Nonperturbative beta function of twelve-flavor SU(3) gauge theory

TL;DR

This study computes the nonperturbative discrete beta function of twelve-flavor SU(3) gauge theory using lattice simulations, identifying an IR fixed point and measuring critical exponents with systematic error analysis.

Contribution

It provides the first detailed lattice determination of the IR fixed point and critical exponent for twelve-flavor SU(3) gauge theory using improved gradient flow techniques.

Findings

IR fixed point at g*^2 ≈ 7.3 with systematic uncertainties

Critical exponent γg* ≈ 0.26 consistent with perturbative estimates

Systematic effects significantly influence fixed point determination

Abstract

We study the discrete beta function of SU(3) gauge theory with Nf=12 massless fermions in the fundamental representation. Using an nHYP-smeared staggered lattice action and an improved gradient flow running coupling $\tilde g_c^2(L)$ we determine the continuum-extrapolated discrete beta function up to $g_c^2 \approx 8.2$. We observe an IR fixed point at $g_{\star}^2 = 7.3\left(_{-2}^{+8}\right)$ in the $c = \sqrt{8t} / L = 0.25$ scheme, and $g_{\star}^2 = 7.3\left(_{-3}^{+6}\right)$ with c=0.3, combining statistical and systematic uncertainties in quadrature. The systematic effects we investigate include the stability of the $(a / L) \to 0$ extrapolations, the interpolation of $\tilde g_c^2(L)$ as a function of the bare coupling, the improvement of the gradient flow running coupling, and the discretization of the energy density. In an appendix we observe that the resulting systematic errors increase dramatically upon combining smaller $c \lesssim 0.2$ with smaller $L \leq 12$, leading to an IR fixed point at $g_{\star}^2 = 5.9(1.9)$ in the c=0.2 scheme, which resolves to $g_{\star}^2 = 6.9\left(_{-1}^{+6}\right)$ upon considering only $L \geq 16$. At the IR fixed point we measure the leading irrelevant critical exponent to be $\gamma_g^{\star} = 0.26(2)$, comparable to perturbative estimates.