corresponding to
BPS states preserving 1/4, 1/2 or 3/4 of D=4 N=1 supersymmetry, and we show how
the supersymmetry algebra implies their stability. These states form the
boundary of the convex cone associated with the Jordan algebra of $4\times 4$
real symmetric matrices, and we explore some implications of the associated
geometry. For the Wess-Zumino model we derive the conditions for preservation
of 1/4 supersymmetry when one of two parallel domain-walls is rotated and in
addition show that this model does not admit any classical configurations with
3/4 supersymmetry. Our analysis also provides information about BPS states of
N=1 D=4 anti-de Sitter supersymmetry.
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S-Duality and Noncommutative Gauge Theory: It is conjectured that strongly coupled, spatially noncommutative
$\mathcal{N}=4$ Yang-Mills theory has a dual description as a weakly coupled
open string theory in a near critical electric field, and that this dual theory
is fully decoupled from closed strings. Evidence for this conjecture is given
by the absence of physical closed string poles in the non-planar one-loop open
string diagram. The open string theory can be viewed as living in a geometry in
which space and time coordinates do not commute.
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Hamiltonian formalism for Bose excitations in a plasma with a
non-Abelian interaction: We have developed the Hamiltonian theory for collective longitudinally
polarized colorless excitations (plasmons) in a high-temperature gluon plasma
using the general formalism for constructing the wave theory in nonlinear media
with dispersion, which was developed by V.E. Zakharov. In this approach, we
have explicitly obtained a special canonical transformation that makes it
possible to simplify the Hamiltonian of interaction of soft gluon excitations
and, hence, to derive a new effective Hamiltonian. The approach developed here
is used for constructing a Boltzmann-type kinetic equation describing elastic
scattering of collective longitudinally polarized excitations in a gluon plasma
as well as the effect of the so-called nonlinear Landau damping. We have
performed detailed comparison of the effective amplitude of the plasmon-plasmon
interaction, which is determined using the classical Hamilton theory, with the
corresponding matrix element calculated in the framework of high-temperature
quantum chromodynamics; this has enabled us to determine applicability limits
for the purely classical approach described in this study.
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Instantons in the U(1) Born-Infeld Theory and Noncommutative Gauge
Theory: We derive a BPS-type bound for four-dimensional Born-Infeld action with
constant B field background. The supersymmetric configuration saturates this
bound and is regarded as an analog of instanton in U(1) gauge theory.
Furthermore, we find the explicit solutions of this BPS condition. These
solutions have a finite action proportional to the instanton number and
represent D(p-4)-branes within a Dp-brane although they have a singularity at
the origin. Some relations to the noncommutative U(1) instanton are discussed.
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Gauge transformations are not canonical transformations: In classical mechanics, we can describe the dynamics of a given system using
either the Lagrangian formalism or the Hamiltonian formalism, the choice of
either one being determined by whether one wants to deal with a second degree
differential equation or a pair of first degree ones. For the former approach,
we know that the Euler-Lagrange equation of motion remains invariant under
additive total derivative with respect to time of any function of coordinates
and time in the Lagrangian function, whereas the latter one is invariant under
canonical transformations. In this short paper we address the question whether
the transformation that leaves the Euler-Lagrange equation of motion invariant
is also a canonical transformation and show that it is not.
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Nonperturbative renormalization of the lattice Sommerfield vector model: The lattice Sommerfield model, describing a massive vector gauge field
coupled to a light fermion in 2d, is an ideal candidate to verify perturbative
conclusions. In contrast with continuum exact solutions, we prove that there is
no infinite field renormalization, implying the reduction of the degree of the
ultraviolet divergence, and that anomalies are non renormalized. Such features
are the counterpart of analogue properties at the basis of the Standard model
perturbative renormalizability. The results are non-perturbative, in the sense
that the averages of gauge invariant observables are expressed in terms of
convergent expansions uniformly in the lattice and volume.
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Neutral Signature Gauged Supergravity Solutions: We classify all supersymmetric solutions of minimal D=4 gauged supergravity
with (2,2) signature and a positive cosmological constant which admit exactly
one Killing spinor. This classification produces a geometric structure which is
more general than that found for previous classifications of N=2 supersymmetric
solutions of this theory. We illustrate how the N=2 solutions which consist of
a fibration over a 3-dimensional Lorentzian Gauduchon-Tod base space can be
written in terms of this more generic geometric structure.
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N=1 Heterotic/F-Theory Duality: We review aspects of N=1 duality between the heterotic string and F-theory.
After a description of string duality intended for the non-specialist the
framework and the constraints for heterotic/F-theory compactifications are
presented. The computations of the necessary Calabi-Yau manifold and vector
bundle data, involving characteristic classes and bundle moduli, are given in
detail. The matching of the spectrum of chiral multiplets and of the number of
heterotic five-branes respectively F-theory three-branes, needed for anomaly
cancellation in four-dimensional vacua, is pointed out. Several examples of
four-dimensional dual pairs are constructed where on both sides the geometry of
the involved manifolds relies on del Pezzo surfaces.
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Polyakov-Loops and Fermionic Zero Modes in QCD2 on the Torus: A simple derivation of the free energy and expectation values of
Polyakov-loops in $QCD_2$ via path integral methods is given. In the chosen
gauge (which can be generalized to 4 dimensions) without Gribov-copies the
Fadeev-Popov determinant and the integration over the space component of the
gauge field cancel exactly and we are left only with an integration over the
zero components of the gauge field in the Cartan sub-algebra. This way the
Polyakov-loop operators become Vertex-operators in a simple quantum mechanical
model. The number of fermionic zero modes is related to the winding-numbers of
$A_0$ in this gauge.
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Signs of the time: Melonic theories over diverse number systems: Melonic field theories are defined over the $p$-adic numbers with the help of
a sign character. Our construction works over the reals as well as the
$p$-adics, and it includes the fermionic and bosonic Klebanov-Tarnopolsky
models as special cases; depending on the sign character, the symmetry group of
the field theory can be either orthogonal or symplectic. Analysis of the
Schwinger-Dyson equation for the two-point function in the leading melonic
limit shows that power law scaling behavior in the infrared arises for
fermionic theories when the sign character is non-trivial, and for bosonic
theories when the sign character is trivial. In certain cases, the
Schwinger-Dyson equation can be solved exactly using a quartic polynomial
equation, and the solution interpolates between the ultraviolet scaling
controlled by the spectral parameter and the universal infrared scaling. As a
by-product of our analysis, we see that melonic field theories defined over the
real numbers can be modified by replacing the time derivative by a bilocal
kinetic term with a continuously variable spectral parameter. The infrared
scaling of the resulting two-point function is universal, independent of the
spectral parameter of the ultraviolet theory.
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Super-quantum curves from super-eigenvalue models: In modern mathematical and theoretical physics various generalizations, in
particular supersymmetric or quantum, of Riemann surfaces and complex algebraic
curves play a prominent role. We show that such supersymmetric and quantum
generalizations can be combined together, and construct supersymmetric quantum
curves, or super-quantum curves for short. Our analysis is conducted in the
formalism of super-eigenvalue models: we introduce $\beta$-deformed version of
those models, and derive differential equations for associated
$\alpha/\beta$-deformed super-matrix integrals. We show that for a given model
there exists an infinite number of such differential equations, which we
identify as super-quantum curves, and which are in one-to-one correspondence
with, and have the structure of, super-Virasoro singular vectors. We discuss
potential applications of super-quantum curves and prospects of other
generalizations.
