String Theory Journal Club

Projective superspace formalism is a manifestly supersymmetric approach to describe extended supersymmetric theories off-shell. In this method standard superspace coordinates are appended by a bosonic auxiliary CP^1=S^2 (where the R-symmetry group acts) factor and the superfields depend on this variable meromorphically, (infinite set of components). SU(2)_R symmetry transformations realized as coordinate transformations on this CP^1. I will introduce this formalism for the case of standard 4-dimensional N=2 supersymmetric Yang-Mills theory and then discuss a specific technique of separating the prepotential gauge field into parts that depend on this CP^1 factor and a part that does not. This technique leads to compact expressions for Lagrangians of given theories and also makes it straightforward to reduce higher supersymmetry into lower susy components.