Towards a strong-coupling theory of QCD at finite density

TL;DR

This paper develops a strong-coupling perturbation theory for QCD at finite density, mapping it to an antiferromagnetic model with baryonic impurities, and explores phase diagrams using large-N and mean-field methods.

Contribution

It introduces a novel strong-coupling approach to finite-density QCD, incorporating baryonic impurities and analyzing phase structures with advanced theoretical techniques.

Findings

Phase diagram in (N_c,N_f) plane at zero temperature and density

Phase diagram in (n_B,T) plane for a simplified U(3) model

Effective Hamiltonian resembles an antiferromagnet with baryonic impurities

Abstract

We apply strong-coupling perturbation theory to the QCD lattice Hamiltonian. We begin with naive, nearest-neighbor fermions and subsequently break the doubling symmetry with next-nearest-neighbor terms. The effective Hamiltonian is that of an antiferromagnet with an added kinetic term for baryonic "impurities," reminiscent of the t-J model of high-T_c superconductivity. As a first step, we fix the locations of the baryons and make them static. Following analyses of the t-J model, we apply large-N methods to obtain a phase diagram in the (N_c,N_f) plane at zero temperature and baryon density. Next we study a simplified U(3) toy model, in which we add baryons to the vacuum. We use a coherent state formalism to write a path integral which we analyze with mean field theory, obtaining a phase diagram in the (n_B,T) plane.