Phase structure of lattice QCD for general number of flavors

TL;DR

This paper explores the phase structure of lattice QCD across various flavor numbers, revealing a transition from confined to deconfined phases and identifying the conditions for trivial or non-trivial infrared fixed points.

Contribution

It provides a comprehensive numerical analysis of the phase diagram for N_F=6 to 360 flavors, proposing a detailed phase structure based on the number of flavors and coupling regions.

Findings

For N_F ≥ 7, a bulk first order phase transition line exists.

Massless quarks only in the deconfined phase.

Confinement and chiral symmetry breaking occur only for N_F ≤ 6.

Abstract

We investigate the phase structure of lattice QCD for the general number of flavors in the parameter space of gauge coupling constant and quark mass, employing the one-plaquette gauge action and the standard Wilson quark action. Performing a series of simulations for the number of flavors $N_F=6$--360 with degenerate-mass quarks, we find that when $N_F \ge 7$ there is a line of a bulk first order phase transition between the confined phase and a deconfined phase at a finite current quark mass in the strong coupling region and the intermediate coupling region. The massless quark line exists only in the deconfined phase. Based on these numerical results in the strong coupling limit and in the intermediate coupling region, we propose the following phase structure, depending on the number of flavors whose masses are less than $\Lambda_d$ which is the physical scale characterizing the phase transition in the weak coupling region: When $N_F \ge 17$, there is only a trivial IR fixed point and therefore the theory in the continuum limit is free. On the other hand, when $16 \ge N_F \ge 7$, there is a non-trivial IR fixed point and therefore the theory is non-trivial with anomalous dimensions, however, without quark confinement. Theories which satisfy both quark confinement and spontaneous chiral symmetry breaking in the continuum limit exist only for $N_F \le 6$.