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Wrapping in maximally supersymmetric and marginally deformed N=4
Yang-Mills: In this note we give evidence for an equality of the spectra, including
wrapping, of the SU(2)-sector spin chain for real deformations beta and
beta+1/L, in marginally beta-deformed N=4 Yang-Mills, which appears after
relaxing the cyclicity constraint. Evidence for the equality is given by
evaluating the first wrapping correction to the energy of the undeformed magnon
of momentum pi, and the beta=1/2, physical magnon, for several spin chain
lengths L. We also show that the term of maximal transcendentality coincides
for both magnons to all L. As a by-product we provide an expression for the
first wrapping correction to the beta = 1/2 single-magnon operator dimension,
valid for all even L. We then apply the symmetry to the magnon dispersion
relation of N=4, obtaining its first wrapping correction for a discrete set of
magnon momenta.
|
Differential geometry with a projection: Application to double field
theory: In recent development of double field theory, as for the description of the
massless sector of closed strings, the spacetime dimension is formally doubled,
i.e. from D to D+D, and the T-duality is realized manifestly as a global O(D,D)
rotation. In this paper, we conceive a differential geometry characterized by a
O(D,D) symmetric projection, as the underlying mathematical structure of double
field theory. We introduce a differential operator compatible with the
projection, which, contracted with the projection, can be covariantized and may
replace the ordinary derivatives in the generalized Lie derivative that
generates the gauge symmetry of double field theory. We construct various gauge
covariant tensors which include a scalar and a tensor carrying two O(D,D)
vector indices.
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Moulting Black Holes: We find a family of novel supersymmetric phases of the D1-D5 CFT, which in
certain ranges of charges have more entropy than all known ensembles. We also
find bulk BPS configurations that exist in the same range of parameters as
these phases, and have more entropy than a BMPV black hole; they can be thought
of as coming from a BMPV black hole shedding a "hair" condensate outside of the
horizon. The entropy of the bulk configurations is smaller than that of the CFT
phases, which indicates that some of the CFT states are lifted at strong
coupling. Neither the bulk nor the boundary phases are captured by the elliptic
genus, which makes the coincidence of the phase boundaries particularly
remarkable. Our configurations are supersymmetric, have non-Cardy-like entropy,
and are the first instance of a black hole entropy enigma with a controlled CFT
dual. Furthermore, contrary to common lore, these objects exist in a region of
parameter space (between the "cosmic censorship bound" and the "unitarity
bound") where no black holes were thought to exist.
|
Superconformal mechanics: We survey the salient features and problems of conformal and superconformal
mechanics and portray some of its developments over the past decade. Both
classical and quantum issues of single- and multiparticle systems are covered.
|
A note on string solutions in AdS_3: We systematically search for classical open string solutions in AdS_3 within
the general class expressed by elliptic functions (i.e., the genus-one
finite-gap solutions). By explicitly solving the reality and Virasoro
conditions, we give a classification of the allowed solutions. When the
elliptic modulus degenerates, we find a class of solutions with six null
boundaries, among which two pairs are collinear. By adding the S^1 sector, we
also find four-cusp solutions with null boundaries expressed by the elliptic
functions.
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The universality of black hole thermodynamics: The thermodynamic properties of black holes -- temperature, entropy and
radiation rates -- are usually associated with the presence of a horizon. We
argue that any Extremely Compact Object (ECO) must have the {\it same}
thermodynamic properties. Quantum fields just outside the surface of an ECO
have a large negative Casimir energy similar to the Boulware vacuum of black
holes. If the thermal radiation emanating from the ECO does not fill the
near-surface region at the local Unruh temperature, then we find that no
solution of gravity equations is possible. In string theory, black holes
microstates are horizonless quantum objects called fuzzballs that are expected
to have a surface $\sim l_p$ outside $r=2GM$; thus the information puzzle is
resolved while preserving the semiclassical thermodynamics of black holes.
|
Chiral Symmetry Breaking and Stability of the Magnetized Vacuum: The recent claim [arXiv:hep-th/0603070, arXiv:hep-th/0605020] that there
exists in QED a maximum magnetic field of 10^{42} G, above which the magnetized
vacuum becomes unstable with respect to the so-called "positronium collapse" is
critically examined and unequivocally refuted.
|
Covariant Quantization of BFNC Super Yang-Mills Theories and Supergauge
Invariance: To construct renormalizable gauge model in Bosonic-Fermionic noncommutative
(BFNC) superspace, we replace the ordinary products of super Yang-Mills model
by BFNC star products. To study the renormalization property of the deformed
action, we obtain the one-loop 1PI effective action by using background field
method at the first order of BFNC parameters. We also verify the BFNC
supergauge invariance of the effective action. Because there are new terms in
effective action, the deformed action is not renormalizable. This imply that
additional terms should be added to the deformed action.
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Closed Superstring in Noncommutative Compact Spacetime: In this paper we study the effects of noncommutativity on a closed
superstring propagating in the spacetime that is compactified on tori. The
effects of compactification and noncommutativity appear in the momentum,
quantization, supercurrent, super-conformal generators and in the boundary
state of the closed superstring emitted from a D$_p$-brane with the
NS$\otimes$NS background $B$-field.
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k-Mouflage gravity: We introduce a large class of scalar-tensor theories where gravity becomes
stronger at large distances via the exchange of a scalar that mixes with the
graviton. At small distances, i.e. large curvature, the scalar is screened via
an analog of the Vainshtein mechanism of massive gravity. The crossover
distance between the two regimes can be made cosmological by an appropriate
choice of the parameters.
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Open & Closed vs. Pure Open String One-Loop Amplitudes: We express one-loop string amplitudes involving both open and closed strings
as sum over pure open string amplitudes. These findings generalize the
analogous tree-level result to higher loops and extend the tree-level
observation that in gravitational amplitudes a graviton can be traded for two
gluons. Our results are derived from analytic continuation of closed string
world-sheet coordinates on the cylinder resulting in pairs of real open string
coordinates located at the two cylinder boundaries subject to a one-loop
kernel. The latter depends on the loop momentum flowing between the two
cylinder boundaries and relates to intersection theory for twisted cycles.
Finally, contact is made with one-loop open string monodromy relations. The
latter contain a boundary term, which is related to non-physical contours on
the cylinder. A physical interpretation of the latter in terms of a closed
string insertion is given.
