Comparing topological charge definitions using topology fixing actions

TL;DR

This paper compares different topological charge definitions on the lattice using topology fixing actions, analyzing their agreement and effects on physical quantities like the static potential.

Contribution

It evaluates the effectiveness of hyperbolic and determinant ratio actions in fixing topology and compares topological charge definitions under these conditions.

Findings

Topological charge definitions agree well when topology is fixed.

Topology fixing impacts finite volume effects in static potential.

The degree of topology fixing depends on action parameters.

Abstract

We investigate both the hyperbolic action and the determinant ratio action designed to fix the topological charge on the lattice. We show to what extent topology is fixed depending on the parameters of these actions, keeping the physical situation fixed. At the same time the agreement between different definitions of topological charge - the field theoretic and the index definition - is directly correlated to the degree topology is fixed. Moreover, it turns out that the two definitions agree very well. We also study finite volume effects arising in the static potential and related quantities due to topology fixing.