T-duality, Gerbes and Loop Spaces

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.

32 pages, 5 figures,

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• New gaugings and non-geometry
• Backreacted T-folds and non-geometric regions in configuration space
• Topological Sigma Models with H-Flux
• T-Duality as a Duality of Loop Group Bundles
• Defects, dualities and the geometry of strings via gerbes. I. Dualities and state fusion through defects
• Towards an extended/higher correspondence -- Generalised geometry, bundle gerbes and global Double Field Theory
• Topological T-duality, Automorphisms and Classifying Spaces
• Topological T-duality and T-folds
• Extended Field Theories as higher Kaluza-Klein theories