Han, F.Mathai, V.2015-10-132015-10-132015Communications in Mathematical Physics, 2015; 337(1):127-1500010-36161432-0916http://hdl.handle.net/2440/95222We 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.en© Springer-Verlag Berlin Heidelberg 2015Journal article003002301610.1007/s00220-014-2270-z0003535047000062-s2.0-849399458652-s2.0-84922386023173768Mathai, V. [0000-0002-1100-3595]