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Chiral symmetry in $SU(N_c)$ gauge theories at high density

We study $SU(N_c)$ lattice gauge theories with $N_f$ flavors of massless staggered fermions in the presence of quark chemical potential $μ$. A recent exact result that in the strong coupling limit (vanishing inverse gauge coupling $β$) and for sufficiently large $μ$ the theory is in a chiral symmetric phase is here extended into the finite gauge coupling region. A cluster expansion combining a fermion spacelike hopping expansion and a strong coupling plaquette expansion is shown to converge for sufficiently large $μ$ and small $β$ at any temperature $T$. All expectations of chirally non-invariant local fermion operators vanish identically, or, equivalently, their correlations cluster exponentially within the expansion implying absence of spontaneous chiral symmetry breaking. The resulting phase at low $T$ may be described as a "quarkyonic" matter phase. Some implications for the phase diagram of $SU(N_c)$ theories are discussed.