T-duality, Gerbes and Loop Spaces

Details T-duality, Gerbes and Loop Spaces T-duality, Gerbes and Loop Spaces

2007-10-26

arxiv.org/abs/0710.5151v1

Physics

High Energy Physics

High Energy Physics - Theory

32 pages, 5 figures,

Scientific paper

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.

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