Covariant Fracton Electrodynamics in Six Dimensions

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.

29 pages

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