Lifshitz gauge duality

Motivated by a variety of realizations of the compact Lifshitz model I derive its fractonic gauge dual. The resulting U(1) vector gauge theory efficiently and robustly encodes the restricted mobility of its dipole conserving charged matter and the corresponding topological vortex defects. The gauge theory provides a transparent formulation of the three phases of the Lifshitz model and gives a field theoretic formulation of the associated two-stage Higgs transitions.