# Ing. Ivo Petr, Ph.D.

## Publikace

### Poisson-Lie transformations and Generalized Supergravity Equations

Autoři
Hlavatý, L.; Petr, I.
Rok
2021
Publikováno
European Physical Journal C. 2021, 81(484), ISSN 1434-6044.
Typ
Článek
Pracoviště
Anotace
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.

### Poisson-Lie plurals of Bianchi cosmologies and Generalized Supergravity Equations

Autoři
Hlavatý, L.; Petr, I.
Rok
2020
Publikováno
Journal of High Energy Physics. 2020, 2020(04), ISSN 1029-8479.
Typ
Článek
Pracoviště
Anotace
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 $Div\,\Theta$ of the non-commutative structure $\Theta$ used for non-Abelian T-duality or integrable deformations does not give correct $\mathcal{J}$ for Poisson--Lie T-plurality.

### T-folds as Poisson-Lie plurals

Autoři
Hlavatý, L.; Petr, I.
Rok
2020
Publikováno
European Physical Journal C. 2020, 80(892), ISSN 1434-6044.
Typ
Článek
Pracoviště
Anotace
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.

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

Autoři
Hlavatý, L.; Petr, I.
Rok
2019
Publikováno
Journal of High Energy Physics. 2019, 2019(4), ISSN 1029-8479.
Typ
Článek
Pracoviště
Anotace
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.

### Poisson–Lie identities and dualities of Bianchi cosmologies

Autoři
Hlavatý, L.; Petr, I.
Rok
2019
Publikováno
European Physical Journal C. 2019, 79(855), ISSN 1434-6044.
Typ
Článek
Pracoviště
Anotace
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, $\beta$-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.

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

Autoři
Hlavatý, L.; Petr, I.; Petrásek, F.
Rok
2018
Publikováno
Classical and Quantum Gravity. 2018, 35(7), ISSN 0264-9381.
Typ
Článek
Pracoviště
Anotace
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 1, 2, 3 and 4D subgroups of the 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 in general be eliminated 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 (pp-)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.

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

Autoři
Petrásek, F.; Hlavatý, L.; Petr, I.
Rok
2017
Publikováno
Classical and Quantum Gravity. 2017, 34(15), ISSN 0264-9381.
Typ
Článek
Pracoviště
Anotace
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).

### Plane-parallel waves as duals of the flat background

Autoři
Petr, I.; Hlavatý, L.
Rok
2015
Publikováno
Classical and Quantum Gravity. 2015, 32(3), ISSN 0264-9381.
Typ
Článek
Pracoviště
Anotace
We give a classification of non-Abelian T-duals ('T' standing for topological or toroidal) of the flat metric in D = 4 dimensions with respect to the four-dimensional continuous subgroups of the Poincaré group. After dualizing the flat background, we identify the 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 solutions of the classical field equations for all the sigma models in terms of dʼAlembert solutions of the wave equation.