On the stability of Dirac sheet configurations

TL;DR

This paper investigates the stability of Dirac sheet configurations in SU(2) lattice gauge theory, linking their stability to the Polyakov loop and holonomy, supported by both analytical predictions and numerical lattice results.

Contribution

It demonstrates the relation between Dirac sheet stability and Polyakov loop values, providing an analytic prediction confirmed by lattice simulations.

Findings

Dirac sheets are stable near the deconfinement transition with non-trivial Polyakov loops.

Analytic predictions match numerical lattice results for stability dependence.

Stability is connected to the marginal stability of constant magnetic fields.

Abstract

Using cooling for SU(2) lattice configurations, purely Abelian constant magnetic field configurations were left over after the annihilation of constituents that formed metastable Q=0 configurations. These so-called Dirac sheet configurations were found to be stable if emerging from the confined phase, close to the deconfinement phase transition, provided their Polyakov loop was sufficiently non-trivial. Here we show how this is related to the notion of marginal stability of the appropriate constant magnetic field configurations. We find a perfect agreement between the analytic prediction for the dependence of stability on the value of the Polyakov loop (the holonomy) in a finite volume and the numerical results studied on a finite lattice in the context of the Dirac sheet configurations.