Covariant Fractons and Weitzenb\"ock Torsion

TL;DR

This paper explores the connection between covariant fracton gauge theory and a gravity theory based on Weitzenb"ock torsion, revealing that fracton solutions form a subset of gravity solutions and offering new insights into their relationship.

Contribution

It demonstrates that covariant fracton gauge theory solutions are a subsector of Moller-Hayashi-Shirafuji gravity solutions, linking fractons to gravitational theories.

Findings

Covariant fracton solutions are a subset of Moller-Hayashi-Shirafuji gravity solutions.

The study provides a new perspective on fractons as a gauge theory related to gravity.

It clarifies the role of covariant fractons within the context of torsion-based gravity theories.

Abstract

The relation between covariant fracton gauge theory and Moller-Hayashi-Shirafuji theory of gravity is investigated. The former is the gauge theory of a rank-two symmetric tensor with gauge symmetry given by the double derivative of a scalar parameter; the latter is the most general theory, whose action is quadratic in the Weitzenb\"ock torsion. We show that the solutions of covariant fracton gauge theory describe a subsector of the space of solutions of Moller-Hayashi-Shirafuji theory, providing a new insight in the relation between covariant fractons and gravity, and elucidating the meaning of covariant fracton theory as a new type of gauge theory.