Higgs-confinement phase transitions with fundamental representation matter

TL;DR

This paper investigates the conditions under which Higgs and confining phases in gauge theories with fundamental matter are distinct, especially when a global U(1) symmetry is broken in both phases, leading to a phase boundary detectable by a topological vortex order parameter.

Contribution

It demonstrates that Higgs and confining regimes can be separated by a phase boundary when a global U(1) symmetry is broken in both, introducing a new topological order parameter for phase distinction.

Findings

Higgs and confining phases can be sharply distinguished under certain symmetry-breaking conditions.

A novel topological vortex order parameter can detect phase boundaries.

The analysis extends from 3D gauge theories to implications in 4D QCD.

Abstract

We discuss the conditions under which Higgs and confining regimes in gauge theories with fundamental representation matter fields can be sharply distinguished. It is widely believed that these regimes are smoothly connected unless they are distinguished by the realization of global symmetries. However, we show that when a $U(1)$ global symmetry is spontaneously broken in \emph{both} the confining and Higgs regimes, the two phases can be separated by a phase boundary. The phase transition between the two regimes may be detected by a novel topological vortex order parameter. We first illustrate these ideas by explicit calculations in gauge theories in three spacetime dimensions. Then we show how our analysis generalizes to four dimensions, where it implies that nuclear matter and quark matter are sharply distinct phases of QCD with an approximate $SU(3)$ flavor symmetry.