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 $H^3$ 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.

29 pages, mild revision

References in corpus (5)

• The rank-level duality for non-abelian theta functions
• On The Structure Of The Chan-Paton Factors For D-Branes In Type II Orientifolds
• WZW orientifolds and finite group cohomology
• String theory on elliptic curve orientifolds and KR-theory
• Twisted D-branes of the SU(N)_K WZW model and level-rank duality

Cited by in corpus (8)

• Ramond-Ramond fields and twisted differential K-theory
• Twisted differential generalized cohomology theories and their Atiyah-Hirzebruch spectral sequence
• The cohomology of projective unitary groups
• Twisted Morava K-theory and connective covers of Lie groups
• A new approach to twisted K-theory of compact Lie groups
• Adams operations on twisted $K$-theory of compact Lie groups
• Computations in higher twisted $K$-theory
• The multi-degree of coverings on Lie groups