The Z(2) gauge model revisited: as a possible testbed for the confinement and chiral symmetry phase transition of SU(2) lattice gauge theory

TL;DR

This paper investigates the Z(2) gauge model as a simplified testbed for understanding the relationship between confinement and chiral symmetry phase transitions in SU(2) lattice gauge theory, using a smoothing technique to reveal topological features.

Contribution

It demonstrates that the Z(2) gauge model exhibits a topological discontinuity coinciding with the confinement-deconfinement transition, suggesting its potential as a simplified model for studying these phenomena.

Findings

Topological discontinuity aligns with the phase transition point.

Smoothing reveals topological features related to confinement.

Z(2) model may serve as a testbed for chiral transition studies.

Abstract

Adopting the cooling technique to smooth the discontinuous Z(2) lattice gauge field, we found that on SU(2) gauge configurations obtained by this smoothing there exists clear discontinuity of the topological property at almost the same point as the confinement-deconfinement phase transition of the original Z(2) gauge theory. This observation suggests the possibility that Z(2) gauge model might be a testbed for analyzing the relation between the confinement and the chiral phase transition in which the topological objects are believed to play crucial roles.