The Roberge-Weiss transition as a probe for conformality in many-flavor QCD

TL;DR

This paper proposes a new lattice method using the Roberge-Weiss transition temperature to identify the conformal window in many-flavor QCD, and finds evidence that Nf=8 flavors are within this window.

Contribution

The authors introduce a novel approach based on the Roberge-Weiss transition to determine the onset of conformality in QCD with many flavors from lattice simulations.

Findings

T_RW vanishes in the chiral limit for Nf=8, indicating conformality.

The method links the Roberge-Weiss transition to the conformal window boundary.

Evidence suggests Nf=8 flavors are inside the conformal window.

Abstract

We consider the problem of identifying the onset of the conformal window for QCD with $N_f$ massless flavors in the fundamental representation, and propose a new effective method to determine it from lattice simulations. This method is based on the investigation of the so-called Roberge-Weiss transition temperature $T_{RW}$, which is encountered at specific values of the imaginary baryon chemical potential, and can also be interpreted as the inverse of the critical spatial size at which charge conjugation is spontaneously broken in a finite box. Since $T_{RW}$ corresponds to a genuine phase transition for any value of the quark masses, it is a well-defined quantity; we argue that the critical $N_f$ at which $T_{RW}$ vanishes in the chiral limit coincides with the onset of the conformal window. We implement our proposal by investigating QCD with $N_f = 8$ flavors, discretized via stout improved staggered fermions and the tree-level improved Symanzik pure gauge action, at Euclidean temporal extents $N_t = 8, 10, 12, 16, 24$. In this case, we find evidence that $T_{RW}$ already vanishes in the chiral limit, indicating that $N_f = 8$ is already in the conformal window.