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One-loop Amplitudes in the Worldline Formalism: We summarize recent progress in applying the worldline formalism to the
analytic calculation of one-loop N-point amplitudes. This string-inspired
approach is well-adapted to avoiding some of the calculational inefficiencies
of the standard Feynman diagram approach, most notably by providing master
formulas that sum over diagrams differing only by the position of external legs
and/or internal propagators. We illustrate the mathematical challenge involved
with the low-energy limit of the N-photon amplitudes in scalar and spinor QED,
and then present an algorithm that, in principle, solves this problem for the
much more difficult case of the N-point amplitudes at full momentum in phi^3
theory. The method is based on the algebra of inverse derivatives in the
Hilbert space of periodic functions orthogonal to the constant ones, in which
the Bernoulli numbers and polynomials play a central role.
|
On the Hagedorn behavior of the superstring propating in a cosmological
time dependent background: In this work the LvN quantization of the type IIB superstring is carried on
in a time dependent plane wave background with a constant self-dual
Ramond-Ramond 5-form and a linear dilaton in the light-like direction. Such an
endeavour allows us to define an invariant density matrix and study important
issues in real time string thermodynamics. In particular, the Hagendorn
temperature is calculated as function of the thermalization time.
|
Classification of constraints using chain by chain method: We introduce "chain by chain" method for constructing the constraint
structure of a system possessing both first and second class constraints. We
show that the whole constraints can be classified into completely irreducible
first or second class chains. We found appropriate redefinition of second class
constraints to obtain a symplectic algebra among them.
|
Low-Energy Behavior of Gluons and Gravitons from Gauge Invariance: We show that at tree level, on-shell gauge invariance can be used to fully
determine the first subleading soft-gluon behavior and the first two subleading
soft-graviton behaviors. Our proofs of the behaviors for n-gluon and n-graviton
tree amplitudes are valid in D dimensions and are similar to Low's proof of
universality of the first subleading behavior of photons. In contrast to
photons coupling to massive particles, in four dimensions the soft behaviors of
gluons and gravitons are corrected by loop effects. We comment on how such
corrections arise from this perspective. We also show that loop corrections in
graviton amplitudes arising from scalar loops appear only at the second soft
subleading order. This case is particularly transparent because it is not
entangled with graviton infrared singularities. Our result suggests that if we
set aside the issue of infrared singularities, soft-graviton Ward identities of
extended BMS symmetry are not anomalous through the first subleading order.
|
Gravitational Chern-Simons Lagrangian terms and spherically symmetric
spacetimes: We show that for general spherically symmetric configurations, contributions
of general gravitational and mixed gauge-gravitational Chern-Simons terms to
the equations of motion vanish identically in $D>3$ dimensions. This implies
that such terms in the action do not affect Birkhoff's theorem or any
previously known spherically symmetric solutions. Furthermore, we investigate
the thermodynamical properties using the procedure described in an accompanying
paper. We find that in $D>3$ static spherically symmetric case Chern-Simons
terms do not contribute to the entropy either. Moreover, if one requires only
for the metric tensor to be spherically symmetric, letting other fields
unrestricted, the results extend almost completely, with only one possible
exception --- Chern-Simons Lagrangian terms in which the gravitational part is
just the $n=2$ irreducible gravitational Chern-Simons term.
|
Off-shell string physics: Recent advances in non-critical string theory allow a unique continuation,
preserving conformal invariance, of critical Polyakov string amplitudes to
off-shell momenta. These continuations possess unusual, apparently stringy,
characteristics, which are unlikely to be reproduced in a string field theory.
Thus our results may be an indication that some fundamentally new formulation,
other than string field theory, will be required to extend our understanding of
critical strings beyond the Polyakov path integral. Three-point functions are
explicitly calculated. The tree-level effective potential is computed for the
tachyon. (This preprint includes some computations used to arrive at results
mentioned in hep-th/9211016.)
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On the virial coefficients of nonabelian anyons: We study a system of nonabelian anyons in the lowest Landau level of a strong
magnetic field. Using diagrammatic techniques, we prove that the virial
coefficients do not depend on the statistics parameter. This is true for all
representations of all nonabelian groups for the statistics of the particles
and relies solely on the fact that the effective statistical interaction is a
traceless operator.
|
New Approximations to the Fradkin representation for Green's functions: A new variant of the exact Fradkin representation of the Green's function
$G_c(x,y|gU)$, defined for arbitrary external potential $U$, is presented.
Although this new approach is very similar in spirit to that previously derived
by Fried and Gabellini, for certain calculations this specific variant, with
its prescribed approximations, is more readily utilizable. Application of the
simplest of these forms is made to the $\lambda\Phi^4$ theory in four
dimensions.
As an independent check of these approximate forms, an improved version of
the Schwinger-DeWitt asymptotic expansion of parametrix function is derived.
|
String field actions from W-infinity: Starting from $W_{\infty}$ as a fundamental symmetry and using the coadjoint
orbit method, we derive an action for one dimensional strings. It is shown that
on the simplest nontrivial orbit this gives the single scalar collective field
theory. On higher orbits one finds generalized KdV type field theories with
increasing number of components. Here the tachyon is coupled to higher tensor
fields.
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Observing the fate of the false vacuum with a quantum laboratory: We design and implement a quantum laboratory to experimentally observe and
study dynamical processes of quantum field theories. Our approach encodes the
field theory as an Ising model, which is then solved by a quantum annealer. As
a proof-of-concept, we encode a scalar field theory and measure the probability
for it to tunnel from the false to the true vacuum for various tunnelling
times, vacuum displacements and potential profiles. The results are in accord
with those predicted theoretically, showing that a quantum annealer is a
genuine quantum system that can be used as a quantum laboratory. This is the
first time it has been possible to experimentally measure instanton processes
in a freely chosen quantum field theory. This novel and flexible method to
study the dynamics of quantum systems can be applied to any field theory of
interest. Experimental measurements of the dynamical behaviour of field
theories are independent of theoretical calculations and can be used to infer
their properties without being limited by the availability of suitable
perturbative or nonperturbative computational methods. In the near future,
measurements in such a quantum laboratory could therefore be used to improve
theoretical and computational methods conceptually and may enable the
measurement and detailed study of previously unobserved quantum phenomena.
|
Diffusion coefficient and DC conductivity of anisotropic static black
hole: In this study we apply two different methods in the context of $AdS/CFT$
correspondence and calculate the diffusion coefficient and $DC$ conductivity of
a four-dimensional spatially anisotropic static black hole. First, the
\emph{modified} transport coefficients is obtained by stretched horizon method
and Fick's law in the context of the membrane paradigm. In order to do such
calculation, we use the Maxwell equations with electromagnetic gauge field
propagating in two dimensions. Two dimensional propagating gauge field leads to
the complex transport coefficients which is proved by present paper. In second
step, we explain electro-thermal method and employ an effective vector field
and extract retarded Green's function on the classical boundary. Then, $DC$
conductivity and diffusion coefficient are obtained by using Kubo formula. Our
calculation can be applied on two well-known examples of anisotropic black
holes as the Einstein-Maxwell-dilaton-axion model and
AdS-Einstein-Maxwell-dilaton-axion in massive gravity.
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A Holographic Quantum Hall Ferromagnet: A detailed numerical study of a recent proposal for exotic states of the
D3-probe D5 brane system with charge density and an external magnetic field is
presented. The state has a large number of coincident D5 branes blowing up to a
D7 brane in the presence of the worldvolume electric and magnetic fields which
are necessary to construct the holographic state. Numerical solutions have
shown that these states can compete with the the previously known chiral
symmetry breaking and maximally symmetric phases of the D3-D5 system. Moreover,
at integer filling fractions, they are incompressible with integer quantized
Hall conductivities. In the dual superconformal defect field theory, these
solutions correspond to states which break the chiral and global flavor
symmetries spontaneously. The region of the temperature-density plane where the
D7 brane has lower energy than the other known D5 brane solutions is
identified. A hypothesis for the structure of states with filling fraction and
Hall conductivity greater than one is made and tested by numerical computation.
