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arXiv · 1603.00969

Group dualities, T-dualities, and twisted K-theory

Varghese Mathai·Jonathan Rosenberg
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Abstract

This paper explores further the connection between Langlands duality and T-duality for compact simple Lie groups, which appeared in work of Daenzer-Van Erp and Bunke-Nikolaus. We show that Langlands duality gives rise to isomorphisms of twisted K-groups, but that these K-groups are trivial except in the simplest case of SU(2) and SO(3). Along the way we compute explicitly the map on $H^3$ induced by a covering of compact simple Lie groups, which is either 1 or 2 depending in a complicated way on the type of the groups involved. We also give a new method for computing twisted K-theory using the Segal spectral sequence, giving simpler computations of certain twisted K-theory groups of compact Lie groups relevant for D-brane charges in WZW theories and rank-level dualities. Finally we study a duality for orientifolds based on complex Lie groups with an involution.

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Varghese Mathai, Jonathan Rosenberg. 2017-03-13. Group dualities, T-dualities, and twisted K-theory. https://doi.org/10.1112/jlms.12085

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