Group dualities, T-dualities, and twisted K-theory
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 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.
Keywords
Cite
@article{arxiv.1603.00969,
title = {Group dualities, T-dualities, and twisted K-theory},
author = {Varghese Mathai and Jonathan Rosenberg},
journal= {arXiv preprint arXiv:1603.00969},
year = {2018}
}
Comments
29 pages, mild revision