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

TL;DR

This paper explores the symmetries and T-duality of dg-manifolds, establishing a framework that connects generalized geometry and algebraic structures through derived symmetries and explicit isomorphisms.

Contribution

It introduces the concept of T-dual dg-manifolds, constructs the T-duality map, and links algebraic structures in generalized geometry to derived dg-Leibniz algebras.

Findings

Constructed the T-duality map as a degree -1 cohomology isomorphism.

Established an explicit isomorphism between symmetry dg-algebras of T-dual dg-manifolds.

Connected algebraic structures in generalized geometry to derived dg-Leibniz algebras.

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.