Sigma models for genuinely non-geometric backgrounds

TL;DR

This paper investigates the existence of genuinely non-geometric backgrounds in string theory using sigma models, constructing specific Courant algebroids and proposing extended models that can describe such backgrounds.

Contribution

It introduces a class of Courant algebroids with fluxes and proposes extended 3D sigma models in phase space capable of capturing genuinely non-geometric backgrounds.

Findings

Standard Courant algebroid-based models are always geometric.

Extended phase space sigma models can describe non-geometric backgrounds.

Connections to double field theory are established from a world sheet perspective.

Abstract

The existence of genuinely non-geometric backgrounds, i.e. ones without geometric dual, is an important question in string theory. In this paper we examine this question from a sigma model perspective. First we construct a particular class of Courant algebroids as protobialgebroids with all types of geometric and non-geometric fluxes. For such structures we apply the mathematical result that any Courant algebroid gives rise to a 3D topological sigma model of the AKSZ type and we discuss the corresponding 2D field theories. It is found that these models are always geometric, even when both 2-form and 2-vector fields are neither vanishing nor inverse of one another. Taking a further step, we suggest an extended class of 3D sigma models, whose world volume is embedded in phase space, which allow for genuinely non-geometric backgrounds. Adopting the doubled formalism such models can be related to double field theory, albeit from a world sheet perspective.