QCD in the heavy dense regime: Large $N_c$ and quarkyonic matter

TL;DR

This paper investigates the behavior of QCD in the heavy dense regime using lattice methods, revealing that at large $N_c$, the transition to baryonic matter is first-order and pressure scales with $N_c$, supporting the quarkyonic matter concept.

Contribution

It extends previous lattice QCD studies to general $N_c$, demonstrating the first-order transition and $N_c$ scaling of pressure, aligning with quarkyonic matter characteristics.

Findings

Transition becomes first-order at large $N_c$

Pressure scales as $N_c$ in the dense regime

Results support the quarkyonic matter hypothesis

Abstract

After combined character and hopping expansions and integration over the spatial gauge links, lattice QCD reduces to a three-dimensional $SU(3)$ Polyakov loop model with complicated interactions. A simple truncation of the effective theory is valid for heavy quarks on reasonably fine lattices and can be solved by linked cluster expansion in its effective couplings. This was used ealier to demonstrate the onset transition to baryon matter in the cold and dense regime. Repeating these studies for general $N_c$, one finds that for large $N_c$ the onset transition becomes first-order, and the pressure scales as $p\sim N_c$ through three consecutive orders in the hoppoing expansion. These features are consistent with the formal definition of quarkyonic matter given in the literature. We discuss the implications for $N_c=3$ and physical QCD.