Fixed twist dynamics of SO(3) gauge theory

TL;DR

This paper investigates the phase structure of 3+1 dimensional SO(3) lattice gauge theory under fixed-twist backgrounds, revealing how monopole chemical potentials influence phase transitions and confinement properties across sectors.

Contribution

It introduces a detailed analysis of fixed-twist sectors in SO(3) gauge theory, employing monopole chemical potentials and effective models to understand phase transitions and confinement.

Findings

The first-order bulk transition is shifted and weakened to second order.

A confined phase exists in every fixed twist sector.

Most results provide insights applicable to ergodic theories with summed twist sectors.

Abstract

We perform a throughout study of 3+1 dim. SO(3) LGT for any fixed-twist background. We concentrate in particular on the physically significant trivial and 1-twist sectors. Introducing a Z(2) monopole chemical potential the 1st order bulk transition is moved down in the strong coupling region and weakened to 2nd order in the 4-dim Ising model universality class. In this extended phase diagram we gain access to a confined phase in every fixed twist sector of the theory. The Pisa disorder operator is employed together with the Polyakov loop to study the confinement-deconfinement transition in each sector. Due to the specific properties of both operators, most results can be used to gain insight in the ergodic theory, where all twist sectors should be summed upon. An explicit mapping of each fixed twist theory to effective positive plaquette models with fixed twisted boundary conditions is applied to better establish their properties in the different phases.