Discrete $p$-Form Symmetry and Higher Coulomb Phases

TL;DR

This paper explores how theories with  p-form symmetry can exhibit a Coulomb phase featuring Abelian p-form electrodynamics, expanding understanding of phase structures in such theories.

Contribution

It demonstrates that  p-form symmetric theories can naturally host a Coulomb phase with Abelian p-form gauge fields, supported by continuum and lattice examples.

Findings

The Coulomb phase appears in  p-form symmetric theories.

Continuum and lattice models exhibit the predicted Coulomb phase.

The phase structure includes Higgs, confining, and Coulomb phases.

Abstract

We argue that a field theory with a $\mathbb Z_N$ $p$-form symmetry generically admits, in addition to a Higgs phase and a 'confining' phase, a Coulomb phase in which the infrared theory contains Abelian $p$-form electrodynamics, similar to the behaviour of Yang-Mills theory coupled to adjoint or fundamental matter. We illustrate our claim with continuum and lattice examples.