On Dirac sheet configurations of SU(2) lattice fields

TL;DR

This paper investigates stable magnetic configurations in SU(2) lattice gauge fields near the deconfinement transition, revealing stable Dirac sheet structures with purely magnetic action and discussing their topological and dyonic interpretations.

Contribution

It identifies and interprets stable magnetic configurations with sub-instanton action in SU(2) lattice fields, linking them to Dirac sheets and dyonic structures.

Findings

Stable magnetic configurations with action below $S_{inst}$ found in both phases.

Configurations exhibit purely magnetic action with zero topological charge.

In the confined phase, some configurations are absolutely stable and show Abelian magnetic fields.

Abstract

Finite temperature Euclidean SU(2) lattice gauge fields close to the deconfinement phase transition are subjected to cooling. We find relatively stable or absolutely stable configurations with an action below the one-instanton action $S_{inst}=2\pi^2$ both in the deconfinement and the confinement phases. In this paper we attempt an interpretation of these lowest action configurations. Their action is purely magnetic and amounts to $S/S_{inst} \approx N_t/N_s$, where $N_t$ ($N_s$) is the timelike (spacelike) lattice size, while the topological charge vanishes. In the confined phase part of the corresponding lattice configurations turns out to be absolutely stable with respect to the cooling process in which case Abelian projection reveals a homogeneous, purely Abelian magnetic field closed over the "boundary" in one of the spatial directions. Referring to the dyonic structure established for the confinement phase near $T_c$ and based on the observation made for this phase that such events below the instanton action $S_{inst}$ emerge from dyon-antidyon annihilation, the question of stability (metastability) is discussed for both phases. The hypothetically different dyonic structure of the deconfinement phase, inaccessible by cooling, could explain the metastability.