Random matrix model for the QCD Kondo effect

Abstract: 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-$N$ limit with $N$ the matrix size and show that the model has three phases: the pure Kondo phase with no chiral condensate, the pure chirally broken phase with no Kondo condensate, and the coexistence phase. The model predicts that the pairing form of the Kondo condensate in the coexistence phase is significantly altered compared to the pure Kondo phase. For each of these phases we rigorously derive the low-energy effective theory of Nambu-Goldstone modes and obtain compact closed expressions for the partition function with external sources. We also include a chiral chemical potential into the model and examine the vacuum structure.