arXiv subjects

Ivo Petr

Publications and source records attributed to Ivo Petr.

14 recordsLinked to original sources

arXiv2026

Eight-dimensional Manin triples, Yang-Baxter deformations and solutions of Supergravity Equations

Extensive list of 4+4-dimensional Manin triples that was presented recently can be used to find new solutions of supergravity equations via Poisson-Lie T-plurality. To get the solutions we start with 1+3-dimensional flat backgrounds on Poisson-Lie groups corresponding to semi-Abelian Manin triples. For application of the Poisson-Lie T-plurality we identify Manin triples that form various decompositions of the same Drinfeld double. Beside flat backgrounds and plane-parallel waves solving supergravity equations, plurality transformation also produces curved backgrounds with torsion satisfying (generalized) supergravity equations. Many of the Poisson-Lie transformations can be understood as homogeneous Yang-Baxter deformations. Of special interest are the non-unimodular deformations leading to solutions of generalized supergravity equations.

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arXiv2025

Classification of standard Manin triples in dimension 4+4

Four- and six-dimensional Drinfeld doubles were classified in the past in terms of Manin triples. We provide an important step towards the classification of eight-dimensional Drinfeld doubles by presenting an extensive list of Manin triples formed by pairs of four-dimensional Lie algebras. Due to the high complexity of the classification we focus on Manin triples formed by algebras in a certain standard form. The list contains 188 non-isomorphic Manin triples plus their duals. To apply the results, we construct several four-dimensional WZW models on non-semisimple Lie groups. Some of the WZW models are known from the literature, but new cases are presented as well. As a consequence of the construction method, the WZW models are Poisson--Lie dualizable.

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arXiv2025

On spectator dependence of Jacobi-Lie T-plurality

Recently introduced Jacobi-Lie T-plurality turned out to be a solution-generating technique in string theory. Being based on Leibniz algebras instead of Drinfeld doubles, it can be understood as a generalization of Poisson-Lie T-plurality. In this paper we investigate Jacobi-Lie T-plurality with spectators, and focus particularly on modification of the spectator fields by an arbitrary function $f$. Using this modification new sigma model backgrounds can be constructed as Jacobi-Lie models. For low-dimensional Leibniz algebras classified a few years ago and warping factor $f(\omega)=\gamma\, e^{\omega}$ we find sigma model backgrounds satisfying Supergravity Equations and check that their plurals again satisfy Supergravity Equations.

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arXiv2024

Plane-parallel waves as Jacobi-Lie models

T-duality and its generalizations are widely recognized either as symmetries or solution-generating techniques in string theory. Recently introduced Jacobi-Lie T-plurality is based on Leibniz algebras whose structure constants ${f_{ab}}^c, {f_c}^{ab}, Z_a, Z^a$ satisfy further conditions. Low dimensional Jacobi-Lie bialgebras were classified a few years ago. We study four- and six-dimensional algebras with structure constants ${f_b}^{ba} = Z^a = 0$ and show that there are several classes consisting of mutually isomorphic algebras. Using isomorphisms between Jacobi-Lie bialgebras we investigate three- and four-dimensional sigma models related by Jacobi-Lie T-plurality with and without spectators. In the Double Field Theory formulation constant generalized fluxes $F_A$ are used in the literature to transform dilaton field. We extend the procedure to non-constant fluxes and verify that obtained backgrounds and dilatons solve Supergravity Equations. Most of the resulting backgrounds have vanishing curvature scalars and, as can be seen by finding Brinkmann coordinates, represent plane-parallel waves solving Supergravity Equations.

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arXiv2023

Jacobi-Lie Models and Supergravity Equations

Poisson-Lie T-duality/plurality was recently generalized to Jacobi-Lie T-plurality formulated in terms of Double Field Theory and based on Leibniz algebras given by structure coefficients $f_{ab}{}^{c},f_{c}{}^{ab},$ and $Z_a,Z^a$. We investigate three- and four-dimensional sigma models corresponding to six-dimensional Leibniz algebras with $f_b{}^{ba}\neq 0$, $Z^a=0$. We show that these algebras are plural one to another and, moreover, to an algebra with $f_b{}^{ba}= 0$, $Z^a=0$. These pluralities are used for construction of Jacobi-Lie models. It was conjectured that plural models should satisfy Generalized Supergravity Equations. We have found examples of models satisfying ``true'' Generalized Supergravity Equations where no trivialization to usual Supergravity Equations is possible. On the other hand, we show that there are also models corresponding to algebras with $f_b{}^{ba}\neq 0$, $Z^a=0$ where the Killing vector appearing in Generalized Supergravity Equations either vanishes or can be removed by suitable gauge transformation. Such models then satisfy usual Supergravity Equations, i.e. vanishing beta function equations.

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arXiv2021

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.

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arXiv2020

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.

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arXiv2020

Poisson-Lie plurals of Bianchi cosmologies and Generalized Supergravity Equations

Poisson-Lie T-duality and plurality are important solution generating techniques in string theory and (generalized) supergravity. Since duality/plurality does not preserve conformal invariance, the usual beta function equations are replaced by Generalized Supergravity Equations containing vector $\mathcal{J}$. In this paper we apply Poisson-Lie T-plurality on Bianchi cosmologies. We present a formula for the vector $\mathcal{J}$ as well as transformation rule for dilaton, and show that plural backgrounds together with this dilaton and $\mathcal{J}$ satisfy the Generalized Supergravity Equations. The procedure is valid also for non-local dilaton and non-constant $\mathcal{J}$. We also show that $Div\,Θ$ of the non-commutative structure $Θ$ used for non-Abelian T-duality or integrable deformations does not give correct $\mathcal{J}$ for Poisson-Lie T-plurality.

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arXiv2019

Poisson-Lie identities and dualities of Bianchi cosmologies

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 $\mathfrak{b}\bowtie \mathfrak{a}$ containing Bianchi algebras $\mathfrak{b}$ we identify general forms of Poisson--Lie identities and dualities. We show that these can be decomposed into simple factors, namely automorphisms of Manin triples, B-shifts, $β$-shifts, and "full" or "factorized" dualities. Further, we study effects of these transformations and utilize the decompositions to obtain new backgrounds which, supported by corresponding dilatons, satisfy Generalized Supergravity Equations.

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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.

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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).

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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.

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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.

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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.

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