arXiv subjects

Ladislav Hlavaty

Publications and source records attributed to Ladislav Hlavaty.

17 recordsLinked to original sources

arXiv2022

Compatibility of Poisson--Lie transformations with symmetries of Generalized Supergravity Equations

We investigate two types of transformations that keep NS-NS Generalized Supergravity Equations satisfied : $χ$-symmetry that shifts dilaton and gauge transformations that change both dilaton and vector field $J$. Due to these symmetries there is a large set of dilatons and vector fields $J$ that (for a fixed metric and B-field) satisfy Generalized Supergravity Equations but only some of them can be be used as input for Poisson--Lie transformations. Conditions that define the admissible dilatons are given and examples are presented.

hep-th↗

arXiv2020

Classification of six-dimensional Leibniz algebras ${\mathcal E}_3

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: Six-dimensional Lie algebras that can be considered extension of semi-Abelian four-dimensional Drinfeld double and unique extensions of non-Abelian Bianchi algebras. For all of the algebras explicit forms of generalized frame fields are given.

hep-th↗

arXiv2019

Poisson-Lie T-plurality revisited. Is T-duality unique?

We investigate (non-)Abelian T-duality from the perspective of Poisson-Lie T-plurality. We show that sigma models related by duality/plurality are given not only by Manin triples obtained from decompositions of Drinfel'd double, but also by their particular embeddings, i.e. maps that relate bases of these decompositions. This allows us to get richer set of dual or plural sigma models than previously thought. That's why we ask how T-duality is defined and what should be the `canonical' duality or plurality transformation.

hep-th↗

arXiv2018

Plane-parallel waves as duals of the flat background II: T-duality with spectators

We give the classification of T-duals of the flat background in four dimensions with respect to one-, two-, and three-dimensional subgroups of the Poincaré group using non-Abelian T-duality with spectators. As duals we find backgrounds for sigma models in the form of plane-parallel waves or diagonalizable curved metrics often with torsion. Among others, we find exactly solvable time-dependent isotropic pp-wave, singular pp-waves, or generalized plane wave (K-model).

hep-th↗

arXiv2018

Plane-parallel waves as duals of the flat background III: T-duality with torsionless $B$-field

By addition of non-zero, but torsionless $B$-field, we expand the classification of (non-)Abelian T-duals of the flat background in four dimensions with respect to one-, two-, three-, and four-dimensional subgroups of Poincaré group. We discuss the influence of the additional $B$-field on the process of dualization and identify essential parts of the torsionless $B$-field that cannot be eliminated in general by coordinate or gauge transformation of the dual background. These effects are demonstrated using particular examples. Due to their physical importance, we focus on duals whose metrics represent plane-parallel waves. Besides the previously found metrics, we find new pp-waves depending on parameters originating from the torsionless $B$-field. These pp-waves are brought into their standard forms in Brinkmann and Rosen coordinates.

hep-th↗

arXiv2016

On uniqueness of T-duality with spectators

We investigate the dependence of nonabelian T-duality on various identification of the group of target space isometries of nonlinear sigma models with its orbits, i.e. with respect to the location of the group unit on manifolds invariant under the isometry group. We show that T-duals constructed by isometry groups of dimension less than the dimension of the (pseudo)riemannian manifold may depend not only on the initial metric but also on the choice of manifolds defining positions of group units on each of the submanifold invariant under the isometry group. We investigate whether this dependence can be compensated by coordinate transformation.

hep-th↗

arXiv2014

Plane-parallel waves as duals of the flat background

We give a classification of non-Abelian T-duals of the flat metric in D=4 dimensions with respect to the four-dimensional continuous subgroups of the Poincare group. After dualizing the flat background, we identify majority of dual models as conformal sigma models in plane-parallel wave backgrounds, most of them having torsion. We give their form in Brinkmann coordinates. We find, besides the plane-parallel waves, several diagonalizable curved metrics with nontrivial scalar curvature and torsion. Using the non-Abelian T-duality, we find general solution of the classical field equations for all the sigma models in terms of d'Alembert solutions of the wave equation.

