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

Anisotropic Kondo line defect and ODE/IM correspondence