On the Landau Ginzburg theory of MAG projected SU(2) lattice gauge theory

TL;DR

This paper develops an effective scalar field theory for MAG monopoles in SU(2) lattice gauge theory, showing a scalar bound state with a mass that scales towards the continuum limit, linking monopole dynamics to continuum physics.

Contribution

It introduces a scalar field theory for MAG monopoles derived from lattice monopole trajectories, revealing a bound state with a mass consistent with continuum scaling.

Findings

Existence of a scalar bound state in MAG monopole trajectories

The screening mass scales towards the continuum limit

Mass approximately 1.3 GeV when using the string tension as scale

Abstract

Maximal Abelian gauge fixing and subsequent Abelian projection of SU(2) lattice gauge theory defines closed trajectories of magnetic monopoles. These trajectories can be interpreted in terms of an effective scalar field theory of the MAG monopoles using the worldline representation of the functional determinants. Employing the monopole worldlines detected in the numerical simulation, we show that a scalar bound state exists. The screening mass $m$ of this state properly scales towards the continuum limit. We find m ~ 1.3 $GeV when the string tension sigma = 440 MeV is used as reference scale.