T-duality, Generalized Geometry and Non-Geometric Backgrounds

TL;DR

This work develops a generalized-geometry framework for T-duality and non-geometric backgrounds by treating O(d,d) transformations as local gauge actions on generalized structures. It derives local pure spinor expressions dual to SU(3) structures, establishes the invariance of N=1 flux vacua equations under T-duality, and defines generalized charges via the Courant bracket that encode geometric and non-geometric fluxes. The analysis highlights that Q and R charges are frame-dependent and may be globally non-gaugeable, revealing global obstructions tied to base cohomology and non-geometric monodromies, while identifying generalized parallelizable backgrounds where R vanishes and dualities act coherently. Together, these results provide a coherent language linking T-duality, generalized geometry, and non-geometric fluxes with implications for flux compactifications and low-energy effective theories.

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.