Lattice study for conformal windows of SU(2) and SU(3) gauge theories with fundamental fermions

TL;DR

This study investigates the conformal windows of SU(2) and SU(3) gauge theories with fundamental fermions using lattice simulations, revealing a bulk chiral phase transition in SU(2) and no evidence of infrared conformality in SU(3).

Contribution

The paper provides new lattice-based insights into the phase structure of SU(2) and SU(3) gauge theories with multiple flavors, including the nature of chiral transitions and the absence of conformality at certain couplings.

Findings

SU(2) exhibits a bulk chiral phase transition at strong coupling.

SU(3) coupling scaling suggests no infrared conformality up to $g_{GF}^2 \, \lesssim 6$.

Eigenvalue distributions match chiral random matrix theory predictions for SU(2).

Abstract

We present our investigation of SU(2) gauge theory with 8 flavours, and SU(3) gauge theory with 12 flavours. For the SU(2) case, at strong bare coupling, $\beta \lesssim 1.45$, the distribution of the lowest eigenvalue of the Dirac operator can be described by chiral random matrix theory for the Gaussian symplectic ensemble. Our preliminary result indicates that the chiral phase transition in this theory is of bulk nature. For the SU(3) theory, we use high-precision lattice data to perform the step-scaling study of the coupling, $g_{{\rm GF}}$, in the Gradient Flow scheme. We carefully examine the reliability of the continuum extrapolation in the analysis, and conclude that the scaling behaviour of this SU(3) theory is not governed by possible infrared conformality at $g_{{\rm GF}}^{2} \lesssim 6$.