A percolation transition in Yang-Mills matter at finite number of colours

TL;DR

This paper explores a phase transition in baryonic matter at finite quark chemical potential, revealing a percolation transition driven by the number of colours, which impacts correlations and confinement properties.

Contribution

It introduces the concept of a percolation transition in Yang-Mills matter as a function of the number of colours at finite chemical potential, a novel perspective in QCD phase structure.

Findings

Percolation transition occurs at a critical number of colours $N_c$.

Large-distance correlations can exist at high $N_c$ despite confinement.

The results imply a new phase transition when varying $N_c$ at fixed chemical potential.

Abstract

We examine baryonic matter at quark chemical potential of the order of the confinement scale, $\mu_q\sim \lqcd$. In this regime, quarks are supposed to be confined but baryons are close to the ``tightly packed limit'' where they nearly overlap in configuration space. We show that this system will exhibit a percolation phase transition {\em when varied in the number of colours} $N_c$: at high $N_c$, large distance correlations at quark level are possible even if the quarks are essentially confined. At low $N_c$, this does not happen. We discuss the relevance of this for dense nuclear matter, and argue that our results suggest a new ``phase transition'', varying $N_c$ at constant $\mu_q$.