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

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2015

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Han, F.
Mathai, V.

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Communications in Mathematical Physics, 2015; 337(1):127-150

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Fei Han, Varghese Mathai

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We define exotic twisted 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 T-equivariant cohomology of LZ.We establish a localisation theorem for the completed periodic exotic twisted 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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© Springer-Verlag Berlin Heidelberg 2015

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