# Finite Temperature Properties of SO(3) Lattice Gauge Theories and their implications for the continuum limit

## TL;DR

This paper investigates the finite temperature behavior of SO(3) lattice gauge theories, revealing metastable states and their relation to phase transitions, with implications for understanding the continuum limit and symmetry properties.

## Contribution

It demonstrates the existence of metastable states in SO(3) lattice gauge theory and analyzes their connection to phase transitions and continuum limit implications.

## Key findings

- Metastable states are related to bulk and finite temperature transitions.
- Polyakov line in the adjoint representation traces metastable states.
- Second order finite temperature transition is compatible with first order in SO(3).

## Abstract

It is shown that $SO(3)$ lattice gauge theory on finite size lattices has metastable states related to the ground states of both the bulk transition and the finite temperature transition. The Polyakov line variable in the adjoint representation of $SU(2)$ is used to trace the origin of these metastable states. It is also argued that a second order finite temperature transition in the continuum theory is not inconsistent with the first order transition in $SO(3)$ lattice gauge theory and the absence of a $Z(2)$ global symmetry.