Fractonic gauge theory of smectics

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