Higgs Phases and Boundary Criticality

TL;DR

This paper explores how boundary conditions in lattice gauge theories with Higgs fields lead to boundary phase transitions and spontaneous symmetry breaking, revealing gapless edge modes and connections to topological phases.

Contribution

It demonstrates boundary phase transitions and symmetry breaking in both Abelian and non-Abelian Higgs models, linking boundary phenomena to Higgs and SPT phase relations.

Findings

Boundary phase transition in 4D Abelian Higgs model in 3D XY class

Non-Abelian boundary symmetry breaking in SU(N) models verified numerically

Higher-form Higgs fields induce boundary confinement-deconfinement transitions

Abstract

Motivated by recent work connecting Higgs phases to symmetry protected topological (SPT) phases, we investigate the interplay of gauge redundancy and global symmetry in lattice gauge theories with Higgs fields in the presence of a boundary. The core conceptual point is that a global symmetry associated to a Higgs field, which is pure-gauge in a closed system, acts physically at the boundary under boundary conditions which allow electric flux to escape the system. We demonstrate in both Abelian and non-Abelian models that this symmetry is spontaneously broken in the Higgs regime, implying the presence of gapless edge modes. Starting with the U(1) Abelian Higgs model in 4D, we demonstrate a boundary phase transition in the 3D XY universality class separating the bulk Higgs and confining regimes. Varying the boundary coupling while preserving the symmetries shifts the location of the boundary phase transition. We then consider non-Abelian gauge theories with fundamental and group-valued Higgs matter, and identify the analogous non-Abelian global symmetry acting on the boundary generated by the total color charge. For SU($N$) gauge theory with fundamental Higgs matter we argue for a boundary phase transition in the O($2N$) universality class, verified numerically for $N=2,3$. For group-valued Higgs matter, the boundary theory is a principal chiral model exhibiting chiral symmetry breaking. We further demonstrate this mechanism in theories with higher-form Higgs fields. We show how the higher-form matter symmetry acts at the boundary and can spontaneously break, exhibiting a boundary confinement-deconfinement transition. We also study the electric-magnetic dual theory, demonstrating a dual magnetic defect condensation transition at the boundary. We discuss some implications and extensions of these findings and what they may imply for the relation between Higgs and SPT phases.