Loop Operators and the Kondo Problem

TL;DR

This paper investigates the renormalisation group flow of boundary states in WZW models using loop operators, revealing how they relate to quantum monodromies and boundary transfer matrices in D-brane configurations.

Contribution

It introduces a consistent regularisation and renormalisation scheme for loop operators affecting boundary states, clarifying their connection to defect lines and quantum monodromies.

Findings

Loop operators measure quantum monodromies at infrared fixed points.

Renormalisation scheme respects global symmetries of the model.

Results clarify the link between boundary transfer matrices and defect lines.

Abstract

We analyse the renormalisation group flow for D-branes in WZW models from the point of view of the boundary states. To this end we consider loop operators that perturb the boundary states away from their ultraviolet fixed points, and show how to regularise and renormalise them consistently with the global symmetries of the problem. We pay particular attention to the chiral operators that only depend on left-moving currents, and which are attractors of the renormalisation group flow. We check (to lowest non-trivial order in the coupling constant) that at their stable infrared fixed points these operators measure quantum monodromies, in agreement with previous semiclassical studies. Our results help clarify the general relationship between boundary transfer matrices and defect lines, which parallels the relation between (non-commutative) fields on (a stack of) D-branes and their push-forwards to the target-space bulk.