  We propose a quantum field theory description of the X-cube model of fracton
topological order. The field theory is not (and cannot be) a topological
quantum field theory (TQFT), since unlike the X-cube model, TQFTs are invariant
(i.e. symmetric) under continuous spacetime transformations. However, the
theory is instead invariant under a certain subgroup of the conformal group. We
describe how braiding statistics and ground state degeneracy are reproduced by
the field theory, and how the the X-cube Hamiltonian and field theory can be
minimally coupled to matter fields. We also show that even on a manifold with
trivial topology, spatial curvature can induce a ground state degeneracy that
is stable to arbitrary local perturbations! Our formalism may allow for the
description of other fracton field theories, where the only necessary input is
an equation of motion for a charge density.
