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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
Article

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.

Keywords

Line Bundle Open Cover Loop Space Equivariant Cohomology Chern Character 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© 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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