A parallel with the quantum Hall ferromagnetism or magnetic catalysis
phenomenon which is observed in graphene is drawn. As well as demonstrating
that the phenomenon can exist in a strongly coupled system, this work makes a
number of predictions of symmetry breaking patterns and phase transitions for
such systems.
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Regulator dependence of fixed points in quantum Einstein gravity with
$R^2$ truncation: We performed a functional renormalization group analysis for the quantum
Einstein gravity including a quadratic term in the curvature. The ultraviolet
non-gaussian fixed point and its critical exponent for the correlation length
are identified for different forms of regulators in case of dimension 3. We
searched for that optimized regulator where the physical quantities show the
least regulator parameter dependence. It is shown that the Litim regulator
satisfies this condition. The infrared fixed point has also been investigated,
it is found that the exponent is insensitive to the third coupling introduced
by the $R^2$ term.
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Reduced Chern-Simons Quiver Theories and Cohomological 3-Algebra Models: We study the BPS spectrum and vacuum moduli spaces in dimensional reductions
of Chern-Simons-matter theories with N>=2 supersymmetry to zero dimensions. Our
main example is a matrix model version of the ABJM theory which we relate
explicitly to certain reduced 3-algebra models. We find the explicit maps from
Chern-Simons quiver matrix models to dual IKKT matrix models. We address the
problem of topologically twisting the ABJM matrix model, and along the way
construct a new twist of the IKKT model. We construct a cohomological matrix
model whose partition function localizes onto a moduli space specified by
3-algebra relations which live in the double of the conifold quiver. It
computes an equivariant index enumerating framed BPS states with specified
R-charges which can be expressed as a combinatorial sum over certain filtered
pyramid partitions.
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Supersymmetric WZW $σ$ Model on Full and Half Plane: We study classical integrability of the supersymmetric U(N) $\sigma$ model
with the Wess-Zumino-Witten term on full and half plane. We demonstrate the
existence of nonlocal conserved currents of the model and derive general
recursion relations for the infinite number of the corresponding charges in a
superfield framework. The explicit form of the first few supersymmetric charges
are constructed. We show that the considered model is integrable on full plane
as a concequence of the conservation of the supersymmetric charges. Also, we
study the model on half plane with free boundary, and examine the conservation
of the supersymmetric charges on half plane and find that they are conserved as
a result of the equations of motion and the free boundary condition. As a
result, the model on half plane with free boundary is integrable. Finally, we
conclude the paper and some features and comments are presented.
|
Complex BPS domain walls and phase transition in mass in supersymmetric
QCD: We study the domain walls connecting different chirally asymmetric vacua in
supersymmetric QCD. We show that BPS - saturated solutions exist only in the
limited range of mass. When m exceeds some critical value, the domain wall
either ceases to be BPS - saturated or disappears altogether. In any case, the
properties of the system are qualitatively changed.
|
Gravitational Waves in Effective Quantum Gravity: In this short paper we investigate quantum gravitational effects on
Einstein's equations using effective field theory techniques. We consider the
leading order quantum gravitational correction to the wave equation. Besides
the usual massless mode, we find a pair of modes with complex masses. These
massive particles have a width and could thus lead to a damping of
gravitational waves if excited in violent astrophysical processes producing
gravitational waves such as e.g. black hole mergers. We discuss the
consequences for gravitational wave events such as GW 150914 recently observed
by the Advanced LIGO collaboration.
|
BRST Symmetries for the Tangent Gauge Group: For any principal bundle $P$, one can consider the subspace of the space of
connections on its tangent bundle $TP$ given by the tangent bundle $T{\cal A}$
of the space of connections ${\cal A}$ on $P$. The tangent gauge group acts
freely on $T{\cal A}$. Appropriate BRST operators are introduced for quantum
field theories that include as fields elements of $T{\cal A}$, as well as
tangent vectors to the space of curvatures. As the simplest application, the
BRST symmetry of the so-called $BF$-Yang-Mills theory is described and the
relevant gauge fixing conditions are analyzed. A brief account on the
topological $BF$ theories is also included and the relevant Batalin-Vilkovisky
operator is described.
|
Singlet Vector Models on Lens Spaces: We present exact computations of partition functions of singlet vector models
(infinite level Chern-Simons-matter theories) on lens spaces L(p, 1). We
identify light topological configurations and their spectra, and we comment on
the relevance of our results in studying both the UV completions of Vasiliev's
higher-spin theories and the dS/CFT correspondence in the large N limit.
|
Thermodynamic Bethe Ansatz for boundary sine-Gordon model: (R-channel) TBA is elaborated to find the effective central charge dependence
on the boundary parameters for the massless boundary sine-Gordon model with the
coupling constant $(8\pi) /\beta^2 = 1+ \lambda $ with $\lambda$ a positive
integer. Numerical analysis of the massless boundary TBA demonstrates that at
an appropriate boundary parameter range (cusp point) there exists a singularity
crossing phenomena and this effect should be included in TBA to have the right
behavior of the effective central charge.
|
Higher Spin Conformal Geometry in Three Dimensions and Prepotentials for
Higher Spin Gauge Fields: We study systematically the conformal geometry of higher spin bosonic gauge
fields in three spacetime dimensions. We recall the definition of the Cotton
tensor for higher spins and establish a number of its properties that turn out
to be key in solving in terms of prepotentials the constraint equations of the
Hamiltonian (3 + 1) formulation of four-dimensional higher spin gauge fields.
The prepotentials are shown to exhibit higher spin conformal symmetry. Just as
for spins 1 and 2, they provide a remarkably simple, manifestly duality
invariant formulation of the theory. While the higher spin conformal geometry
is developed for arbitrary bosonic spin, we explicitly perform the Hamiltonian
analysis and derive the solution of the constraints only in the illustrative
case of spin 3. In a separate publication, the Hamiltonian analysis in terms of
prepotentials is extended to all bosonic higher spins using the conformal tools
of this paper, and the same emergence of higher spin conformal symmetry is
confirmed.
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The AdS^2_θ/CFT_1 Correspondence and Noncommutative Geometry I: A
QM/NCG Correspondence: A consistent QM/NCG duality is put forward as a model for the AdS^2/CFT_1
correspondence. This is a duality/correspondence between 1) the dAFF conformal
quantum mechanics (QM) on the boundary (which is only "quasi-conformal" in the
sense that there is neither an SO(1,2)-invariant vacuum state nor there are
strictly speaking primary operators), and between 2) the noncommutative
geometry of AdS^2_{\theta} in the bulk (which is only "quasi-AdS" in the sense
of being only asymptotically AdS^2). The Laplacian operators on noncommutative
AdS^2_{\theta} and commutative AdS^2 have the same spectrum and thus their
correlators are conjectured to be identical. These bulk correlation functions
are found to be correctly reproduced by appropriately defined boundary quantum
observables in the dAFF quantum mechanics. Moreover, these quasi-primary
operators on the boundary form a subalgebra of the operator algebra of
noncommutative AdS^2_{\theta}.
