  Despite a long history of studies of vortex crystals in rotating superfluids,
their melting due to quantum fluctuations is poorly understood. Here we develop
a fracton-elasticity duality to investigate a two-dimensional vortex lattice
within the fast rotation regime, where the Lifshitz model of the collective
Tkachenko mode serves as the leading-order low-energy effective theory. We
incorporate topological defects and discuss several quantum melting scenarios
triggered by their proliferation. Furthermore, we lay the groundwork for a dual
non-linear emergent gravity description of the superfluid vortex crystals.
