Higgs Phases and Boundary Criticality

For half a century now there has been a rich ongoing debate as to whether Higgs and confined phases of gauge theories are the same or distinct phases. A famous 1980 proof by Fradkin and Shenker demonstrates they are thermodynamically the same bulk phase, but they remain separated by a first order line with a critical endpoint, very similar to the liquid-water phase boundary. In this analogy the Higgs phase is the liquid phase and the confined phase is the gas. They exhibit phenomenologically distinct properties despite only being separated by a supercritical region. In this work we have explored the distinction of Higgs and confinement with open boundaries through a combination of analytic arguments and numerical simulations. We show that the Higgs regime of the phase diagram exhibits boundary symmetry breaking, while the confined regime does not. We demonstrate that this is a ubiquitous phenomenon in Higgs models whether the gauge group be Abelian or non-Abelian, and whether the gauge field is 1-form or higher-form.