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We study a topological field theory describing confining phases of gaugetheories in four dimensions. It can be formulated on a lattice using a discrete2-form field talking values in a finite abelian group (the magnetic gaugegroup). We show that possible theta-angles in such a theory are quantized andlabeled by quadratic functions on the magnetic gauge group. When thetheta-angles vanish, the theory is dual to an ordinary topological gaugetheory, but in general it is not isomorphic to it. We also explain how tocouple a lattice Yang-Mills theory to a TQFT of this kind so that the 't Hooftflux is well-defined, and quantized values of the theta-angles are allowed. Thequantized theta-angles include the discrete theta-angles recently identified byAharony, Seiberg and Tachikawa.

Topological Field Theory on a Lattice, Discrete Theta-Angles and Confinement