Covariant Fracton Electrodynamics in Six Dimensions

TL;DR

This paper develops a covariant, six-dimensional fracton electrodynamics theory with a symmetric tensor gauge field, elucidating mobility restrictions and conservation laws through gauge invariance.

Contribution

It introduces a relativistic covariant formulation of fracton electrodynamics in six dimensions using a symmetric tensor gauge field with scalar gauge symmetry.

Findings

The stress-energy tensor's trace becomes a total derivative in six dimensions.

Charge and dipole moment conservation enforce immobility and mobility of certain excitations.

The theory connects to higher-moment generalized global symmetries.

Abstract

We formulate a covariant version of Maxwell-like fracton electrodynamics in six dimensions using a symmetric tensor gauge field with scalar gauge symmetry $\delta A_{\mu\nu}=\partial_\mu\partial_\nu\Lambda$. This provides a relativistic setting in which the characteristic fractonic restriction on mobility follows directly from gauge invariance and the allowed coupling to matter. We construct the stress--energy tensor and show that its trace has a universal dimension-dependent structure that becomes a total derivative in $d=6$. In the presence of sources, the theory enforces conservation of charge and dipole moment, capturing the immobility of isolated charges and the mobility of dipolar bound states. This structure can also be viewed as a higher-moment form of generalized global symmetry.