  We present a gauge theory formulation of a two-dimensional quantum smectic
and its relatives, motivated by their realizations in correlated quantum
matter. The description gives a unified treatment of phonons and topological
defects, respectively encoded in a pair of coupled gauge fields and
corresponding charges. The charges exhibit subdimensional constrained quantum
dynamics and anomalously slow highly anisotropic diffusion of disclinations
inside a smectic. This approach gives a transparent description of a
multi-stage quantum melting transition of a two-dimensional commensurate
crystal (through an incommensurate crystal - a supersolid) into a quantum
smectic, that subsequently melts into a quantum nematic and isotropic
superfluids, all in terms of a sequence of Higgs transitions.
