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arXiv · 1405.1320

Exotic twisted equivariant cohomology of loop spaces, twisted Bismut-Chern character and T-duality

Fei Han·Varghese Mathai
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Abstract

We define exotic twisted $S^1$-equivariant cohomology for the loop space $LZ$ of a smooth manifold $Z$ via the invariant differential forms on $LZ$ with coefficients in the (typically non-flat) holonomy line bundle of a gerbe, with differential an equivariantly flat superconnection. We introduce the twisted Bismut-Chern character form, a loop space refinement of the twisted Chern character form, which represent classes in the completed periodic exotic twisted $S^1$-equivariant cohomology of $LZ$. We establish a localisation theorem for the completed periodic exotic twisted $S^1$-equivariant cohomology for loop spaces and apply it to establish T-duality in a background flux in type II String Theory from a loop space perspective.

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Fei Han, Varghese Mathai. 2015-01-20. Exotic twisted equivariant cohomology of loop spaces, twisted Bismut-Chern character and T-duality. https://doi.org/10.1007/s00220-014-2270-z

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