TOPOLOGICAL MATTER IN 4 DIMENSIONS

Topological models involving matter couplings to Donaldson-Witten theo ry are presented. The construction is carried out using both the topol ogical algebra and its central extension, which arise from the twistin g of N=2 supersymmetry in four dimensions. The framework on which the construction is based is constituted by the superspace associated to t hese algebras. The models show new features of topological quantum fie ld theories which could provide either a mechanism for topological sym metry breaking, or the analog of two-dimensional mirror symmetry in fo ur dimensions.