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

Abstract

We define exotic twisted $S^1$-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, which represent classes in the completed periodic exotic twisted $S^1$-equivariant cohomology of $LZ$. We establish a localisation theorem for the completed periodic exotic twisted $S^1$-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.

arXiv comment23 pages. To appear in CMP

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• On the Topology and Flux of T-Dual Manifolds
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Cited by in corpus (11)

• Ramond-Ramond fields and twisted differential K-theory
• Twisted chiral de Rham complex, generalized geometry, and T-duality
• Twisted differential generalized cohomology theories and their Atiyah-Hirzebruch spectral sequence
• T-duality of singular spacetime compactifications in an H-flux
• T-Duality, Jacobi Forms and Witten Gerbe Modules
• Exotic Courant algebroids and T-duality
• $S^1$-equivariant Chern-Weil constructions on loop space
• T-duality and the exotic chiral de Rham complex
• T-duality with $H$-flux for $2d$ $\sigma$-models
• T-duality, vertical holonomy line bundles and loop Hori formulae
• Exotic Twisted Equivariant K-Theory