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On the uniqueness of ghost-free special gravity: Special gravity refers to interacting theories of massless gravitons in
Minkowski space-time which are invariant under the abelian gauge invariance
$h_{ab}\rightarrow h_{ab}+\partial_{(a}\chi_{b)}$ only. In this article we
determine the most general form of special gravity free of Ostrogradski ghosts,
meaning its equation of motion is of at most second order. Together with the
recent works, this result could be helpful in formulating proofs of General
Relativity as the unique physical theory of self-interacting massless
gravitons. We also study how to construct gauge invariant couplings to matter
fields.
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DC resistivity of quantum critical, charge density wave states from
gauge-gravity duality: In contrast to metals with weak disorder, the resistivity of weakly-pinned
charge density waves (CDWs) is not controlled by irrelevant processes relaxing
momentum. Instead, the leading contribution is governed by incoherent,
diffusive processes which do not drag momentum and can be evaluated in the
clean limit. We compute analytically the dc resistivity for a family of
holographic charge density wave quantum critical phases and discuss its
temperature scaling. Depending on the critical exponents, the ground state can
be conducting or insulating. We connect our results to dc electrical transport
in underdoped cuprate high $T_c$ superconductors. We conclude by speculating on
the possible relevance of unstable, semi-locally critical CDW states to the
strange metallic region.
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BRST quantization of matrix models with constraints and two-dimensional
Yang-Mills theory on the cylinder: BRST quantization of the one-dimensional constrained matrix model which
describes two-dimensional Yang-Mills theory on the cylinder is performed.
Classical and quantum BRST generators and BRST-invariant hamiltonians are
constructed. Evolution operator is expressed in terms of BRST path integral.
Advantages of the BRST quantization over the reduced phase space approach
leading to the theory of $N$ free fermions are discussed.
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Coherent states in noncommutative quantum mechanics: Gazeau-Klauder coherent states in noncommutative quantum mechanics are
considered. We find that these states share similar properties to those of
ordinary canonical coherent states in the sense that they saturate the related
position uncertainty relation, obey a Poisson distribution and possess a flat
geometry. Using the natural isometry between the quantum Hilbert space of
Hilbert Schmidt operators and the tensor product of the classical configuration
space and its dual, we reveal the inherent vector feature of these states.
|
Trap Surface Formation in High-Energy Black Holes Collision: We investigate classical formation of a trap surface in $D$-dimensional
Einstein gravity in the process of a head-on collision of two high-energy
particles, which are treated as Aichelburg-Sexl shock waves. From the condition
of the trap surface volume local maximality we deduce an explicit form of the
inner trap surface. Imposing the continuity condition on the fronts we obtain a
time-dependent solution for the trap surface. We discuss trap surface
appearance and evolution.
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N=4 supersymmetric 3-particles Calogero model: We constructed the most general N=4 superconformal 3-particles systems with
translation invariance. In the basis with decoupled center of mass the
supercharges and Hamiltonian possess one arbitrary function which defines all
potential terms. We have shown that with the proper choice of this function one
may describe the standard, $A_2$ Calogero model as well as $BC_2, B_2,C_2$ and
$D_2$ Calogero models with N=4 superconformal symmetry. The main property of
all these systems is that even with the coupling constant equal to zero they
still contain nontrivial interactions in the fermionic sector. In other words,
there are infinitely many non equivalent N=4 supersymmetric extensions of the
free action depending on one arbitrary function. We also considered
quantization and explicitly showed how the supercharges and Hamiltonian are
modified.
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The Compactification of QCD$_4$ to QCD$_2$ in a Flux Tube: We show from the action integral that in the special environment of a flux
tube, QCD$_4$ in (3+1) dimensional space-time can be approximately compactified
into QCD$_2$ in (1+1) dimensional space-time. In such a process, we find out
how the coupling constant $g_{2D}$ in QCD$_2$ is related to the coupling
constant $g_{4D}$ in QCD$_4$. We show how the quark and the gluon in QCD$_2$
acquire contributions to their masses arising from their confinement within the
tube, and how all these quantities depend on the excitation of the partons in
the transverse degrees of freedom. The compactification facilitates the
investigation of some dynamical problems in QCD$_4$ in the simpler dynamics of
QCD$_2$ where the variation of the gluon fields leads to a bound state.
|
Introduction to Khovanov Homologies. I. Unreduced Jones superpolynomial: An elementary introduction to Khovanov construction of superpolynomials.
Despite its technical complexity, this method remains the only source of a
definition of superpolynomials from the first principles and therefore is
important for development and testing of alternative approaches. In this first
part of the review series we concentrate on the most transparent and
unambiguous part of the story: the unreduced Jones superpolynomials in the
fundamental representation and consider the 2-strand braids as the main
example. Already for the 5_1 knot the unreduced superpolynomial contains more
items than the ordinary Jones.
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Canonical Transformations and Path Integral Measures: This paper is a generalization of previous work on the use of classical
canonical transformations to evaluate Hamiltonian path integrals for quantum
mechanical systems. Relevant aspects of the Hamiltonian path integral and its
measure are discussed and used to show that the quantum mechanical version of
the classical transformation does not leave the measure of the path integral
invariant, instead inducing an anomaly. The relation to operator techniques and
ordering problems is discussed, and special attention is paid to incorporation
of the initial and final states of the transition element into the boundary
conditions of the problem. Classical canonical transformations are developed to
render an arbitrary power potential cyclic. The resulting Hamiltonian is
analyzed as a quantum system to show its relation to known quantum mechanical
results. A perturbative argument is used to suppress ordering related terms in
the transformed Hamiltonian in the event that the classical canonical
transformation leads to a nonquadratic cyclic Hamiltonian. The associated
anomalies are analyzed to yield general methods to evaluate the path integral's
prefactor for such systems. The methods are applied to several systems,
including linear and quadratic potentials, the velocity-dependent potential,
and the time-dependent harmonic oscillator.
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Space-time symmetries and the Yang-Mills gradient flow: The recent introduction of the gradient flow has provided a new tool to probe
the dynamics of quantum field theories. The latest developments have shown how
to use the gradient flow for the exploration of symmetries, and the definition
of the corresponding renormalized Noether currents. In this paper we introduce
infinitesimal translations along the gradient flow for gauge theories, and
study the corresponding Ward identities. This approach is readily generalized
to the case of gauge theories defined on a lattice, where the regulator breaks
translation invariance. The Ward identities in this case lead to a
nonperturbative renormalization of the energy-momentum tensor. We discuss an
application of this method to the study of dilatations and scale invariance on
the lattice.
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Two interacting conformal Carroll particles: In this note we analyse two different models of two interacting conformal
Carroll particles that can be obtained as the Carrollian limit of two
relativistic conformal particles. The first model describes particles with zero
velocity and exhibits infinite dimensional symmetries which are reminiscent of
the BMS symmetries. A second model of interaction of Carrollian particles is
proposed, where the particles have non zero velocity and therefore, as a
consequence of the limit c to 0, are tachyons. Infinite dimensional symmetries
are present also in this model.
