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Type: Journal article
Title: Twisted chiral de Rham complex, generalized geometry, and T-duality
Author: Linshaw, A.
Varghese, M.
Citation: Communications in Mathematical Physics, 2015; 339(2):663-697
Publisher: Springer
Issue Date: 2015
ISSN: 0010-3616
Statement of
Andrew Linshaw, Varghese Mathai
Abstract: The chiral de Rham complex of Malikov, Schechtman, and Vaintrob, is a sheaf of differential graded vertex algebras that exists on any smooth manifold Z , and contains the ordinary de Rham complex at weight zero. Given a closed 3-form H on Z , we construct the twisted chiral de Rham differential D H , which coincides with the ordinary twisted differential in weight zero. We show that its cohomology vanishes in positive weight and coincides with the ordinary twisted cohomology in weight zero. As a consequence, we propose that in a background flux, Ramond–Ramond fields can be interpreted as D H -closed elements of the chiral de Rham complex. Given a T-dual pair of principal circle bundles Z , Zˆ with fluxes H , Hˆ , we establish a degree-shifting linear isomorphism between a central quotient of the i R [ t ] -invariant chiral de Rham complexes of Z and Zˆ . At weight zero, it restricts to the usual isomorphism of S 1 - invariant differential forms, and induces the usual isomorphism in twisted cohomology. This is interpreted as T-duality in type II string theory from a loop space perspective. A key ingredient in defining this isomorphism is the language of Courant algebroids, which clarifies the notion of functoriality of the chiral de Rham complex.
Keywords: Twisted cohomology; principal circle bundle; Ramond field; Rham complex; closed element; vertex algebra; loop space; generalize geometry; courant algebroids; differential form; background flux; smooth manifold; space perspective; string theory; dynamical system
Rights: © Springer-Verlag Berlin Heidelberg 2015
RMID: 0030030648
DOI: 10.1007/s00220-015-2403-z
Grant ID:
Appears in Collections:Mathematical Sciences publications

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