4,168 research outputs found
Classical Integrable N=1 and Super Sinh-Gordon Models with Jump Defects
The structure of integrable field theories in the presence of jump defects is
discussed in terms of boundary functions under the Lagrangian formalism.
Explicit examples of bosonic and fermionic theories are considered. In
particular, the boundary functions for the N=1 and N=2 super sinh-Gordon models
are constructed and shown to generate the Backlund transformations for its
soliton solutions. As a new and interesting example, a solution with an
incoming boson and an outgoing fermion for the N=1 case is presented. The
resulting integrable models are shown to be invariant under supersymmetric
transformation.Comment: talk presented at the V International Symposium on Quantum Theory and
Symmetries, Valladolid, Spain, July 22-28,200
The sine-Gordon model with integrable defects revisited
Application of our algebraic approach to Liouville integrable defects is
proposed for the sine-Gordon model. Integrability of the model is ensured by
the underlying classical r-matrix algebra. The first local integrals of motion
are identified together with the corresponding Lax pairs. Continuity conditions
imposed on the time components of the entailed Lax pairs give rise to the
sewing conditions on the defect point consistent with Liouville integrability.Comment: 24 pages Latex. Minor modifications, added comment
Equivalences between spin models induced by defects
The spectrum of integrable spin chains are shown to be independent of the
ordering of their spins. As an application we introduce defects (local spin
inhomogeneities in homogenous chains) in two-boundary spin systems and, by
changing their locations, we show the spectral equivalence of different
boundary conditions. In particular we relate certain nondiagonal boundary
conditions to diagonal ones.Comment: 14 pages, 16 figures, LaTeX, Extended versio
Boundary Reflection Matrix for Affine Toda Field Theory
We present one loop boundary reflection matrix for Toda field
theory defined on a half line with the Neumann boundary condition. This result
demonstrates a nontrivial cancellation of non-meromorphic terms which are
present when the model has a particle spectrum with more than one mass. Using
this result, we determine uniquely the exact boundary reflection matrix which
turns out to be \lq non-minimal' if we assume the strong-weak coupling \lq
duality'.Comment: 14 pages, Late
Exact Solutions in Five-Dimensional Axi-dilaton Gravity with Euler-Poincare Term
We examine the effective field equations that are obtained from the
axi-dilaton gravity action with a second order Euler-Poincare term and a
cosmological constant in all higher dimensions. We solve these equations for
five-dimensional spacetimes possessing homogeneity and isotropy in their
three-dimensional subspaces. For a number of interesting special cases we show
that the solutions fall into two main classes: The first class consists of
time-dependent solutions with spherical or hyperboloidal symmetry which require
certain fine-tuning relations between the coupling constants of the model and
the cosmological constant. Solutions in the second class are locally static and
prove the validity of Birkhoff's staticity theorem in the axi-dilaton gravity.
We also give a special class of static solutions, among them the well-known
black hole solutions in which the usual electric charge is superseded by an
axion charge.Comment: New formulas and references adde
Cosmological Evolution of a Purely Conical Codimension-2 Brane World
We study the cosmological evolution of isotropic matter on an infinitely thin
conical codimension-two brane-world. Our analysis is based on the boundary
dynamics of a six-dimensional model in the presence of an induced gravity term
on the brane and a Gauss-Bonnet term in the bulk. With the assumption that the
bulk contains only a cosmological constant Lambda_B, we find that the isotropic
evolution of the brane-universe imposes a tuned relation between the energy
density and the brane equation of state. The evolution of the system has fixed
points (attractors), which correspond to a final state of radiation for
Lambda_B=0 and to de Sitter state for Lambda_B>0. Furthermore, considering
anisotropic matter on the brane, the tuning of the parameters is lifted, and
new regions of the parametric space are available for the cosmological
evolution of the brane-universe. The analysis of the dynamics of the system
shows that, the isotropic fixed points remain attractors of the system, and for
values of Lambda_B which give acceptable cosmological evolution of the equation
of state, the line of isotropic tuning is a very weak attractor. The initial
conditions, in this case, need to be fine tuned to have an evolution with
acceptably small anisotropy.Comment: 20 pages, 4 figures, typo correcte
Exact braneworld cosmology induced from bulk black holes
We use a new, exact approach in calculating the energy density measured by an
observer living on a brane embedded in a charged black hole spacetime. We find
that the bulk Weyl tensor gives rise to non-linear terms in the energy density
and pressure in the FRW equations for the brane. Remarkably, these take exactly
the same form as the ``unconventional'' terms found in the cosmology of branes
embedded in pure AdS, with extra matter living on the brane. Black hole driven
cosmologies have the benefit that there is no ambiguity in splitting the
braneword energy momentum into tension and additional matter. We propose a new,
enlarged relationship between the two descriptions of braneworld cosmology. We
also study the exact thermodynamics of the field theory and present a
generalised Cardy-Verlinde formula in this set up.Comment: 17 pages, no figures; v3: Minor change, References added, Version to
appear in CQ
Gauss-Bonnet brane-world cosmology without -symmetry
We consider a single 3-brane situated between two bulk spacetimes that posses
the same cosmological constant, but whose metrics do not posses a
-symmetry. On each side of the brane, the bulk is a solution to
Gauss-Bonnet gravity. This asymmetry modifies junction conditions, and so new
terms arise in the Friedmann equation. If these terms become dominant, these
behave cosmological constant at early times for some case, and might remove the
initial singularity for other case. However, we show that these new terms can
not become dominant ones under usual conditions when our brane is outside an
event horizon. We also show that any brane-world scenarios of this type revert
to a -symmetric form at late times, and hence rule out certain proposed
scenarios.Comment: 8 pages, 3 figures; Minor typos corrected. References added. V3:
Numerical errors are corrected. Fig.1 and Fig.3 are replaced. V4: published
versio
Multisymplectic approach to integrable defects in the sine-Gordon model
Ideas from the theory of multisymplectic systems, introduced recently in integrable systems by the author and Kundu to discuss Liouville integrability in classical field theories with a defect, are applied to the sine-Gordon model. The key ingredient is the introduction of a second Poisson bracket in the theory that allows for a Hamiltonian description of the model that is completely equivalent to the standard one, in the absence of a defect. In the presence of a defect described by frozen Bäcklund transformations, our approach based on the new bracket unifies the various tools used so far to attack the problem. It also gets rid of the known issues related to the evaluation of the Poisson brackets of the defect matrix which involve fields at coinciding space point (the location of the defect). The original Lagrangian approach also finds a nice reinterpretation in terms of the canonical transformation representing the defect conditions
Inverse scattering approach for massive Thirring models with integrable type-II defects
We discuss the integrability of the Bosonic and Grassmannian massive Thirring
models in the presence of defects through the inverse scattering approach. We
present a general method to compute the generating functions of modified
conserved quantities for any integrable field equation associated to the m x m
spectral linear problem. We apply the method to derive in particular the defect
contributions for the number of occupation, energy and momentum of the massive
Thirring models.Comment: 25 pages in IOP Latex style; some modifications to match version
accepted by J Phys A; a section on Liouville integrability adde
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