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On finite-density QCD at large Nc

E. Shuster, D. T. Son

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.

On finite-density QCD at large Nc

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.

Paper Structure

This paper contains 5 sections, 36 equations, 5 figures.

Table of Contents

  1. Introduction
  2. Review of DGR results
  3. Renormalization group approach to DGR instability
  4. DGR instability at finite ${N_{\text{c}}}$
  5. Conclusion

Figures (5)

  • Figure 1: The particle-hole pair
  • Figure 2: Ladder approximation
  • Figure 3: Reducing one-gluon exchange to a point-like interaction in the effective theory
  • Figure 4: The zero-sound diagram
  • Figure 5: Region of DGR instability in the $({N_{\text{c}}},\mu)$ plane from Eq. (\ref{['Ncbound']}). CS and DGR stand for regions with predominant color superconductivity and DGR instability, respectively.