Analysis of saddle-point configurations in 3-dimensional SU(2) gauge theory

TL;DR

This paper investigates saddle point solutions in 3D SU(2) gauge theory, analyzing their properties, fluctuations, and impact on physical quantities like string tension, using cooling algorithms and lattice simulations.

Contribution

It introduces a detailed analysis of saddle point configurations in 3D SU(2) gauge theory, highlighting their properties and effects on physical observables.

Findings

Saddle point configurations exhibit localized peaks in the action.

Eigenvalues of fluctuations around these configurations have been measured.

String tension can be derived by averaging over these saddle points.

Abstract

We discuss the properties of a class of saddle point solutions in SU(2) in three dimensions (SU$(2)_3$), exhibiting localized peaks in the action. These configurations are generated by deterministic cooling and extremizing algorithms from analytic configurations. They share some characteristics with cooled and extremized Monte Carlo generated lattices. We have investigated physical behavior such as the string tension by averaging over this class of saddle point configurations. We have also measured the eigenvalues for harmonic fluctuations around these configurations.