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We construct a class of 2+1 dimensional relativistic quantum field theorieswhich exhibit the Fractional Quantum Hall Effect in the infrared, both in thecontinuum 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 lowenergy spectrum consists of nontrivial topological phases supporting fractionalcurrents, fractionally charged chiral surface modes and bulk anyonicexcitations. Exotic phenomena such as a Fractional Quantum Spin Hall Effect canarise in such models.

Fractional quantum Hall effect in a relativistic field theory