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Exotic Twisted Equivariant Cohomology of Loop Spaces, Twisted Bismut–Chern Character and T-Duality

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Abstract

We define exotic twisted \({\mathbb{T}}\)-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 in Bouwknegt et al. (Commun Math Phys 228:17–49, 2002) and Mathai and Stevenson (Commun Math Phys 236:161–186, 2003), which represents classes in the completed periodic exotic twisted \({\mathbb{T}}\)-equivariant cohomology of LZ.We establish a localisation theorem for the completed periodic exotic twisted \({\mathbb{T}}\)-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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Authors and Affiliations

  1. Department of Mathematics, National University of Singapore, Singapore, 119076, Singapore

    Fei Han

  2. Department of Pure Mathematics, University of Adelaide, Adelaide, 5005, Australia

    Varghese Mathai

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  1. Fei Han
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  2. Varghese Mathai
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Correspondence to Varghese Mathai.

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Communicated by N. A. Nekrasov

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Han, F., Mathai, V. Exotic Twisted Equivariant Cohomology of Loop Spaces, Twisted Bismut–Chern Character and T-Duality. Commun. Math. Phys. 337, 127–150 (2015). https://doi.org/10.1007/s00220-014-2270-z

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  • DOI: https://doi.org/10.1007/s00220-014-2270-z

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