Non-commutative gauge theory of twisted D-branes

TL;DR

This work addresses the dynamics of twisted D-branes on group manifolds by constructing non-commutative gauge theories on their world-volumes. Using exact boundary CFT data and the large level limit k → ∞, it derives associative, matrix-valued world-volume algebras Inv_{G^ω}(F(G) ⊗ Hom(V_a,V_b)) and a YM plus CS type action for twisted branes. A broad class of classical, symmetry preserving condensate solutions is found, showing that all twisted branes can arise as bound states of a distinguished elementary brane, with energy and fluctuation analyses consistent with CFT g-factors and fusion data. These results extend brane dynamics to twisted sectors, offer a dynamical realization of twisted D-brane charges, and hint at connections to twisted K-theory and coset models, with potential finite k deformations and flux effects to explore.

Abstract

In this work we propose new non-commutative gauge theories that describe the dynamics of branes localized along twisted conjugacy classes on group manifolds. Our proposal is based on a careful analysis of the exact microscopic solution and it generalizes the matrix models (`fuzzy gauge theories') that are used to study e.g. the bound state formation of point-like branes in a curved background. We also construct a large number of classical solutions and interpret them in terms of condensation processes on branes localized along twisted conjugacy classes.