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Quantum Clifford-Hopf Algebras for Even Dimensions: In this paper we study the quantum Clifford-Hopf algebras $\widehat{CH_q(D)}$
for even dimensions $D$ and obtain their intertwiner $R-$matrices, which are
elliptic solutions to the Yang- Baxter equation. In the trigonometric limit of
these new algebras we find the possibility to connect with extended
supersymmetry. We also analyze the corresponding spin chain hamiltonian, which
leads to Suzuki's generalized $XY$ model.
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Highlights in Supergravity: CCJ 47 Years Later: We consider an expression for the supercurrent in the superconformal
formulation of N=1 supergravity. A chiral compensator provides the
supersymmetric formulation of the Callan-Coleman-Jackiw (CCJ) improved stress
energy tensor, when the conformal gauge is used. Superconformal and
non-superconformal matter give different conservation laws of the supercurrent,
when coupled to the curvature supermultiplets which underlie the local
superspace geometry. This approach can be applied to any set of auxiliary
fields and it is useful to classify rigid curved superspace geometries.
Examples with four supersymmetries are briefly described.
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Multi-Regge kinematics and the moduli space of Riemann spheres with
marked points: We show that scattering amplitudes in planar N = 4 Super Yang-Mills in
multi-Regge kinematics can naturally be expressed in terms of single-valued
iterated integrals on the moduli space of Riemann spheres with marked points.
As a consequence, scattering amplitudes in this limit can be expressed as
convolutions that can easily be computed using Stokes' theorem. We apply this
framework to MHV amplitudes to leading-logarithmic accuracy (LLA), and we prove
that at L loops all MHV amplitudes are determined by amplitudes with up to L +
4 external legs. We also investigate non-MHV amplitudes, and we show that they
can be obtained by convoluting the MHV results with a certain helicity flip
kernel. We classify all leading singularities that appear at LLA in the Regge
limit for arbitrary helicity configurations and any number of external legs.
Finally, we use our new framework to obtain explicit analytic results at LLA
for all MHV amplitudes up to five loops and all non-MHV amplitudes with up to
eight external legs and four loops.
|
A leading-order comparison between fluid-gravity and membrane-gravity
dualities: In this note, we have compared two different perturbation techniques that are
used to generate dynamical black-brane solutions to Einstein equation in
presence of negative cosmological constant. One is the `derivative expansion',
where the gravity solutions are in one-to-one correspondence with the solutions
of relativistic Navier-Stokes equation. The second is the expansion in terms of
inverse power of space-time dimensions and here the gravity solutions are dual
to a co-dimension one dynamical membrane, embedded in AdS space and coupled to
a velocity field. We have shown that in large number of space-time dimensions,
there exists an overlap regime between these two perturbation techniques and we
matched the two gravity solutions along with their dual systems upto the first
non-trivial order in the expansion parameter on both sides. In the process, we
established a one-to-one map between dynamical black-brane geometry and the AdS
space, which exists even when the number of dimensions is finite.
|
Tree-level processes in very special relativity: In this paper we discuss the Bhabha and Compton scattering for the quantum
electrodynamics defined in the framework of very special relativity (VSR). The
main aspect of the VSR setting is that it admits different types of
interactions appearing in a nonlocal form due to the modified gauge invariance.
We explore the richness of these new couplings in the evaluation of the
differential cross-section for these tree-level processes. We assess the
behavior of the leading VSR Lorentz violation modifications by considering some
special limits for the Bhabha and Compton cross-section expressions.
|
Calogero-Moser hierarchy and KP hierarchy: The space of solutions of the rational Calogero-Moser hierarchy, and the
space of solutions of the KP hierarchy whose tau functions are monic
polynomials in $t_1$ with coefficients depending on $t_n$, $n > 1$, are
identified, generalizing earlier results of Airault-McKean-Moser and Krichever.
|
The Euler-Heisenberg Lagrangian beyond one loop: We review what is presently known about higher loop corrections to the
Euler-Heisenberg Lagrangian and its Scalar QED analogue. The use of those
corrections as a tool for the study of the properties of the QED perturbation
series is outlined. As a further step in a long-term effort to prove or
disprove the convergence of the N photon amplitudes in the quenched
approximation, we present a parameter integral representation of the three-loop
Euler-Heisenberg Lagrangian in 1+1 dimensional QED, obtained in the worldline
formalism.
|
Nets of Subfactors: A subtheory of a quantum field theory specifies von~Neumann subalgebras
$\aa(\oo)$ (the `observables' in the space-time region $\oo$) of the
von~Neumann algebras $\bb(\oo)$ (the `fields' localized in $\oo$). Every local
algebra being a (type $\III_1$) factor, the inclusion $\aa(\oo) \subset
\bb(\oo)$ is a subfactor. The assignment of these local subfactors to the
space-time regions is called a `net of subfactors'. The theory of subfactors is
applied to such nets. In order to characterize the `relative position' of the
subtheory, and in particular to control the restriction and induction of
superselection sectors, the canonical endomorphism is studied. The crucial
observation is this: the canonical endomorphism of a local subfactor extends to
an endomorphism of the field net, which in turn restricts to a localized
endomorphism of the observable net. The method allows to characterize, and
reconstruct, local extensions $\bb$ of a given theory $\aa$ in terms of the
observables. Various non-trivial examples are given.
|
Refined Chern-Simons Theory and Knot Homology: The refined Chern-Simons theory is a one-parameter deformation of the
ordinary Chern-Simons theory on Seifert manifolds. It is defined via an index
of the theory on N M5 branes, where the corresponding one-parameter deformation
is a natural deformation of the geometric background. Analogously with the
unrefined case, the solution of refined Chern-Simons theory is given in terms
of S and T matrices, which are the proper Macdonald deformations of the usual
ones. This provides a direct way to compute refined Chern-Simons invariants of
a wide class of three-manifolds and knots. The knot invariants of refined
Chern-Simons theory are conjectured to coincide with the knot superpolynomials
-- Poincare polynomials of the triply graded knot homology theory. This
conjecture is checked for a large number of torus knots in S^3, colored by the
fundamental representation. This is a short, expository version of
arXiv:1105.5117, with some new results included.
|
Towards Non-archimedean Superstrings: An action for a prospect of a $p$-adic open superstring on a target Minkowski
space is proposed. The action is constructed for `worldsheet' fields taking
values in the $p$-adic field $\mathbb{Q}_p$, but it is assumed to be obtained
from a discrete action on the Bruhat-Tits tree. This action is proven to have
an analog of worldsheet supersymmetry and the superspace action is also
constructed in terms of superfields. The action does not have conformal
symmetry, however it is implemented in the definition of the amplitudes. The
tree-level amplitudes for this theory are obtained for $N$ vertex operators
corresponding to tachyon superfields and a Koba-Nielsen formula is obtained.
