28 research outputs found
Classical solution of a sigma-model in curved background
We have solved a sigma-model in curved background using the fact that the
Poisson-Lie T-duality can transform the curved background into the flat one.
For finding solution of the flat model we have used transformation of
coordinates that makes the metric constant. The T-duality transform was then
explicitly performed.Comment: 7 page
T-folds as Poisson-Lie plurals
In previous papers we have presented many purely bosonic solutions of
Generalized Supergravity Equations obtained by Poisson-Lie T-duality and
plurality of flat and Bianchi cosmologies. In this paper we focus on their
compactifications and identify solutions that can be interpreted as T-folds. To
recognize T-folds we adopt the language of Double Field Theory and discuss how
Poisson-Lie T-duality/plurality fits into this framework. As a special case we
confirm that all non-Abelian T-duals can be compactified as T-folds.Comment: v3 - published versio
Classical solutions of sigma models in curved backgrounds by the Poisson-Lie T-plurality
Classical equations of motion for three-dimensional sigma-models in curved
background are solved by a transformation that follows from the Poisson-Lie
T-plurality and transform them into the equations in the flat background.
Transformations of coordinates that make the metric constant are found and used
for solving the flat model. The Poisson-Lie transformation is explicitly
performed by solving the PDE's for auxiliary functions and finding the relevant
transformation of coordinates in the Drinfel'd double. String conditions for
the solutions are preserved by the Poisson-Lie transformations. Therefore we
are able to specify the type of sigma-model solutions that solve also equations
of motion of three dimensional relativistic strings in the curved backgrounds.
Simple examples are given
Flat coordinates and dilaton fields for three--dimensional conformal sigma models
Riemannian coordinates for flat metrics corresponding to three--dimensional
conformal Poisson--Lie T--dualizable sigma models are found by solving partial
differential equations that follow from the transformations of the connection
components. They are then used for finding general forms of the dilaton fields
satisfying the vanishing beta equations of the sigma models.Comment: 16 pages, no figure
Poisson-Lie T-plurality as canonical transformation
We generalize the prescription realizing classical Poisson-Lie T-duality as
canonical transformation to Poisson-Lie T-plurality. The key ingredient is the
transformation of left-invariant fields under Poisson-Lie T-plurality. Explicit
formulae realizing canonical transformation are presented and the preservation
of canonical Poisson brackets and Hamiltonian density is shown.Comment: 11 pages. Details of calculations added, version accepted for
publicatio
Classification of Poisson-Lie T-dual models with two-dimensional targets
Four-dimensional Manin triples and Drinfeld doubles are classified and
corresponding two-dimensional Poisson-Lie T-dual sigma models on them are
constructed. The simplest example of a Drinfeld double allowing decomposition
into two nontrivially different Manin triples is presented.Comment: 6 pages, LaTeX; correction: two Manin triples originally considered
separately are shown to lead to the same Drinfeld doubl
Nonabelian dualization of plane wave backgrounds
We investigate plane-parallel wave metrics from the point of view of their
(Poisson-Lie) T-dualizability. For that purpose we reconstruct the metrics as
backgrounds of nonlinear sigma models on Lie groups. For construction of dual
backgrounds we use Drinfel'd doubles obtained from the isometry groups of the
metrics. We find dilaton fields that enable to satisfy the vanishing beta
equations for the duals of the homogenous plane-parallel wave metric. Torsion
potentials or B-fields, invariant w.r.t. the isometry group of Lobachevski
plane waves are obtained by the Drinfel'd double construction. We show that a
certain kind of plurality, different from the (atomic) Poisson-Lie T-plurality,
may exist in case that metrics admit several isometry subgroups having the
dimension of the Riemannian manifold. An example of that are two different
backgrounds dual to the homogenous plane-parallel wave metric.Comment: 18 page
Principal models on a solvable group with nonconstant metric
Field equations for generalized principle models with nonconstant metric are
derived and ansatz for their Lax pairs is given. Equations that define the Lax
pairs are solved for the simplest solvable group. The solution is dependent on
one free variable that can serve as the spectral parameter. Painleve analysis
of the resulting model is performed and its particular solutions are foundComment: 8 pages, Latex2e, no figure
Poisson-Lie transformations and Generalized Supergravity Equations
In this paper we investigate Poisson-Lie transformation of dilaton and vector
field J appearing in Generalized Supergravity Equations. While the formulas
appearing in literature work well for isometric sigma models, we present
examples for which Generalized Supergravity Equations are not preserved.
Therefore, we suggest modification of these formulas.Comment: published versio