Branes on group manifolds, gluon condensâtes, and twisted K-theory

Abstract

In this work we study the dynamics of branes on group manifolds G deep in the stringy regime. After giving a brief overview of the various branes that can be constructed within the boundary conformal field theory approach, we analyze in detail the condensation processes that occur on stacks of such branes. At large volume our discussion is based on certain effective gauge theories on non-commutative 'fuzzy' spaces. Using the 'absorption of the boundary spin'-principle which was formulated by Affleck and Ludwig in their work on the Kondo model, we extrapolate the brane dynamics into the stringy regime. For supersymmetric theories, the resulting condensation processes turn out to be consistent with the existence of certain conserved charges taking values in some non-trivial discrete abelian groups. We obtain strong constraints on these charge groups for G = SU(N). The results may be compared with a recent proposal of Bouwknegt and Mathai according to which charge groups on curved spaces X (with a non-vanishing NSNS 3-form field strength H) are given by the twisted K-groups K*H(X).