133 research outputs found
Combination of inverse spectral transform method and method of characteristics: deformed Pohlmeyer equation
We apply a version of the dressing method to a system of four dimensional
nonlinear Partial Differential Equations (PDEs), which contains both Pohlmeyer
equation (i.e. nonlinear PDE integrable by the Inverse Spectral Transform
Method) and nonlinear matrix PDE integrable by the method of characteristics as
particular reductions. Some other reductions are suggested.Comment: 12 page
QFT on homothetic Killing twist deformed curved spacetimes
We study the quantum field theory (QFT) of a free, real, massless and
curvature coupled scalar field on self-similar symmetric spacetimes, which are
deformed by an abelian Drinfel'd twist constructed from a Killing and a
homothetic Killing vector field. In contrast to deformations solely by Killing
vector fields, such as the Moyal-Weyl Minkowski spacetime, the equation of
motion and Green's operators are deformed. We show that there is a *-algebra
isomorphism between the QFT on the deformed and the formal power series
extension of the QFT on the undeformed spacetime. We study the convergent
implementation of our deformations for toy-models. For these models it is found
that there is a *-isomorphism between the deformed Weyl algebra and a reduced
undeformed Weyl algebra, where certain strongly localized observables are
excluded. Thus, our models realize the intuitive physical picture that
noncommutative geometry prevents arbitrary localization in spacetime.Comment: 23 pages, no figures; v2: extended discussion of physical
consequences, compatible with version to be published in General Relativity
and Gravitatio
Multivortex Solutions of the Weierstrass Representation
The connection between the complex Sine and Sinh-Gordon equations on the
complex plane associated with a Weierstrass type system and the possibility of
construction of several classes of multivortex solutions is discussed in
detail. We perform the Painlev\'e test and analyse the possibility of deriving
the B\"acklund transformation from the singularity analysis of the complex
Sine-Gordon equation. We make use of the analysis using the known relations for
the Painlev\'{e} equations to construct explicit formulae in terms of the
Umemura polynomials which are -functions for rational solutions of the
third Painlev\'{e} equation. New classes of multivortex solutions of a
Weierstrass system are obtained through the use of this proposed procedure.
Some physical applications are mentioned in the area of the vortex Higgs
model when the complex Sine-Gordon equation is reduced to coupled Riccati
equations.Comment: 27 pages LaTeX2e, 1 encapsulated Postscript figur
A new family of symmetric integrable sigma models
(Minor corrections and reference added)Comment: (ITP Budapest Report No. 502) (11 page
Bi-differential calculi and integrable models
The existence of an infinite set of conserved currents in completely
integrable classical models, including chiral and Toda models as well as the KP
and self-dual Yang-Mills equations, is traced back to a simple construction of
an infinite chain of closed (respectively, covariantly constant) 1-forms in a
(gauged) bi-differential calculus. The latter consists of a differential
algebra on which two differential maps act. In a gauged bi-differential
calculus these maps are extended to flat covariant derivatives.Comment: 24 pages, 2 figures, uses amssymb.sty and diagrams.sty, substantial
extensions of examples (relative to first version
Giant magnons and non-maximal giant gravitons
We produce the open strings on that correspond to
the solutions of integrable boundary sine-Gordon theory by making use of the
-magnon solutions provided in \cite{KPV} together with explicit moduli.
Relating the two boundary parameters in a special way we describe the
scattering of giant magnons with non-maximal giant gravitons and
calculate the leading contribution to the associated magnon scattering phase.Comment: 34 pages, 8 figure
Noncoaxial multivortices in the complex sine-Gordon theory on the plane
We construct explicit multivortex solutions for the complex sine-Gordon
equation (the Lund-Regge model) in two Euclidean dimensions. Unlike the
previously found (coaxial) multivortices, the new solutions comprise single
vortices placed at arbitrary positions (but confined within a finite part of
the plane.) All multivortices, including the single vortex, have an infinite
number of parameters. We also show that, in contrast to the coaxial complex
sine-Gordon multivortices, the axially-symmetric solutions of the
Ginzburg-Landau model (the stationary Gross-Pitaevskii equation) {\it do not}
belong to a broader family of noncoaxial multivortex configurations.Comment: 40 pages, 7 figures in colou
Finite-gap Solutions of the Vortex Filament Equation: Isoperiodic Deformations
We study the topology of quasiperiodic solutions of the vortex filament
equation in a neighborhood of multiply covered circles. We construct these
solutions by means of a sequence of isoperiodic deformations, at each step of
which a real double point is "unpinched" to produce a new pair of branch points
and therefore a solution of higher genus. We prove that every step in this
process corresponds to a cabling operation on the previous curve, and we
provide a labelling scheme that matches the deformation data with the knot type
of the resulting filament.Comment: 33 pages, 5 figures; submitted to Journal of Nonlinear Scienc
Alleviating the non-ultralocality of coset sigma models through a generalized Faddeev-Reshetikhin procedure
The Faddeev-Reshetikhin procedure corresponds to a removal of the
non-ultralocality of the classical SU(2) principal chiral model. It is realized
by defining another field theory, which has the same Lax pair and equations of
motion but a different Poisson structure and Hamiltonian. Following earlier
work of M. Semenov-Tian-Shansky and A. Sevostyanov, we show how it is possible
to alleviate in a similar way the non-ultralocality of symmetric space sigma
models. The equivalence of the equations of motion holds only at the level of
the Pohlmeyer reduction of these models, which corresponds to symmetric space
sine-Gordon models. This work therefore shows indirectly that symmetric space
sine-Gordon models, defined by a gauged Wess-Zumino-Witten action with an
integrable potential, have a mild non-ultralocality. The first step needed to
construct an integrable discretization of these models is performed by
determining the discrete analogue of the Poisson algebra of their Lax matrices.Comment: 31 pages; v2: minor change
Form factors at strong coupling via a Y-system
We compute form factors in planar N=4 Super Yang-Mills at strong coupling.
Namely we consider the overlap between an operator insertion and 2n gluons.
Through the gauge/string duality these are given by minimal surfaces in AdS
space. The surfaces end on an infinite periodic sequence of null segments at
the boundary of AdS. We consider surfaces that can be embedded in AdS_3. We
derive set of functional equations for the cross ratios as functions of the
spectral parameter. These equations are of the form of a Y-system. The integral
form of the Y-system has Thermodynamics Bethe Ansatz form. The area is given by
the free energy of the TBA system or critical value of Yang-Yang functional. We
consider a restricted set of operators which have small conformal dimension
- …