  We provide a parton construction of wavefunctions and effective field
theories for fractional Chern insulators. We also analyze a strong coupling
expansion in lattice gauge theory that enables us to reliably map the parton
gauge theory onto the microsopic Hamiltonian. We show that this strong coupling
expansion is useful because of a special hierarchy of energy scales in
fractional quantum Hall physics. Our procedure is illustrated using the
Hofstadter model and then applied to bosons at 1/2 filling and fermions at 1/3
filling in a checkerboard lattice model recently studied numerically. Because
our construction provides a more or less unique mapping from microscopic model
to effective parton description, we obtain wavefunctions in the same phase as
the observed fractional Chern insulators without tuning any continuous
parameters.
