  Motivated by striped correlated quantum matter, and the recently developed
duality between elasticity of a two-dimensional (2D) crystal and a gauge
theory, we derive a dual coupled U(1) vector gauge theory for a two-dimensional
(2D) quantum smectic, where the disclination is mapped onto the fractonic
charge, that we demonstrate can only move transversely to smectic layers. This
smectic gauge theory dual also emerges from a gauge dual of a quantum crystal
after a Higgs transition corresponding to a single flavor of its dipole
condensation, an anisotropic quantum melting via dislocation proliferation. A
condensation of the second flavor of dislocations is described by another Higgs
transition describing the smectic-to-nematic melting. We also utilize the
electrostatic limit of this duality to formulate a melting of a 2D classical
smectic in terms of a higher derivative sine- Gordon model, demonstrating its
instability to a nematic at any nonzero temperature. Generalizing this
classical duality to a 3D smectic, gives formulation of a 3D nematic-to-smectic
transition in terms of an anisotropic Abelian-Higgs model.
