N=8 Superspace Constraints for Three-dimensional Gauge Theories

Abstract : We present a systematic analysis of the N=8 superspace constraints in three space-time dimensions. The general coupling between vector and scalar supermultiplets is encoded in an SO(8) tensor W_{AB} which is a function of the matter fields and subject to a set of algebraic and super-differential relations. We show how the conformal BLG model as well as three-dimensional Yang-Mills theory provide solutions to these constraints and can both be formulated in this universal framework.