Topological field theories associated with three-dimensional Seiberg-Witten monopoles

Three-dimensional topological field theories associated with the three-dimensional version of Abelian and non-Abelian Seiberg-Witten monopoles are presented. These three-dimensional monopole equations are obtained by a dimensional reduction of the four-dimensional ones. The starting actions to be considered are Gaussian types with random auxiliary fields. As the local gauge symmetries with topological shifts are found to be first-stage-reducible, the Batalin-Vilkovisky algorithm is suitable for quantization. Then the BRST transformation rules are automatically obtained. Nontrivial observables associated with Chern classes are obtained from the geometric sector and are found to correspond to those of the topological field theory of Bogomol'nyi monopoles.