A Partially Massless Superconductor

TL;DR

This paper introduces a Higgs mechanism for partially massless gravitons using a covariant fracton-like effective field theory on de Sitter space, revealing a novel superconducting-like phase with unique edge modes.

Contribution

It constructs a new covariant effective field theory for partially massless gravitons and demonstrates a Higgs mechanism involving fractonic matter condensation, a novel approach in gravity theories.

Findings

Gauging the dipolar shift symmetry leads to a massive graviton.

Condensation of fractonic matter breaks dipole symmetry, producing a galileon Goldstone mode.

The resulting phase exhibits superconducting-like features such as gapless edge modes.

Abstract

We describe a Higgs mechanism for the partially massless graviton. In order to do so, we first construct a covariant fracton-like effective field theory on de Sitter space that linearly realizes a dipolar shift symmetry. The global symmetry of this theory can be gauged by coupling it to a partially massless spin-2 gauge field. When the fractonic matter condenses, the dipole symmetry is spontaneously broken, the resulting Goldstone mode is a galileon and the partially massless graviton combines with this mode and becomes fully massive. At long distances, the phenomenology of this theory is captured by a quasi-topological field theory and displays many features analogous to those of the superconducting phase in electromagnetism, including gapless edge modes and persistent currents. We also describe the generalization to higher spins.