Fracton gauge fields from higher-dimensional gravity

Abstract

We show that the fractonic dipole-conserving algebra can be obtained as an Aristotelian (and pseudo-Carrollian) contraction of the Poincar\'e algebra in one dimension higher. Such contraction allows to obtain fracton electrodynamics from a relativistic higher-dimensional theory upon dimensional reduction. The contraction procedure produces several scenarios including the some of the theories already discussed in the literature. A curved space generalization is given, which is gauge invariant when the Riemann tensor of the background geometry is harmonic.