# Phase structure of QCD for general number of flavors

## TL;DR

This paper explores the phase structure of QCD across a wide range of flavors, revealing the conditions for triviality, non-trivial fixed points, and confinement, with implications for understanding the theory's behavior at different flavor counts.

## Contribution

It provides a comprehensive analysis of QCD phase structure for any number of flavors, combining numerical and perturbative results to identify fixed points and confinement conditions.

## Key findings

- For N_F ≥ 17, QCD is trivial with a trivial fixed point.
- For 7 ≤ N_F ≤ 16, QCD has a non-trivial fixed point but no confinement.
- For N_F ≤ 6, QCD exhibits confinement and spontaneous chiral symmetry breaking.

## Abstract

We investigate and elucidate the phase structure of QCD for general number of flavors $N_F$ with Wilson quarks, varying $N_F$ from 2 up to 300. Based on numerical results combined with the result of the perturbation theory we propose the following picture: When $N_F \ge 17$, there is only a trivial fixed point and therefore the theory in the continuum limit is trivial. On the other hand, when $16 \ge N_F \ge 7$, there is a non-trivial 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 $N_F \le 6$. We also discuss the structure of the deconfining phase at finite temperatures for the small number of flavors such as $N_F=2$ and 3, through a systematic study of it for general number of flavors.