Finally, four-point amplitudes are computed explicitly and they are compared to
previous work on $p$-adic superstring amplitudes.
|
Quantum Deconstruction of a 5D SYM and its Moduli Space: We deconstruct the fifth dimension of the 5D SYM theory with SU(M) gauge
symmetry and Chern-Simons level k=M and show how the 5D moduli space follows
from the non-perturbative analysis of the 4D quiver theory. The 5D coupling
h=1/(g_5)^2 of the un-broken SU(M) is allowed to take any non-negative values,
but it cannot be continued to h<0 and there are no transitions to other phases
of the theory. The alternative UV completions of the same 5D SYM -- via M
theory on the C^3/Z_2M orbifold or via the dual five-brane web in type IIB
string theory -- have identical moduli spaces: h >= 0 only, and no flop
transitions. We claim these are intrinsic properties of the SU(M) SYM theory
with k=M.
|
Quantum parity conservation in planar quantum electrodynamics: Quantum parity conservation is verified at all orders in perturbation theory
for a massless parity-even $U(1)\times U(1)$ planar quantum electrodynamics
(QED$_3$) model. The presence of two massless fermions requires the
Lowenstein-Zimmermann (LZ) subtraction scheme, in the framework of the
Bogoliubov-Parasiuk-Hepp-Zimmermann-Lowenstein (BPHZL) renormalization method,
in order to subtract the infrared divergences induced by the ultraviolet
subtractions at 1- and 2-loops, however thanks to the superrenormalizability of
the model the ultraviolet divergences are bounded up to 2-loops. Finally, it is
proved that the BPHZL renormalization method preserves parity for the model
taken into consideration, contrary to what happens to the ordinary massless
parity-even $U(1)$ QED$_3$.
|
CFT Duals for Accelerating Black Holes: The near horizon geometry of the rotating C-metric, describing accelerating
Kerr-Newman black holes, is analysed. It is shown that, at extremality, even
though not it is isomorphic to the extremal Kerr-Newman, it remains a warped
and twisted product of $AdS_2 \times S^2$. Therefore the methods of the
Kerr/CFT correspondence can successfully be applied to build a CFT dual model,
whose entropy reproduce, through the Cardy formula, the Beckenstein-Hawking
entropy of the accelerating black hole. The mass of accelerating Kerr-Newman
black hole, which fulfil the first law of thermodynamics, is presented. Further
generalisation in presence of an external Melvin-like magnetic field, used to
regularise the conical singularity characteristic of the C-metrics, shows that
the Kerr/CFT correspondence can be applied also for the accelerating and
magnetised extremal black holes.
|
Geodesic motion on the group of boundary diffeomorphisms from Einstein's
equations: In arXiv:1904.12869 it was shown how in an adiabatic limit the vacuum
Einstein equations on a compact spatial region can be re-expressed as geodesic
equations on the group of diffeomorphisms of the boundary. This is reminiscent
of the program initiated by V. Arnold to reformulate models of continuum
mechanics in terms of geodesic motion on diffeomorphism groups. We revisit some
of the results of arXiv:1904.12869 in this light, pointing out parallels and
differences with the typical examples in geometric continuum mechanics. We work
out the case of 2 spatial dimensions in some detail.
|
Non-Abelian Vortices on Riemann Surfaces: an Integrable Case: We consider U(n+1) Yang-Mills instantons on the space \Sigma\times S^2, where
\Sigma is a compact Riemann surface of genus g. Using an SU(2)-equivariant
dimensional reduction, we show that the U(n+1) instanton equations on
\Sigma\times S^2 are equivalent to non-Abelian vortex equations on \Sigma.
Solutions to these equations are given by pairs (A,\phi), where A is a gauge
potential of the group U(n) and \phi is a Higgs field in the fundamental
representation of the group U(n). We briefly compare this model with other
non-Abelian Higgs models considered recently. Afterwards we show that for g>1,
when \Sigma\times S^2 becomes a gravitational instanton, the non-Abelian vortex
equations are the compatibility conditions of two linear equations (Lax pair)
and therefore the standard methods of integrable systems can be applied for
constructing their solutions.
|
On the Chiral Fermions in the Twistor--Like Formulation of D=10
Heterotic String: An n=8 worldsheet superfield action is proposed for describing chiral
fermions in the twistor-like formulation of an N=1, D=10 heterotic superstring.
|
Fermionic contribution to the anomalous dimension of twist-2 operators
in N=4 SYM theory, critical indices and integrability: We compute the contribution to the anomalous dimension of the twist-2
operators in N=4 SYM theory, which is proportional to the number of fermion
loops inside Feynman diagrams or, formally, to the number of fermions. The
result was obtained by the method based on the calculation of critical indices
at the critical point by analogy with previous similar computations in scalar
theories and in QCD. The obtained result is much simpler with compare to
analogous results in QCD and almost satisfies the maximal transcedentality
principle. A possible relation between the obtained result and integrability is
discussed.
|
Monopole-antimonopole Interaction Potential: We numerically study the interactions of twisted monopole-antimonopole pairs
in the 't Hooft-Polyakov model for a range of values of the scalar to vector
mass ratio. We also recover the sphaleron solution at maximum twist discovered
by Taubes, and map out its energy and size as functions of parameters.
|
Notes on Connes' Construction of the Standard Model: The mathematical apparatus of non commutative geometry and operator algebras
which Connes has brought to bear to construct a rational scheme for the
internal symmetries of the standard model is presented from the physicist's
point of view. Gauge symmetry, anomaly freedom, conservation of electric
charge, parity violation and charge conjugation all play a vital role. When put
together with a relatively simple set of algebraic algorithms they deliver many
of the features of the standard model which otherwise seem rather ad hoc.
|
Integrable lattice models from four-dimensional field theories: This note gives a general construction of an integrable lattice model (and a
solution of the Yang-Baxter equation with spectral parameter) from a
four-dimensional field theory which is a mixture of topological and
holomorphic. Spin-chain models arise in this way from a twisted, deformed
version of N=1 gauge theory.
|
De Sitter Space in Supergravity and M Theory: Two ways in which de Sitter space can arise in supergravity theories are
discussed. In the first, it arises as a solution of a conventional
supergravity, in which case it necessarily has no Killing spinors. For example,
de Sitter space can arise as a solution of N=8 gauged supergravities in four or
five dimensions. These lift to solutions of 11-dimensional supergravity or D=10
IIB supergravity which are warped products of de Sitter space and non-compact
spaces of negative curvature. In the second way, de Sitter space can arise as a
supersymmetric solution of an unconventional supergravity theory, which
typically has some kinetic terms with the `wrong' sign; such solutions are
invariant under a de Sitter supergroup. Such solutions lift to supersymmetric
solutions of unconventional supergravities in D=10 or D=11, which nonetheless
arise as field theory limits of theories that can be obtained from M-theory by
timelike T-dualities and related dualities. Brane solutions interpolate between
these solutions and flat space and lead to a holographic duality between
theories in de Sitter vacua and Euclidean conformal field theories. Previous
results are reviewed and generalised, and discussion is included of
Kaluza-Klein theory with non-compact internal spaces, brane and cosmological
solutions, and holography on de Sitter spaces and product spaces.
|
String Scattering Amplitudes in High Energy Limits: A very review of string scattering amplitudes in two important high energy
limits: hard scattering and Regge scattering. Recent results of the symmetries
in string theory by studying high energy string scattering anplitudes are
showed.
