T-duality and exceptional generalized geometry through symmetries of dg-manifolds

Ernesto Lupercio; Camilo Rengifo; Bernardo Uribe

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arXiv · 1208.6048

T-duality and exceptional generalized geometry through symmetries of dg-manifolds

Ernesto Lupercio·Camilo Rengifo·Bernardo Uribe

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Abstract

We study dg-manifolds which are R[2]-bundles over R[1]-bundles over manifolds, we calculate its symmetries, its derived symmetries and we introduce the concept of T-dual dg-manifolds. Within this framework we construct the T-duality map as a degree -1 map between the cohomologies of the T-dual dg-manifolds and we show an explicit isomorphism between the differential graded algebra of the symmetries of the T-dual dg-manifolds. We furthermore show how the algebraic structure underlying B_n generalized geometry could be recovered as derived dg-Leibniz algebra of the fixed points of the T-dual automorphism acting on the symmetries of a self T-dual dg-manifold, and we show how other types of algebraic structures underlying exceptional generalized geometry could be obtained as derived symmetries of certain dg-manifolds.

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BibTeX RIS

Ernesto Lupercio, Camilo Rengifo, Bernardo Uribe. 2014-05-13. T-duality and exceptional generalized geometry through symmetries of dg-manifolds. https://arxiv.org/abs/1208.6048

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