hep-th↗

arXiv2014

New solvable sigma models in plane--parallel wave background

We explicitly solve the classical equations of motion for strings in backgrounds obtained as non-abelian T-duals of a homogeneous isotropic plane-parallel wave. To construct the dual backgrounds, semi-abelian Drinfeld doubles are used which contain the isometry group of the homogeneous plane wave metric. The dual solutions are then found by the Poisson-Lie transformation of the explicit solution of the original homogeneous plane wave background. Investigating their Killing vectors, we have found that the dual backgrounds can be transformed to the form of more general plane-parallel waves.

hep-th↗

arXiv2013

On renormalization of Poisson-Lie T-plural sigma models

Covariance of the one-loop renormalization group equations with respect to Poisson-Lie T-plurality of sigma models is discussed. The role of ambiguities in renormalization group equations of Poisson-Lie sigma models with truncated matrices of parameters is investigated.

hep-th↗

arXiv2012

Poisson-Lie Sigma Models on Drinfel'd double

Poisson sigma models represent an interesting use of Poisson manifolds for the construction of a classical field theory. Their definition in the language of fibre bundles is shown and the corresponding field equations are derived using a coordinate independent variational principle. The elegant form of equations of motion for so called Poisson-Lie groups is derived. Construction of the Poisson-Lie group corresponding to a given Lie bialgebra is widely known only for coboundary Lie bialgebras. Using the adjoint representation of Lie group and Drinfel'd double we show that Poisson-Lie group can be constructed for general Lie bialgebra.

math.DG↗

arXiv2010

Manin supertriples and Drinfel'd superdoubles in low dimensions

Defining the real Lie superalgebra as real $Z_2$--graded vector space we classify real Manin supertriples and Drinfel'd superdoubles of superdimensions (2,2), (4,2) and (2,4). They can be used for construction of sigma-models on supergroups related by Poisson-Lie T-plurality.

math-ph↗

arXiv2008

Description of D-branes invariant under the Poisson-Lie T-plurality

We write the conditions for open strings with charged endpoints in the language of gluing matrices. We identify constraints imposed on the gluing matrices that are essential in this setup and investigate the question of their invariance under the Poisson-Lie T-plurality transformations. We show that the chosen set of constraints is equivalent to the statement that the lifts of D-branes into the Drinfel'd double are right cosets with respect to a maximally isotropic subgroup and therefore it is invariant under the Poisson-Lie T-plurality transformations.

hep-th↗

arXiv2008

Quantum integrability of nonultralocal models through Baxterisation of quantised braided algebra

A scheme suitable for describing quantum nonultralocal models including supersymmetric ones is proposed. Braided algebras are generalised to be used through Baxterisation for constructing braided quantum Yang--Baxter equations. Supersymmetric and some known nonultralocal models are derived in the framework of the present approach. As further applications of this scheme construction of new quantum integrable nonultralocal models like mKdV and anyonic supersymmetric models including deformed anyonic super algebra are outlined.

hep-th↗

arXiv2008

On the Poisson-Lie T-plurality of boundary conditions

Conditions for the gluing matrix defining consistent boundary conditions of two-dimensional nonlinear sigma-models are analyzed and reformulated. Transformation properties of the right-invariant fields under Poisson-Lie T-plurality are used to derive a formula for the transformation of the boundary conditions. Examples of transformation of D-branes in two and three dimensions are presented. We investigate obstacles arising in this procedure and propose possible solutions.

hep-th↗

arXiv2007

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.

hep-th↗

arXiv2005

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.

hep-th↗

arXiv1992

Quantum Braided Groups

A new type of algebras that represent a generalization of both quantum groups and braided groups is defined. These algebras are given by a pair of solutions of the Yang--Baxter equation that satisfy some additional conditions. Several examples are presented.

hep-th↗