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

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 $g_{{\rm GF}}^{2} \lesssim 6$.