A mathematical formalism for the Kondo effect in WZW branes

TL;DR

This paper develops a rigorous mathematical framework to describe the Kondo effect in WZW branes, connecting conformal field theory with boundary condition evolution and breaking conformal invariance.

Contribution

It introduces a formalism that captures the Kondo effect mathematically within conformal field theory, providing a precise approach to boundary condition transformations.

Findings

Mathematically formalizes the Kondo effect in WZW models

Provides a rigorous approach to boundary condition evolution

Proposes a mathematical statement of the Kondo effect conjecture

Abstract

In this paper, we show how to adapt our rigorous mathematical formalism for closed/open conformal field theory so that it captures the known physical theory of branes in the WZW model. This includes a mathematically precise approach to the Kondo effect, which is an example of evolution of one conformally invariant boundary condition into another through boundary conditions which can break conformal invariance, and a proposed mathematical statement of the Kondo effect conjecture. We also review some of the known physical results on WZW boundary conditions from a mathematical perspective.