Solving two-dimensional large-N QCD with a nonzero density of baryons and arbitrary quark mass

TL;DR

This paper solves two-dimensional large-N QCD with nonzero baryon density and arbitrary quark mass, revealing a baryon crystal structure, quark-hadron continuity, and phase transitions, while emphasizing the importance of gluonic zero modes.

Contribution

It provides an exact solution for large-N QCD at finite baryon density, including gluonic zero modes, and uncovers novel crystal and phase structures.

Findings

Baryon crystal with helix-like structure at finite density

Ground state energy matches free massless quark equation of state at high density

Phase transition at chemical potential equal to baryon mass divided by N

Abstract

We solve two-dimensional large-N QCD in the presence of a nonzero baryon number B, and for arbitrary quark mass m and volume L. We fully treat the dynamics of the gluonic zero modes and check how this affects results from previous studies of the B=0 and B=1 systems. For a finite density of baryons, and for any m>0, we find that the ground state contains a baryon crystal with expectation values for psi-bar gamma_mu psi that have a helix-like spatial structure. We study how these evolve with B and see that the volume integral of psi-bar psi strongly changes with the baryon density. We compare this emerging crystal structure with the sine-Gordon crystal, which is expected to be a good approximation for light quarks, and find that it is a very good approximation for surprisingly heavy quarks. We also calculate the way the ground state energy E changes as a function of the baryon number B, and find that for sufficiently large densities the function E(B) is well described by the equation of state for free massless quarks, thus suggesting a quark-Hadron continuity. From dE(B)/dB we calculate the quark chemical potential mu as a function of B and see that the baryons repel each other. The way mu depends on B also allows us to translate our findings to the grand-canonical ensemble. The resulting phase structure along the mu-axis contains a phase transition that occurs at a value of mu equal to the baryon mass divided in N, and that separates a mu-independent phase with intact translation symmetry from a mu-dependent phase with spontaneously broken translation symmetry. Finally, our calculations confirm the presence of a partial large-N Eguchi-Kawai volume independence, as described in Phys.Rev.D79:105021, that arises only if one treats the gluonic zero modes correctly.