  Employing the fracton-elastic duality, we develop a low-energy effective
theory of a zero-temperature vortex crystal in a two-dimensional bosonic
superfluid which naturally incorporates crystalline topological defects. We
extract static interactions between these defects and investigate several
continuous quantum transitions triggered by the Higgs condensation of vortex
vacancies/interstitials and dislocations. We propose that the quantum melting
of the vortex crystal towards the hexatic or smectic phase may occur via a pair
of continuous transitions separated by an intermediate vortex supersolid phase.
