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.
Highlights
In gauge theories with fundamental representation matter fields, one can often dial parameters in a manner which smoothly interpolates between a Higgs regime and a confining regime without undergoing any change in the realization of global symmetries [1,2,3,4]
In the Higgs regime gauge fields become massive via the usual Higgs phenomenon, while in the confining regime gauge fields become gapped due to the nonperturbative physics of confinement, with an approximately linear potential appearing between heavy fundamental test charges over a finite range of length scales which is limited by the lightest meson mass
We will analyze model theories, motivated by the physics of dense QCD, where Higgs and confining regimes cannot be distinguished by the realization of global symmetries, and yet these are sharply distinct phases necessarily separated by a quantum phase transition in the parameter space of the theory
Summary
In gauge theories with fundamental representation matter fields, one can often dial parameters in a manner which smoothly interpolates between a Higgs regime and a confining regime without undergoing any change in the realization of global symmetries [1,2,3,4]. With no intervening phase transitions [3,4] These examples, which we will refer to as the “Fradkin-ShenkerBanks-Rabinovici theorem,” have inspired a widely held expectation that there can be no useful gauge-invariant order parameter distinguishing Higgs and confining phases in any gauge theory with fundamental representation matter fields.. We will analyze model theories, motivated by the physics of dense QCD, where Higgs and confining regimes cannot be distinguished by the realization of global symmetries, and yet these are sharply distinct phases necessarily separated by a quantum phase transition in the parameter space of the theory. This Uð1Þ global symmetry is spontaneously broken in both the Higgs and confining regimes of interest In this class of gauge theories, we argue that one can define a natural nonlocal order parameter which does distinguish the Higgs and confinement regimes. In Appendixes A–C we collect some technical results on vortices, discuss embedding our Abelian model within a non-Abelian theory, and consider the consequences of gauging of our Uð1Þ global symmetry to produce a Uð1Þ × Uð1Þ gauge theory
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