Anisotropic Kondo line defect and ODE/IM correspondence

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.

34 pages, 5 figures; v2: added references and a discussion on the relation with the transfer matrix; v3: typos fixed

References in corpus (3)

• Exact WKB methods in $SU(2)$ $N_f=1$
• Notes on parafermionic QFT's with boundary interaction
• Counting monster potentials

Cited by in corpus (1)

• 4-dimensional Chern-Simons theory and integrable field theories