T-duality, Gerbes and Loop Spaces

TL;DR

This paper explores the role of gerbes in T-duality for sigma models with torus fibrations, highlighting how gerbe connections influence global constraints and the conditions under which T-duality is feasible.

Contribution

It introduces a gerbe-based framework for understanding T-duality, generalizing the correspondence space and linking symmetries to Hamiltonian actions.

Findings

Gerbe connections encode gauging obstructions in T-duality.

Geometric T-duality requires Hamiltonian torus actions.

Obstruction to T-duality is non-Hamiltonian symmetry actions.

Abstract

We revisit sigma models on target spaces given by a principal torus fibration $X\to M$, and show how treating the 2-form B as a gerbe connection captures the gauging obstructions and the global constraints on the T-duality. We show that a gerbe connection on X, which is invariant with respect to the torus action, yields an affine double torus fibration Y over the base space M - the generalization of the correspondence space. We construct a symplectic form on the cotangent bundle to the loop space LY and study the relation of its symmetries to T-duality. We find that geometric T-duality is possible if and only if the torus symmetry is generated by Hamiltonian vector fields. Put differently, the obstruction to T-duality is the non-Hamiltonian action of the symmetry group.