Dense baryonic matter in strong coupling lattice gauge theory

TL;DR

This paper explores the properties of dense baryonic matter in lattice QCD at strong coupling, revealing spontaneous symmetry breaking and low-energy excitations with novel dispersion relations.

Contribution

It introduces a Hamiltonian model for dense baryonic matter in strong coupling lattice QCD and analyzes its symmetries and excitations at large N_c.

Findings

Ground state breaks chiral symmetry and lattice rotation symmetry.

Presence of type I and type II Goldstone bosons with distinct dispersion relations.

Large N_c limit allows tractable analysis of the partition function.

Abstract

We investigate the strong coupling limit of lattice QCD in the Hamiltonian formulation for systems with non-zero baryon density. In leading order the Hamiltonian looks like an antiferromagnet that is invariant under global U(N_f)xU(N_f) and local SU(N_c). Physically it describes meson dynamics with a fixed background of baryon density. We study this Hamiltonian with several baryon number distributions, and concentrate on the global symmetries of the ground state and on the properties of low lying excitations. In particular, for uniform non-zero baryon density we write the partition function as a path integral that is tractable in the limit of large N_c. We find that the ground state spontaneously breaks chiral symmetry as well as discrete lattice rotations in a way that depends on N_f and the density. The low energy excitations include type I and type II Goldstone bosons. The energies of the latter are of order 1/N_c, and are quadratic in momentum. Bosons of either type can develop anisotropic dispersion relations.