Analysis of the QCD Kondo phase using random matrices

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.

Figures (2)

• Figure 1: The condensates at the minimum of the free energy \ref{['eq:fre']} are plotted as a function of $\xi$. ($b$ is not plotted because $a=b$ for all $\xi$.) Here, $a$ and $c$ characterize the Kondo condensate, while $\sigma$ corresponds to the chiral condensate.
• Figure 2: The Kondo condensates $K_{{\rm R}\uparrow}$ and $K_{{\rm L}\downarrow}$ are plotted as a function of the chiral chemical potential $\mu_5$. Here, the subscripts R/L and $\uparrow/\downarrow$ denote the chirality of the light quark and the spin component of the heavy quark, respectively.