The three-loop beta-function of SU(N) lattice gauge theories with overlap fermions

TL;DR

This paper computes the 2-loop coefficient of the coupling constant renormalization function in SU(N) lattice gauge theories with overlap fermions, revealing its dependence on the overlap parameter and providing data for various parameters.

Contribution

It presents the first calculation of the 2-loop coefficient of Z_g in lattice gauge theories with overlap fermions, including its dependence on the overlap parameter rho.

Findings

Z_g depends explicitly on the number of fermion flavors and colors.

Results show a nontrivial dependence of Z_g on the overlap parameter rho.

Tabulated data for different rho values used in simulations.

Abstract

We briefly report our calculation of the 2-loop coefficient of the coupling constant renormalization function Z_g in lattice perturbation theory. The quantity under study is defined through g_0 = Z_g g, where g_0 (g) is the bare (renormalized) coupling constant. The 2-loop expression for Z_g can be directly related to the 3-loop bare beta-function beta_L(g_0). Our calculation is performed using overlap fermions and Wilson gluons, and the background field technique has been chosen for convenience. Our results depend explicitly on the number of fermion flavors (N_f) and colors (N). Since the dependence of Z_g on the overlap parameter rho cannot be extracted analytically, we tabulate our results for different values of rho in the allowed range (0<rho<2), focusing on values which are being used most frequently in simulations. Plots of the 1- and 2-loop results for Z_g versus rho exhibit a nontrivial dependence on the overlap parameter. A longer write-up of this work may be found in 0709.4368.