On finite-density QCD at large Nc

TL;DR

This paper investigates the conditions under which the Deryagin-Grigoriev-Rubakov (DGR) instability occurs in finite-density QCD at large but finite Nc, showing it is unlikely for Nc=3 and discussing potential ground states at very large Nc.

Contribution

The study extends the understanding of the DGR instability to finite Nc, identifying a narrow chemical potential window and showing it only occurs at extremely large Nc, unlike in real-world QCD.

Findings

DGR instability occurs only within a finite chemical potential window at large Nc.

The instability is suppressed for Nc=3, suggesting a different ground state such as color superconductivity.

At very large Nc, the DGR instability may become relevant, indicating possible new phases.

Abstract

Deryagin, Grigoriev, and Rubakov (DGR) have shown that in finite-density QCD at infinite Nc the Fermi surface is unstable with respect to the formation of chiral waves with wavenumber twice the Fermi momentum, while the BCS instability is suppressed. We show here that at large, but finite Nc, the DGR instability only occurs in a finite window of chemical potentials from above Lambda_QCD to mu_critical = exp(gamma ln^2 Nc + O(ln Nc ln ln Nc))Lambda_QCD, where gamma = 0.02173. Our analysis shows that, at least in the perturbative regime, the instability occurs only at extremely large Nc, Nc > 1000 Nf, where Nf is the number of flavors. We conclude that the DGR instability is not likely to occur in QCD with three colors, where the ground state is expected to be a color superconductor. We speculate on possible structure of the ground state of finite-density QCD with very large Nc.