Continuum limit in abelian projected SU(2) lattice gauge theory

TL;DR

This paper investigates how the abelian string tension and monopole density behave as the lattice spacing approaches zero in SU(2) gauge theory, showing the abelian string tension converges to the nonabelian one and analyzing monopole scaling.

Contribution

It provides evidence that the abelian string tension approaches the nonabelian string tension in the continuum limit and compares gauge fixing methods for monopole density analysis.

Findings

Abelian string tension converges to nonabelian string tension in the continuum limit.

Infrared monopole density scales correctly, while total density diverges due to ultraviolet effects.

Simulated annealing improves gauge fixing results compared to iterative methods.

Abstract

We study the continuum limit of the abelian string tension and the density of abelian monopoles calculated after carefully fixing the maximal abelian gauge by employing the simulated annealing algorithm. We present the evidence that the abelian string tension converges to the nonabelian one in the continuum limit. For the monopole density we confirm earlier findings that the density of the properly defined infrared monopoles has correct scaling while the total density seems divergent in the continuum limit due to ultraviolate contributions. We also compare with results obtained with the usual iterative gauge fixing algorithm.