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We propose a novel random matrix model that describes the QCD Kondo effect.The model correctly implements both the chiral symmetry of light quarks and the$\mathrm{SU}(2)$ spin symmetry of heavy quarks. We take the large-$N$ limitwith $N$ the matrix size and show that the model has three phases: the pureKondo phase with no chiral condensate, the pure chirally broken phase with noKondo condensate, and the coexistence phase. The model predicts that thepairing form of the Kondo condensate in the coexistence phase is significantlyaltered compared to the pure Kondo phase. For each of these phases werigorously derive the low-energy effective theory of Nambu-Goldstone modes andobtain compact closed expressions for the partition function with externalsources. We also include a chiral chemical potential into the model and examinethe vacuum structure.

Random matrix model for the QCD Kondo effect