Fractons on curved spacetime in $2+1$ dimensions

TL;DR

This paper explores a novel fracton gauge theory in 2+1 dimensions coupled to curved spacetime, generalizing dipole gauge invariance and revealing infinite-dimensional asymptotic symmetries.

Contribution

It introduces a second order formulation of dipole Chern-Simons theory that extends gauge invariance to curved geometries and constructs higher-dimensional generalizations.

Findings

Couples fracton gauge theory to Aristotelian geometry.

Identifies electric monopole solutions and analyzes their charges.

Shows asymptotic symmetries are infinite-dimensional.

Abstract

We study dipole Chern-Simons theory with and without a cosmological constant in $2+1$ dimensions. We write the theory in a second order formulation and show that this leads to a fracton gauge theory coupled to Aristotelian geometry which can also be coupled to matter. This coupling exhibits the remarkable property of generalizing dipole gauge invariance to curved spacetimes, without placing any limitations on the possible geometries. We also use the second order formulation to construct a higher dimensional generalization of the action. Finally, for the $(2+1)$-dimensional Chern-Simons theory we find solutions and interpret these as electric monopoles, analyze their charges and argue that the asymptotic symmetries are infinite-dimensional.