Quantization of Wilson loops in Wess-Zumino-Witten models

TL;DR

This paper presents a non-perturbative quantization method for Wilson loops in WZW models, revealing their algebraic properties and dualities, and demonstrating their utility in boundary RG flow analysis.

Contribution

It introduces a novel non-perturbative quantization of Wilson loops in WZW models and explores their duality and applications in boundary RG flows.

Findings

Quantized Wilson loops commute with Kac-Moody algebra

Wilson loops are dual to boundary perturbations under open/closed string duality

Operators help identify fixed points in boundary RG flow

Abstract

We describe a non-perturbative quantization of classical Wilson loops in the WZW model. The quantized Wilson loop is an operator acting on the Hilbert space of closed strings and commuting either with the full Kac-Moody chiral algebra or with one of its subalgebras. We prove that under open/closed string duality, it is dual to a boundary perturbation of the open string theory. As an application, we show that such operators are useful tools for identifying fixed points of the boundary renormalization group flow.