Covariant Interacting Fractons

TL;DR

This paper introduces a covariant gauge theory for fractons using a tensor gauge field derived from a Fr"olicher-Nijenhuis bracket, connecting it to known fracton models in the linear limit.

Contribution

It develops a covariant gauge theory framework for fractons with a tensor gauge field, extending the mathematical structure of gauge theories to fractonic systems.

Findings

The gauge field is a rank-two tensor with fractonic behavior when symmetric.

Linearized equations match the covariant fracton model of Bertolini and Maggiore.

A natural analogue of Yang-Mills equations is formulated using the Fr"olicher-Nijenhuis bracket.

Abstract

We show that there exists a natural analogue of the Yang-Mills equations using the Fr\"olicher-Nijenhuis bracket between vector-valued differential forms. The gauge field is a rank-two tensor, and when one constrains it to be symmetric, then the system exhibits fractonic behaviours. In the linearised limit, the constrained equations of motion reduce to those of the covariant fracton model [Bertolini-Maggiore 2022].