Topological Field Theories associated with Three Dimensional Seiberg-Witten monopoles

Abstract

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, Batalin-Vilkovisky algorithm is suitable for quantization. Then BRST transformation rules are automatically obtained. Non-trivial observables associated with Chern classes are obtained from geometric sector and are found to correspond to those of the topological field theory of Bogomol'nyi monopoles.