Anisotropic Kondo line defect and ODE/IM correspondence

TL;DR

This paper explores the anisotropic Kondo line defects within chiral SU(2) WZW models, establishing an ODE/IM correspondence through four-dimensional Chern-Simons theory, and verifies it via perturbative and WKB analyses.

Contribution

It introduces a novel ODE/IM correspondence for anisotropic Kondo problems using four-dimensional Chern-Simons theory and verifies it through explicit calculations.

Findings

Derived infrared dynamics of anisotropic line defects

Verified ODE/IM correspondence with perturbative and WKB methods

Established connection between Kondo defects and integrable models

Abstract

We study the anisotropic Kondo line defects in products of chiral $SU(2)$ WZW models. We propose an ODE/IM correspondence for the anisotropic Kondo problems by considering the four-dimensional Chern Simons theory in the trigonometric case. We verify the claim both by explicit perturbative calculations in the ultraviolet and by exact WKB analysis in the infrared. In doing so, we derived the infrared dynamics of a large class of anisotropic line defects.