  Motivated by the prediction of fractonic topological defects in a quantum
crystal, we utilize a reformulated elasticity duality to derive a description
of a fracton phase in terms of coupled vector U(1) gauge theories. The fracton
order and restricted mobility emerge as a result of an unusual Gauss law where
electric field lines of one gauge field act as sources of charge for others. At
low energies this vector gauge theory reduces to the previously studied
fractonic symmetric tensor gauge theory. We construct the corresponding lattice
model and a number of generalizations, which realize fracton phases via a
condensation of string-like excitations built out of charged particles,
analogous to the p-string condensation mechanism of the gapped X-cube fracton
phase.
