2007/10/26 by Dmitriy M. Belov, Belov, Dmitriy M., Chris M. Hull +3
Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #hep-th
paper · pdf · doi:10.48550/arxiv.0710.5151
32 pages, 5 figures,
arxiv created 2007/10/26 · arxiv updated 2009/12/01
We revisit sigma models on target spaces given by a principal torus fibration X→ 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.