  We construct a class of 2+1 dimensional relativistic quantum field theories
which exhibit the Fractional Quantum Hall Effect in the infrared, both in the
continuum and on the lattice. The UV completion consists of a perturbative
$U(1)\times U(1)$ gauge theory with only integer-charged fields, while the low
energy spectrum consists of nontrivial topological phases supporting fractional
currents, fractionally charged chiral surface modes and bulk anyonic
excitations. Exotic phenomena such as a Fractional Quantum Spin Hall Effect can
arise in such models.
