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Type: Journal article
Title: T-duality and the exotic chiral de Rham complex
Author: Linshaw, A.
Varghese, M.
Citation: Communications in Mathematical Physics, 2021; 385(2):1133-1161
Publisher: Springer-Verlag
Issue Date: 2021
ISSN: 0010-3616
Statement of
Andrew Linshaw, Varghese Mathai
Abstract: Let Z be a principal circle bundle over a base manifold M equipped with an integral closed 3-form H called the flux. Let Zˆ be the T-dual circle bundle over M with flux Hˆ. Han and Mathai recently constructed the Z₂-graded space of exotic differential forms Ak¯(Zˆ). It has an additional Z-grading such that the degree zero component coincides with the space of invariant twisted differential forms Ωk¯(Zˆ,Hˆ)Tˆ, and it admits a differential that extends the twisted differential dHˆ=d+Hˆ. The T-duality isomorphism Ωk¯(Z,H)T→Ωk+1(Zˆ,Hˆ)Tˆ of Bouwknegt, Evslin and Mathai extends to an isomorphism Ωk¯(Z,H)→Ak+1 (Zˆ). In this paper, we introduce the exotic chiral de Rham complex Ach,Hˆ,k¯(Zˆ) which contains Ak¯(Zˆ) as the weight zero subcomplex. We give an isomorphism Ωch,H,k¯(Z)→Ach,Hˆ,k+1 (Zˆ) where Ωch,H,k¯(Z) denotes the twisted chiral de Rham complex of Z, which chiralizes the above T-duality map.
Description: Published online: 29 May 2021
Rights: © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2021
DOI: 10.1007/s00220-021-04106-x
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