Non-geometric Backgrounds and the First Order String Sigma Model

TL;DR

This paper explores a first order string sigma model incorporating bi-vectors, two-forms, and metrics, revealing how non-geometric backgrounds relate to membrane actions and generalized brackets, with implications for T-duality and flux backgrounds.

Contribution

It introduces a first order sigma model framework that captures non-geometric string backgrounds and their relation to membrane theories and generalized Courant brackets.

Findings

The model encodes non-geometric backgrounds via bi-vectors and fluxes.

Membrane actions describe R-space, a T-dual of T^3 with flux.

Gauged WZW models provide examples with bi-vector couplings.

Abstract

We study the first order form of the NS string sigma model allowing for worldsheet couplings corresponding on the target space to a bi-vector, a two-form and an inverse metric. Lifting the topological sector of this action to three dimensions produces several Wess-Zumino like terms which encode the bi-vector generalization of the Courant bracket. This bracket may be familiar to physicists through the (H_{ijk},F_{ij}^{k},Q_i^{jk},R^{ijk}) notation for non-geometric backgrounds introduced by Shelton-Taylor-Wecht. The non-geometricity of the string theory in encoded in the global properties of the bi-vector, when the bi-vector is a section then the string theory is geometric. Another interesting situation emerges when one considers membrane actions which are not equivalent to string theories on the boundary of the membrane. Such a situation arises when one attempts to describe the so-called R-space (the third T-dual of a T^3 with H_3 flux). This model appears to be, at least classically, described by a membrane sigma model, not a string theory. Examples of geometric backgrounds with bi-vector couplings and non-vanishing Q-coefficients are provided by gauged WZW models.