Equivalence of the Self--Dual Model and Maxwell--Chern--Simons Theory on Arbitrary Manifolds

Equivalence of the Self--Dual Model and Maxwell--Chern--Simons Theory on Arbitrary Manifolds

Using a group-invariant version of the Faddeev--Popov method we explicitly obtain the partition functions of the Self--Dual Model and Maxwell--Chern--Simons theory. We show that their ratio coincides with the partition function of abelian Chern--Simons theory to within a phase factor depending on the geometrical properties of the manifold.