Cluster expansions and chiral symmetry at large density in 2-color QCD

Abstract

$SU(N_c)$ lattice gauge theories with $N_f$ flavors of massless staggered fermions are considered at high quark chemical potential $\mu$ and any temperature $T$. In the strong coupling regime (sufficiently small $\beta$) they have been shown to possess a chiral phase of intact global $U(N_f)\times U(N_f)$ symmetry. The proof is by cluster expansions which converge in the infinite volume limit. Extension to weaker coupling does not appear feasible in the presence of complex fermion determinant. For theories with real determinant, however, such as 2-color QCD with fundamental fermions, or any $N_c$ with even $N_f$ and adjoint fermions, such large $\mu$ cluster expansions can be used to show chiral behavior of fermionic lattice observables at any gauge coupling. Unfortunately, this absence of color superfluidity/superconductivity at high $\mu$ appears to be a lattice artifact due to lattice saturation, a serious problem plaguing the standard finite density formalism on the lattice. Some possible ways of circumventing saturation are discussed.