Lattice BF theory, dumbbells, and composite fermions

We formulate $U(1)$ $bda$ Chern-Simons theory, which is also called BF on a lattice, adapting method proposed by Kantor and Susskind for the groups $\mathbb{R}$ $\mathbb{Z}_N$. Our applies to any finite or infinite abelian group. study discrete symmetries use model provide rigorous treatment of composite fermion theory fractional quantum Hall effect (FQHE), with no ambiguities relating intersecting Wilson/'t Hooft lines. derive Jain's fractions, one can calculate corrections mean field solution within this framework. generalize formalism higher form gauge models in arbitrary dimension, suggest possible non-Abelian extension.