Lattice instanton action from 3D SU(2) Georgi-Glashow model

TL;DR

This paper investigates the effective instanton action in the 3D SU(2) Georgi-Glashow model on the lattice, revealing a Coulomb gas form that reproduces the string tension and suggesting gauge independence in the infrared.

Contribution

It introduces an inverse Monte-Carlo method to determine an almost perfect instanton action in different gauges, demonstrating gauge independence and matching analytical string tension results.

Findings

Instanton actions take a Coulomb gas form.

Reproduces string tension analytically obtained by Polyakov.

Gauge independence of the infrared instanton action.

Abstract

3D Georgi-Glashow model is studied on the lattice in the London limit in an infrared but an intermediate region before the screening appears. Abelian and instanton dominances are observed after abelian projections in a unitary gauge and roughly in the maximally abelian gauge. Using an inverse Monte-Carlo method, we determine an effective instanton action in both gauges. When we restrict ourselves to some regions of parameters $\beta$ and $\kappa$, we obtain an almost perfect instanton action, performing a block-spin transformation on the dual lattice. It takes a form of a Coulomb gas and reproduces fairly well the string tension obtained analytically by Polyakov. The almost perfect actions in both gauges look the same in the infrared region, which suggests gauge independence.