The fate of the critical endpoint at large $N_c$

TL;DR

This paper explores how the QCD phase diagram, especially the critical endpoint, evolves with the number of colors $N_c$, revealing a large $N_c$-dependent structure with a new critical point and phase behaviors.

Contribution

It demonstrates the shifting and emergence of critical points in the QCD phase diagram as $N_c$ increases, providing insights into large $N_c$ QCD phases and pressure scaling.

Findings

Critical point for $N_c=3$ moves toward the $mbda_q$-axis and disappears at large $N_c$.

A new critical point appears along the temperature axis at $N_c=53$ and moves with increasing $N_c$.

Pressure scales with $N_c^0$ in confined phases and $N_c^2$ in deconfined phases.

Abstract

The phase diagram of QCD is investigated by varying number of colors $N_c$ within a Polyakov loop quark-meson chiral model. In particular, our attention is focused on the critical point(s): the critical point present for $N_c=3$ moves toward the $\mu_q$-axis and disappears as soon as the number of color is increased. Yet, a distinct critical point emerges along the temperature axis for $N_c = 53$ and moves toward finite density when increasing $N_c$ further. Thus, the phase diagram at large $N_c$ looks specular w.r.t. the $N_c = 3$ results, with the first order transition in the upper-left and crossover in the down-right regions of the the $(\mu_q,T)$-plane. The pressure is also evaluated in dependence of $N_c$, showing a scaling with $N_c^0$ in the confined and chirally broken phase and with $N_c^2$ in the deconfined one. Moreover, the presence of a chirally symmetric but confined `quarkyonic phase' at large density and moderate temperature with a pressure proportional to $N_c$ is confirmed.