T-duality, Generalized Geometry and Non-Geometric Backgrounds

TL;DR

This paper explores how T-duality and O(d,d) symmetry operate within generalized geometry, especially for non-geometric backgrounds, providing local expressions for pure spinors and analyzing invariance of N=1 vacua equations.

Contribution

It introduces a local generalized geometric framework for describing non-geometric fluxes and their charges, extending the understanding of T-duality in string compactifications.

Findings

Derived local expressions for pure spinors in generalized geometry.

Showed invariance of N=1 vacua equations under T-duality.

Proposed a geometric definition of flux charges using the Courant bracket.

Abstract

We discuss the action of O(d,d), and in particular T-duality, in the context of generalized geometry, focusing on the description of so-called non-geometric backgrounds. We derive local expressions for the pure spinors descibing the generalized geometry dual to an SU(3) structure background, and show that the equations for N=1 vacua are invariant under T-duality. We also propose a local generalized geometrical definition of the charges f, H, Q and R appearing in effective four-dimensional theories, using the Courant bracket. We then address certain global aspects, in particular whether the local non-geometric charges can be gauged away in, for instance, backgrounds admitting a torus action, as well as the structure of generalized parallelizable backgrounds.