New WZW D-branes from the algebra of Wilson loop operators

TL;DR

This paper explores the algebra of Wilson loop operators in WZW models, revealing a rich structure that generates new D-branes and provides insights into their symmetries and geometries, especially for higher rank groups.

Contribution

It introduces a detailed analysis of the Wilson loop algebra in WZW models, uncovering new D-branes and extending the understanding of boundary fixed points beyond SU(2).

Findings

Wilson loop algebra encodes all fixed points of Kondo flows

Higher rank groups exhibit complex algebraic structures

New non-rational D-branes are generated by Wilson loop actions

Abstract

We investigate the algebra generated by the topological Wilson loop operators in WZW models. Wilson loops describe the nontrivial fixed points of the boundary renormalization group flows triggered by Kondo perturbations. Their enveloping algebra therefore encodes all the fixed points which can be reached by sequences of Kondo flows. This algebra is easily described in the case of SU(2), but displays a very rich structure for higher rank groups. In the latter case, its action on known D-branes creates a profusion of new and generically non-rational D-branes. We describe their symmetries and the geometry of their worldvolumes. We briefly explain how to extend these results to coset models.