Communications in Mathematical Physics

, Volume 337, Issue 1, pp 127–150 | Cite as

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

  • Fei Han
  • Varghese Mathai


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.


Line Bundle Open Cover Loop Space Equivariant Cohomology Chern Character 
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© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Department of MathematicsNational University of SingaporeSingaporeSingapore
  2. 2.Department of Pure MathematicsUniversity of AdelaideAdelaideAustralia

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