Algebroids, AKSZ Constructions and Doubled Geometry

We give a self-contained survey of some approaches aimed at a global description of the geometry underlying double field theory. After reviewing the geometry of Courant algebroids and their incarnations in the AKSZ construction, we develop the theory of metric algebroids including their graded geome...

Descripción completa

Guardado en:

Detalles Bibliográficos
Autores principales:	Marotta Vincenzo Emilio, Szabo Richard J.
Formato:	article
Lenguaje:	EN
Publicado:	De Gruyter 2021
Materias:	algebroids sigma-models doubled geometry para-hermitian geometry string theory t-duality 53z05 53c12 81t30 81t40 Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/efe07937dd89474bbacd9309d8297606
Etiquetas:	Agregar Etiqueta Sin Etiquetas, Sea el primero en etiquetar este registro!

id	oai:doaj.org-article:efe07937dd89474bbacd9309d8297606
record_format	dspace
spelling	oai:doaj.org-article:efe07937dd89474bbacd9309d82976062021-12-05T14:10:45ZAlgebroids, AKSZ Constructions and Doubled Geometry2300-744310.1515/coma-2020-0125https://doaj.org/article/efe07937dd89474bbacd9309d82976062021-11-01T00:00:00Zhttps://doi.org/10.1515/coma-2020-0125https://doaj.org/toc/2300-7443We give a self-contained survey of some approaches aimed at a global description of the geometry underlying double field theory. After reviewing the geometry of Courant algebroids and their incarnations in the AKSZ construction, we develop the theory of metric algebroids including their graded geometry. We use metric algebroids to give a global description of doubled geometry, incorporating the section constraint, as well as an AKSZ-type construction of topological doubled sigma-models. When these notions are combined with ingredients of para-Hermitian geometry, we demonstrate how they reproduce kinematical features of double field theory from a global perspective, including solutions of the section constraint for Riemannian foliated doubled manifolds, as well as a natural notion of generalized T-duality for polarized doubled manifolds. We describe the L∞-algebras of symmetries of a doubled geometry, and briefly discuss other proposals for global doubled geometry in the literature.Marotta Vincenzo EmilioSzabo Richard J.De Gruyterarticlealgebroidssigma-modelsdoubled geometrypara-hermitian geometrystring theoryt-duality53z0553c1281t3081t40MathematicsQA1-939ENComplex Manifolds, Vol 8, Iss 1, Pp 354-402 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	algebroids sigma-models doubled geometry para-hermitian geometry string theory t-duality 53z05 53c12 81t30 81t40 Mathematics QA1-939
spellingShingle	algebroids sigma-models doubled geometry para-hermitian geometry string theory t-duality 53z05 53c12 81t30 81t40 Mathematics QA1-939 Marotta Vincenzo Emilio Szabo Richard J. Algebroids, AKSZ Constructions and Doubled Geometry
description	We give a self-contained survey of some approaches aimed at a global description of the geometry underlying double field theory. After reviewing the geometry of Courant algebroids and their incarnations in the AKSZ construction, we develop the theory of metric algebroids including their graded geometry. We use metric algebroids to give a global description of doubled geometry, incorporating the section constraint, as well as an AKSZ-type construction of topological doubled sigma-models. When these notions are combined with ingredients of para-Hermitian geometry, we demonstrate how they reproduce kinematical features of double field theory from a global perspective, including solutions of the section constraint for Riemannian foliated doubled manifolds, as well as a natural notion of generalized T-duality for polarized doubled manifolds. We describe the L∞-algebras of symmetries of a doubled geometry, and briefly discuss other proposals for global doubled geometry in the literature.
format	article
author	Marotta Vincenzo Emilio Szabo Richard J.
author_facet	Marotta Vincenzo Emilio Szabo Richard J.
author_sort	Marotta Vincenzo Emilio
title	Algebroids, AKSZ Constructions and Doubled Geometry
title_short	Algebroids, AKSZ Constructions and Doubled Geometry
title_full	Algebroids, AKSZ Constructions and Doubled Geometry
title_fullStr	Algebroids, AKSZ Constructions and Doubled Geometry
title_full_unstemmed	Algebroids, AKSZ Constructions and Doubled Geometry
title_sort	algebroids, aksz constructions and doubled geometry
publisher	De Gruyter
publishDate	2021
url	https://doaj.org/article/efe07937dd89474bbacd9309d8297606
work_keys_str_mv	AT marottavincenzoemilio algebroidsakszconstructionsanddoubledgeometry AT szaborichardj algebroidsakszconstructionsanddoubledgeometry
_version_	1718371772592553984

Algebroids, AKSZ Constructions and Doubled Geometry

Ejemplares similares