T-duality, Quotients and Currents for Non-Geometric Closed Strings

TL;DR

This paper explores the geometric and non-geometric aspects of closed string backgrounds using T-duality, revealing non-commutative and non-associative structures in Q-flux and R-flux models through conformal field theory techniques.

Contribution

It introduces a canonical and current-based approach to analyze T-duality in non-geometric string backgrounds, highlighting new algebraic structures.

Findings

Identification of non-commutative structures in Q-flux backgrounds

Discovery of non-associative structures in R-flux backgrounds

Application of conformal field theory to non-geometric fluxes

Abstract

We use the canonical description of T-duality as well as the formulation of T-duality in terms of chiral currents to investigate the geometric and non-geometric faces of closed string backgrounds originating from principal torus bundles with constant H-flux. Employing conformal field theory techniques, the non-commutative and non-associative structures among generalized coordinates in the so called Q-flux and R-flux backgrounds emerge by gauging the Abelian symmetries of an enlarged Rocek-Verlinde sigma-model and projecting the associated chiral currents of the enlarged theory to the T-dual coset models carrying non-geometric fluxes.