Gauge Problem of Monopole Dynamics in SU(2) Lattice Gauge Theory

TL;DR

This study investigates monopole dynamics in SU(2) lattice gauge theory across various gauges, demonstrating consistent string tension reproduction and suggesting gauge independence of monopole effects in the infrared.

Contribution

It compares multiple gauges for monopole contributions, determines effective monopole actions, and shows RG flows converge, indicating gauge independence in the infrared.

Findings

All gauges reproduce the SU(2) string tension.

RG flows of monopole couplings converge to a unique curve.

Gauge independence suggested in the infrared region.

Abstract

Gauge problem of monopole dynamics is studied in SU(2) lattice gauge theory. We study first abelian and monopole contributions to the static potential in four smooth gauges, i.e., Laplacian Abelian (LA), Maximally Abelian Wilson Loop (MAWL) and L-type gauges in comparison with Maximally Abelian (MA) gauge. They all reproduce the string tension in good agreement with the SU(2) string tension. MA gauge is not the only choice of the good gauge which is suitable for the color confinement mechanism. Using an inverse Monte-Carlo method and the blockspin transformation, we determine effective monopole actions and the renormalization group (RG) flows of its coupling constants in various abelian projection schemes. Every RG flow looks to converge to a unique curve which suggests gauge independence in the infrared region.