Large $N_c$ behaviour of lattice QCD in the heavy dense regime

TL;DR

This paper derives an effective lattice QCD theory for heavy quarks using strong coupling and hopping expansion, analyzing its behavior at large N_c and revealing a first-order transition and quarkyonic matter characteristics.

Contribution

It extends the effective theory to arbitrary N_c and includes gauge corrections, providing new insights into the large N_c limit and phase structure of dense QCD.

Findings

Onset transition steepens with increasing N_c

Transition is first order in the large N_c limit

Pressure scales as N_c beyond the onset

Abstract

Combining strong coupling and hopping expansion one can derive a dimensionally reduced effective theory of lattice QCD. This theory has a reduced sign problem, is amenable to analytic evaluation and was successfully used to study the cold and dense regime of QCD for sufficiently heavy quarks. We show results from the evaluation of the effective theory for arbitrary $N_c$ up to $\kappa^4$. The inclusion of gauge corrections is also investigated. We find that the onset transition to finite baryon number density steepens with growing $N_c$ even for $T \neq 0$. This suggests that in the large $N_c$ limit the onset transition is first order up to the deconfinement transition. Beyond the onset, the pressure is shown to scale as $p \sim N_c$ through three orders in the hopping expansion, which is characteristic for a phase termed quarkyonic matter in the literature.