Non-geometric String Backgrounds and Worldsheet Algebras

TL;DR

This work addresses non-geometric string backgrounds by deriving the Roytenberg bracket from a worldsheet Hamiltonian that couples a bivector to the Polyakov action, thereby extending the Courant bracket to include general fluxes. The authors construct the worldsheet charge algebra, decompose it into vector, form, and mixed sectors, and demonstrate that the resulting structure encodes $H$, $Q$, and $R$ flux data, recovering Courant theory when the bivector vanishes. They apply the framework to the $T^3$ with $H$-flux and its dual frames, clarifying how geometric and non-geometric phases arise (including the $Q$-space) and discussing limitations in current conservation across dualities. The results illuminate how non-geometric backgrounds can be captured within generalized geometry on the worldsheet and point to global, higher-dimensional, and doubled-geometry extensions, as well as potential connections to M-theory and flux compactifications.

Abstract

Using worldsheet Hamiltonian methods we derive a charge algebra which generalizes the Courant bracket to include fluxes of general index type. This is achieved by coupling a bi-vector to the Hamiltonian of the Polyakov model. This bracket is useful to describe so-called non-geometric backgrounds and has been discussed in the mathematics literature by Dmitry Roytenberg.