Surface operator study in SU(2) gauge field theory

TL;DR

This paper investigates the properties of surface operators in SU(2) gauge theory, focusing on their dependence on surface area and volume in different phases, revealing nontrivial area dependence and absence of volume law.

Contribution

It provides a detailed analysis of surface operator behavior in SU(2) gauge theory, including their area dependence and phase-specific properties.

Findings

Surface operators show nontrivial area dependence in both phases.

No volume law observed for operators on cubic surfaces.

Spatial and temporal operators behave differently across phases.

Abstract

The surface operator in an SU(2) gauge field theory is studied. We analyze Abelian projection of the SU(2) symmetry to the U(1) group calculating the surface parameter. The surface parameter dependence on the surface area and volume is studied in confinement and deconfinement phases. It is shown the spatial and temporal surface operators exhibit nontrivial area dependence in the confinement and deconfinement phases. It is shown also that there is no volume law for the operators defined on a cubic surface.