Analysis of the QCD Kondo phase using random matrices

TL;DR

This paper introduces a new random matrix model for the QCD Kondo phase, revealing three distinct phases and their low-energy effective theories, with analytical insights into the effects of chiral symmetry and chemical potential.

Contribution

The paper develops a novel random matrix model that captures the phase structure of the QCD Kondo effect, including coexistence of Kondo and chiral condensates, with analytical derivation of effective theories.

Findings

Identifies three phases: pure Kondo, pure chiral, and coexistence.

Derives low-energy effective theories for each phase.

Predicts altered pairing form of Kondo condensate in coexistence phase.

Abstract

We propose a novel random matrix model that describes the QCD Kondo phase. The model correctly implements both the chiral symmetry of light quarks and the SU(2) spin symmetry of heavy quarks. We analytically 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 phase, 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.