Covariant Fractons and Weitzenböck Torsion

TL;DR

The paper establishes a precise embedding of covariant fracton gauge theory into the linearised teleparallel gravity framework of Møller-Hayashi-Shirafuji. It identifies the fracton field strength with the linearised Weitzenböck torsion (under a vanishing totally antisymmetric part of the vielbein) and maps the fracton action parameters to MHS constants, revealing that the fracton sector forms a subsector of linearised MHS theory (b_{μν}=0) for generic parameter choices. The analysis employs both spectral (Fourier) methods and BRST cohomology to demonstrate equivalence of the covariant fracton and linearised MHS descriptions, and it shows the fracton moduli space is isomorphic to the b=0 sector of the MHS spectrum for β/α ≠ 2. These results deepen the understanding of covariant fractons as a gravity-like gauge theory and point toward a non-linear extension via teleparallel gravity frameworks. The work provides a coherent bridge between higher-rank gauge theories and torsion-based gravity, with potential implications for constructing consistent non-linear fracton 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 Weitzenböck 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.