Open-string T-duality and applications to non-geometric backgrounds

TL;DR

This paper revisits open-string T-duality using Buscher's procedure, addressing technical gaps, and explores its implications for non-geometric backgrounds, including detailed examples and boundary condition analysis.

Contribution

It provides a comprehensive technical framework for open-string T-duality, including multiple directions and non-trivial topologies, with explicit examples and global boundary condition analysis.

Findings

T-duality transformations for open strings are extended to complex topologies.

Explicit example of T-duality on a three-torus with H-flux is provided.

Global properties of boundary conditions in non-geometric backgrounds are discussed.

Abstract

We revisit T-duality transformations for the open string via Buscher's procedure and work-out technical details which have been missing so far in the literature. We take into account non-trivial topologies of the world-sheet, we consider T-duality along directions with Neumann as well as Dirichlet boundary conditions, and we include collective T-duality along multiple directions. We illustrate this formalism with the example of the three-torus with H-flux and its T-dual backgrounds, and we discuss global properties of open-string boundary conditions on such spaces.