Lattice Monte-Carlo study of pre-conformal dynamics in strongly flavoured QCD in the light of the chiral phase transition at finite temperature

TL;DR

This study uses lattice Monte-Carlo simulations to analyze the finite temperature phase transition in SU(3) QCD with varying fermion flavors, identifying the flavor number where conformal symmetry likely emerges.

Contribution

It provides new estimates for the critical flavor number N_f^* where conformal behavior appears, using multiple independent methods and analyzing the N_f dependence of the transition temperature.

Findings

Estimated N_f^* for conformality around 10.4 to 12.5.

Identified the vanishing of the step scaling function at N_f^*~11.1.

Found T_c/M decreases with N_f, indicating the approach to the conformal window.

Abstract

We study the thermal phase transition in colour SU(3) Quantum Chromodynamics (QCD) with a variable number of fermions in the fundamental representation by using lattice Monte-Carlo simulations. We collect the (pseudo) critical couplings for N_f=(0, 4, 6,8), and we investigate the pre-conformal dynamics associated with the infra-red fixed point in terms of the N_f dependence of the transition temperature. We propose three independent estimates of the number of flavour N_f^* where the conformal phase would emerge, which give consistent results within the largish errors. We consider lines of fixed N_t in the space of (N_f, bare lattice coupling), and locate the vanishing of the step scaling function for N_f^*\sim 11.1\pm 1.6. We define a typical interaction strength (g_TC) at the scale of critical temperature T_c, and we find that g_TC meets the zero temperature critical couplings estimated by the two-loop Schwinger Dyson equation or the IRFP coupling in the four-loop beta-function at N_f^*\sim 12.5\pm 0.7. Further, we study the N_f dependences of T_c/M where M is a UV N_f independent reference scale determined by utilising the coupling at the scale of the lattice spacing. Then, T_c/M turns out to be a decreasing function of N_f, and the vanishing T_c/M indicates the emergence of the conformal window at N_f^* \sim 10.4 \pm 1.2.