Large Field Cutoffs in Lattice Gauge Theory

TL;DR

This paper explores a modified perturbation theory with a large field cutoff to improve lattice gauge theory calculations, aiming to bridge the gap between weak and strong coupling expansions especially for SU(3).

Contribution

It introduces a large field cutoff approach to lattice gauge theory, extending methods successful in scalar theories to SU(3) gauge theories, and compares gauge invariant and dependent criteria for configuration classification.

Findings

Large field cutoff improves convergence of lattice perturbation theory.

Comparison of gauge invariant and dependent criteria for configuration classification.

Potential to better match non-perturbative results with modified perturbation methods.

Abstract

In pure gauge SU(3) near beta = 6, weak and strong coupling expansions break down and the MC method seems to be the only practical alternative. We discuss the possibility of using a modified version of perturbation theory which relies on a large field cutoff and has been successfully applied to the double-well potential (Y. M., PRL 88 141601). Generically, in the case of scalar field theory, the weak coupling expansion is unable to reproduce the exponential suppression of the large field configurations. This problem can be solved by introducing a large field cutoff. The value of this cutoff can be chosen to reduce the discrepancy with the original problem. This optimization can be approximately performed using the strong coupling expansion and bridges the gap between the two expansions. We report recent attempts to extend this procedure for SU(3) gauge theory on the lattice. We compare gauge invariant and gauge dependent (in the Landau gauge) criteria to sort the configurations into ``large-field'' and ``small-field'' configurations. %We discuss the effects of discarding the large field configurations. We discuss the convergence of lattice perturbation theory and the way it can be modified in order to obtain results similar to the scalar case.