Related papers: Plane-parallel waves as Jacobi-Lie models

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…

We present a brief discussion of recent work on duality symmetries in non-trivial string backgrounds. Duality is obtained from a gauged non-linear sigma-model with vanishing gauge field strength. Standard results are reproduced for abelian…

Different compactifications of six-dimensional string theory on $M_4 \times T^2$ are considered. Particular attention is given to the roles of the reduced modes as the $S$ and $T$ fields. It is shown that there is a discrete group of…

We investigate a special class of Poisson--Lie T-plurality transformations of Bianchi cosmologies invariant with respect to non-semisimple Bianchi groups. For six-dimensional semi-Abelian Manin triples $\mathfrak{b}\bowtie \mathfrak{a}$…

This is a general introduction to duality in field theories. The existence and breaking of global symmetries is used as a guideline to systematically prove duality between different field theories. Systems discussed include abelian and…

We proceed to construct a dual pair for the $AdS_3 \times S^3$ background by applying non-Abelian T-duality (here as Poisson-Lie (PL) T-duality on a semi-Abelian double). By using a certain parametrization of the $4$-dimensional Lie group…

We gauge the non-abelian isometries of a sigma model with boundaries. Forcing the field strength of the gauge fields to vanish renders the gauged model equivalent to the ungauged one provided that boundary conditions are taken into account…

Poisson-Lie (PL) T-duality has received much attention over the last five years in connection with integrable string worldsheet theories. At the level of the worldsheet, the algebraic structure underpinning these connections is made…

Leibniz algebras ${\mathcal E}_n$ were introduced as algebraic structure underlying U-duality. Algebras ${\mathcal E}_3$ derived from Bianchi three-dimensional Lie algebras are classified here. Two types of algebras are obtained:…

We use the canonical description of T-duality as well as the formulation of T-duality in terms of chiral currents to investigate the geometric and non-geometric faces of closed string backgrounds originating from principal torus bundles…

The worldsheet theories that describe Poisson-Lie T-dualisable $\sigma$-models on group manifolds as well as integrable $\eta$, $\lambda$ and $\beta$-deformations provide examples of ${\cal E}$-models. Here we show how such ${\cal…

We construct colliding plane wave solutions in higher dimensional gravity theory with dilaton and higher form flux, which appears naturally in the low energy theory of string theory. Especially, the role of the junction condition in…

We present a duality procedure that relates conventional four-dimensional matter-coupled N=1 supergravities to dual formulations in which auxiliary fields are replaced by field-strengths of gauge three-forms. The duality promotes specific…

A recent attempt to extend the geometric Langlands duality to affine Kac-Moody groups, has led Braverman and Finkelberg [arXiv:0711.2083] to conjecture a mathematical relation between the intersection cohomology of the moduli space of…

String theory has the T-duality symmetry when the target space has Abelian isometries. A generalization of the T-duality, where the isometry group is non-Abelian, is known as the non-Abelian T-duality, which works well as a…

The Hamilton-Jacobi formalism generalized to 2-dimensional field theories according to Lepage's canonical framework is applied to several relativistic real scalar fields, e.g. massless and massive Klein-Gordon, Sinh and Sine-Gordon,…

We consider four-dimensional $\mathcal{N}=1$ supergravity models of a kind appearing in string flux compactifications. It has been recently shown that, by using double three-form multiplets instead of ordinary chiral multiplets, one can…

We study certain Z_2-graded, finite-dimensional polynomial algebras of degree 2 which are a special class of deformations of Lie superalgebras, which we call quadratic Lie superalgebras. Starting from the formal definition, we discuss the…

We generalise the electric-magnetic duality in standard Maxwell theory to its non-commutative version. Both space-space and space-time non-commutativity are necessary. The duality symmetry is then extended to a general class of…

Local symmetries is one of the most successful themes in modern theoretical physics. Although they are usually associated to Lie algebras, a gradual increase of interest in more general situations where local symmetries are associated to…