An algebraic classification of solution generating techniques

We consider a two-fold problem: on the one hand, the classification of a family of solution-generating techniques in (modified) supergravity and, on the other hand, the classification of a family of canonical transformations of 2-dimensional σ-models giving rise to integrable-preserving transformati...

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Autores principales:	Riccardo Borsato, Sibylle Driezen, Falk Hassler
Formato:	article
Lenguaje:	EN
Publicado:	Elsevier 2021
Materias:	Physics QC1-999
Acceso en línea:	https://doaj.org/article/f464f3dfb9e84fe0bb20589abb83087f
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spelling	oai:doaj.org-article:f464f3dfb9e84fe0bb20589abb83087f2021-12-04T04:32:41ZAn algebraic classification of solution generating techniques0370-269310.1016/j.physletb.2021.136771https://doaj.org/article/f464f3dfb9e84fe0bb20589abb83087f2021-12-01T00:00:00Zhttp://www.sciencedirect.com/science/article/pii/S0370269321007115https://doaj.org/toc/0370-2693We consider a two-fold problem: on the one hand, the classification of a family of solution-generating techniques in (modified) supergravity and, on the other hand, the classification of a family of canonical transformations of 2-dimensional σ-models giving rise to integrable-preserving transformations. Assuming a generalised Scherk-Schwarz ansatz, in fact, the two problems admit essentially the same algebraic formulation, emerging from an underlying double Lie algebra d. After presenting our derivation of the classification, we discuss in detail the relation to modified supergravity and the additional conditions to recover the standard (unmodified) supergravity. Starting from our master equation — that encodes all the possible continuous deformations allowed in the family of solution-generating techniques — we show that these are classified by the Lie algebra cohomologies H2(h,R) and H3(h,R) of the maximally isotropic subalgebra h of the double Lie algebra d. We illustrate our results with a non-trivial example, the bi-Yang-Baxter-Wess-Zumino model.Riccardo BorsatoSibylle DriezenFalk HasslerElsevierarticlePhysicsQC1-999ENPhysics Letters B, Vol 823, Iss , Pp 136771- (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Physics QC1-999
spellingShingle	Physics QC1-999 Riccardo Borsato Sibylle Driezen Falk Hassler An algebraic classification of solution generating techniques
description	We consider a two-fold problem: on the one hand, the classification of a family of solution-generating techniques in (modified) supergravity and, on the other hand, the classification of a family of canonical transformations of 2-dimensional σ-models giving rise to integrable-preserving transformations. Assuming a generalised Scherk-Schwarz ansatz, in fact, the two problems admit essentially the same algebraic formulation, emerging from an underlying double Lie algebra d. After presenting our derivation of the classification, we discuss in detail the relation to modified supergravity and the additional conditions to recover the standard (unmodified) supergravity. Starting from our master equation — that encodes all the possible continuous deformations allowed in the family of solution-generating techniques — we show that these are classified by the Lie algebra cohomologies H2(h,R) and H3(h,R) of the maximally isotropic subalgebra h of the double Lie algebra d. We illustrate our results with a non-trivial example, the bi-Yang-Baxter-Wess-Zumino model.
format	article
author	Riccardo Borsato Sibylle Driezen Falk Hassler
author_facet	Riccardo Borsato Sibylle Driezen Falk Hassler
author_sort	Riccardo Borsato
title	An algebraic classification of solution generating techniques
title_short	An algebraic classification of solution generating techniques
title_full	An algebraic classification of solution generating techniques
title_fullStr	An algebraic classification of solution generating techniques
title_full_unstemmed	An algebraic classification of solution generating techniques
title_sort	algebraic classification of solution generating techniques
publisher	Elsevier
publishDate	2021
url	https://doaj.org/article/f464f3dfb9e84fe0bb20589abb83087f
work_keys_str_mv	AT riccardoborsato analgebraicclassificationofsolutiongeneratingtechniques AT sibylledriezen analgebraicclassificationofsolutiongeneratingtechniques AT falkhassler analgebraicclassificationofsolutiongeneratingtechniques AT riccardoborsato algebraicclassificationofsolutiongeneratingtechniques AT sibylledriezen algebraicclassificationofsolutiongeneratingtechniques AT falkhassler algebraicclassificationofsolutiongeneratingtechniques
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An algebraic classification of solution generating techniques

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