|
Fusion Hierarchy and Finite-Size Corrections of $U_q[sl(2)]$ Invariant
Vertex Models with Open Boundaries: The fused six-vertex models with open boundary conditions are studied. The
Bethe ansatz solution given by Sklyanin has been generalized to the transfer
matrices of the fused models. We have shown that the eigenvalues of transfer
matrices satisfy a group of functional relations, which are the $su$(2) fusion
rule held by the transfer matrices of the fused models. The fused transfer
matrices form a commuting family and also commute with the quantum group
$U_q[sl(2)]$. In the case of the parameter $q^h=-1$ ($h=4,5,\cdots$) the
functional relations in the limit of spectral parameter $u\to \i\infty$ are
truncated. This shows that the $su$(2) fusion rule with finite level appears
for the six vertex model with the open boundary conditions. We have solved the
functional relations to obtain the finite-size corrections of the fused
transfer matrices for low-lying excitations. From the corrections the central
charges and conformal weights of underlying conformal field theory are
extracted. To see different boundary conditions we also have studied the
six-vertex model with a twisted boundary condition.
|
Dualisation of Dualities, II: Twisted self-duality of doubled fields and
superdualities: We introduce a doubled formalism for the bosonic sector of the maximal
supergravities, in which a Hodge dual potential is introduced for each bosonic
field (except for the metric). The equations of motion can then be formulated
as a twisted self-duality condition on the total field strength \G, which takes
its values in a Lie superalgebra. This doubling is invariant under
dualisations; it allows a unification of the gauge symmetries of all degrees,
including the usual U-dualities that have degree zero. These ``superdualities''
encompass the dualities for all choices of polarisation (i.e. the choices
between fields and their duals). All gauge symmetries appear as subgroups of
finite-dimensional supergroups, with Grassmann coefficients in the differential
algebra of the spacetime manifold.
|
Exact Scattering in the SU(n) Supersymmetric Principal Chiral Model: The complete spectrum of states in the supersymmetric principal chiral model
based on SU(n) is conjectured, and an exact factorizable S-matrix is proposed
to describe scattering amongst these states. The SU(n)_L*SU(n)_R symmetry of
the lagrangian is manifest in the S-matrix construction. The supersymmetries,
on the other hand, are incorporated in the guise of spin-1/2 charges acting on
a set of RSOS kinks associated with su(n) at level n. To test the proposed
S-matrix, calculations of the change in the ground-state energy in the presence
of a coupling to a background charge are carried out. The results derived from
the lagrangian using perturbation theory and from the S-matrix using the TBA
are found to be in complete agreement for a variety of background charges which
pick out, in turn, the highest weight states in each of the fundamental
representations of SU(n). In particular, these methods rule out the possibility
of additional CDD factors in the S-matrix. Comparison of the expressions found
for the free-energy also yields an exact result for the mass-gap in these
models: m/Lambda_{MS-bar}=(n/pi)sin(pi/n).
|
Off-shell symmetry algebra of the AdS_4 x CP^3 superstring: By direct calculation in classical theory we derive the central extension of
the off-shell symmetry algebra for the string propagating in AdS_4 x CP^3. It
turns out to be the same as in the case of the AdS_5 x S^5 string. We also
elaborate on the kappa-symmetry gauge and explain, how it can be chosen in a
way which does not break bosonic symmetries.
|
Surface operators, dual quivers and contours: We study half-BPS surface operators in four dimensional N=2 SU(N) gauge
theories, and analyze their low-energy effective action on the four dimensional
Coulomb branch using equivariant localization. We also study surface operators
as coupled 2d/4d quiver gauge theories with an SU(N) flavour symmetry. In this
description, the same surface operator can be described by different quivers
that are related to each other by two dimensional Seiberg duality. We argue
that these dual quivers correspond, on the localization side, to distinct
integration contours that can be determined by the Fayet-Iliopoulos parameters
of the two dimensional gauge nodes. We verify the proposal by mapping the
solutions of the twisted chiral ring equations of the 2d/4d quivers onto
individual residues of the localization integrand.
|
On the energy deposited by a quark moving in an N=4 SYM plasma: We evaluate the energy momentum tensor of a massive quark as it moves through
an N=4 SYM quark gluon plasma at constant velocity. We find that in the
near-quark region, where the dynamics is expected to be dominated by
dissipative behavior, the energy density may be quantitatively characterized by
a transient at velocities above the speed of sound of the plasma.
|
Gauge invariant cosmological perturbations for the nonminimally coupled
inflaton field: We construct the gauge invariant free action for cosmological perturbations
for the nonminimally coupled inflaton field in the Jordan frame. For this the
phase space formalism is used, which keeps track of all the dynamical and
constraint fields. We perform explicit conformal transformations to demonstrate
the physical equivalence between the Jordan and Einstein frames at the level of
quadratic perturbations. We show how to generalize the formalism to the case of
a more complicated scalar sector with an internal symmetry, such as Higgs
inflation. This work represents a first step in developing gauge invariant
perturbation theory for nonminimally coupled inflationary models.
|
Supergravities with Minkowski x Sphere Vacua: Recently the authors have introduced a new gauged supergravity theory with a
positive definite potential in D=6, obtained through a generalised Kaluza-Klein
reduction from D=7. Of particular interest is the fact that this theory admits
certain Minkowski x Sphere vacua. In this paper we extend the previous results
by constructing gauged supergravities with positive definitive potentials in
diverse dimensions, together with their vacuum solutions. In addition, we prove
the supersymmetry of the generalised reduction ansatz. We obtain a
supersymmetric solution with no form-field fluxes in the new gauged theory in
D=9. This solution may be lifted to D=10, where it acquires an interpretation
as a time-dependent supersymmetric cosmological solution supported purely by
the dilaton. A further uplift to D=11 yields a solution describing a pp-wave.
|
Ramanujan's influence on string theory, black holes and moonshine: Ramanujan influenced many areas of mathematics, but his work on q-series, on
the growth of coefficients of modular forms, and on mock modular forms stands
out for its depth and breadth of applications. I will give a brief overview of
how this part of Ramanujan's work has influenced physics with an emphasis on
applications to string theory, counting of black hole states and moonshine.
This paper contains the material from my presentation at the meeting
celebrating the centenary of Ramanujan's election as FRS and adds some
additional material on black hole entropy and the AdS/CFT correspondence.
|
Noncommutative Tachyonic Solitons. Interaction with Gauge Field: We show that in the presence of U(1) noncommutative gauge interaction the
noncommutative tachyonic system exhibits solitonic solutions for finite value
of the noncommutativity parameter.
|
Poisson Structure Induced (Topological) Field Theories: A class of two dimensional field theories, based on (generically degenerate)
Poisson structures and generalizing gravity-Yang-Mills systems, is presented.
Locally, the solutions of the classical equations of motion are given. A
general scheme for the quantization of the models in a Hamiltonian formulation
is found.
|
On the Standard Model Group in F-theory: We analyze the Standard Model gauge group SU(3) x SU(2) x U(1) constructed in
F-theory. The non-Abelian part SU(3) x SU(2) is described by singularities of
Kodaira type. It is distinguished to naive product of SU(3) and SU(2), revealed
by blow-up analysis, since the resolution procedures cannot be done separately
to each group. The Abelian part U(1) is constructed by obtaining a desirable
global two-form harboring it, using `factorization method' similar to the
decomposition method of the spectral cover; It makes use of an extra section in
the elliptic fiber of the Calabi-Yau manifold, on which F-theory is
compactified. Conventional gauge coupling unification of SU(5) is achieved,
without threshold correction from the flux along hypercharge direction.
|
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