Crystal-to-Fracton Tensor Gauge Theory Dualities*

We discuss the duality between elasticity of two-dimensional crystals and fracton tensor gauge
theories, developed by two of the authors [1,2,3]. This duality leads to numerous predictions for the
phases and phase transitions in fracton systems, such as the existence of gauge theory counterparts
to the (commensurate) crystal, supersolid, hexatic, and isotropic fluid phases of elasticity theory,
that will be discussed. The classical finite temperature limit, provides a complementary description
of the KTHNY theory of 2D melting, formulated in terms of a higher derivative vector sine-Gordon
model. Broader implications of this duality, such as the quantum melting transitions and quantum
phase diagrams, symmetry enriched fracton order, and connection to the interacting topological
crystalline insulators, will be discussed.

[1] Michael Pretko, Zhengzheng Zhai and Leo Radzihovsky, Phys. Rev. B. 100, 134113 (2019).
[2] M. Prekto and L. Radzihovsky, Phys. Rev. Lett. 120, 195301 (2018).
[3] M. Pretko and L. Radzihovsky, Phys. Rev. Lett. 121, 235301 (2018).