Non-abelian lattice gauge theory with a topological action

TL;DR

This paper investigates SU(2) lattice gauge theory using a topological action insensitive to small field perturbations, demonstrating universality with Wilson action across various phenomena and regimes.

Contribution

It introduces and analyzes a topological lattice action for SU(2) gauge theory, showing universality with traditional actions without relying on perturbation theory.

Findings

Perfect agreement with Wilson action in continuum limit

Universality holds for topological lattice actions

Consistent results across multiple physical regimes

Abstract

SU(2) gauge theory is investigated with a lattice action which is insensitive to small perturbations of the lattice gauge fields. Bare perturbation theory can not be defined for such actions at all. We compare non-perturbative continuum results with that obtained by the usual Wilson plaquette action. The compared observables span a wide range of interesting phenomena: zero temperature large volume behavior (topological susceptibility), finite temperature phase transition (critical exponents and critical temperature) and also the small volume regime (discrete beta-function or step-scaling function). In the continuum limit perfect agreement is found indicating that universality holds for these topological lattice actions as well.