Topological order and the vacuum of Yang-Mills theories

TL;DR

This paper investigates topological order in lattice SU(2) Yang-Mills theories, revealing a phase transition characterized by a novel universality class of critical behavior in the center flux, independent of temperature.

Contribution

It introduces a non-local topological order parameter, the center flux, and characterizes its critical behavior and phase structure in lattice Yang-Mills theories.

Findings

Topological sectors classified by a_1(SO(3))=_2 exist only in the ordered phase.

Center flux exhibits critical behavior similar to Kosterlitz-Thouless transitions.

Critical behavior is independent of temperature T.

Abstract

We study, for $SU(2)$ Yang-Mills theories discretized on a lattice, a non-local topological order parameter, the center flux ${{z}}$. We show that: i) well defined topological sectors classified by $\pi_1(SO(3))=\mathbb{Z}_2$ can only exist in the ordered phase of ${{z}}$; ii) depending on the dimension $2 \leq d\leq 4$ and action chosen, the center flux exhibits a critical behaviour sharing striking features with the Kosterlitz-Thouless type of transitions, although belonging to a novel universality class; iii) such critical behaviour does not depend on the temperature $T$. Yang-Mills theories can thus exist in two different continuum phases, characterized by an either topologically ordered or disordered vacuum; this reminds of a quantum phase transition, albeit controlled by the choice of symmetries and not by a physical parameter.