Aspects of topological actions on the lattice

TL;DR

This paper investigates a topological lattice gauge action that forbids large fields and remains invariant under smooth deformations, analyzing its phase structure and monopole behavior in 4d U(1) theory.

Contribution

It introduces and studies a topological lattice action with a field cutoff, comparing its properties to the Wilson action in 4d U(1) gauge theory.

Findings

Both actions exhibit a weakly first-order transition between confining and Coulomb phases.

A critical cutoff value exists where monopoles vanish.

The topological action simplifies free energy measurements.

Abstract

We consider a lattice action which forbids large fields, and which remains invariant under smooth deformations of the field. Such a "topological" action depends on one parameter, the field cutoff, but does not have a classical continuum limit as this cutoff approaches zero. We study the properties of such an action in 4d compact U(1) lattice gauge theory, and compare them with those of the Wilson action. In both cases, we find a weakly first-order transition separating a confining phase where monopoles condense, and a Coulomb phase where monopoles are exponentially suppressed. We also find a different, critical value of the field cutoff where monopoles completely disappear. Finally, we show that a topological action simplifies the measurement of the free energy.