Quadrupole gauge theory: anti-Higgs mechanism and elastic dual

TL;DR

This paper introduces a quadrupole gauge theory exhibiting an anti-Higgs mechanism where spontaneous symmetry breaking leads to more massless excitations, and establishes a duality with exotic elastic systems called incompressible crystals.

Contribution

It extends gauge theory to include quadrupole moments, revealing a novel anti-Higgs mechanism and duality with incompressible crystal phases.

Findings

Spontaneous quadrupole symmetry breaking increases massless modes.

The anti-Higgs mechanism challenges traditional Higgs paradigm.

Duality links quadrupole gauge theory to incompressible crystal phases.

Abstract

Motivated by the duality between elasticity and fracton gauge theory, we study an extension of the gauge group that includes the quadrupole moment. Remarkably, we find that spontaneous breaking of the quadrupole symmetry increases the number of massless excitations. This result appears to challenge the well-established paradigm, according to which gauge fields acquire mass through the Higgs mechanism, and the would-be Goldstone bosons are rendered massive. We refer to this phenomenon as the anti-Higgs mechanism. Furthermore, we demonstrate that the quadrupole gauge theory is dual to an exotic class of elastic systems, which we dub incompressible crystals. The anti-Higgs mechanism in the dual theory corresponds to a phase transition from the incompressible crystal state to an ordinary (compressible) solid.