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.

受带状相关量子物质以及二维（2D）晶体的弹性和规范理论之间最近发展的对偶性的推动，我们导出了二维（2D）量子近晶的双耦合U（1）矢量规范理论，其中向错被映射到分形电荷上，我们证明了它只能横向移动到近晶层。该近晶晶格理论对偶也从对应于其偶极子缩合的单一风味的希格斯跃迁之后的量子晶体的晶格对偶出现，该各向异性通过位错扩散而熔化。另一种希格斯跃迁描述了位错的第二种风味的缩合，该希格斯跃迁描述了近晶至向列的熔融。我们还利用这种对偶性的静电极限，根据更高的导数正弦-戈登模型，来表示二维经典近晶的熔化，表明其在任何非零温度下对向列的不稳定性。将这种经典对偶性概括为3D近晶的，就可以用各向异性的Abelian-Higgs模型来表示3D向列至近晶的过渡。