N = 1/2 gauge theory and its instanton moduli space from open strings in RR background

We derive the four dimensional N = 1/2 super Yang-Mills theory from tree- level computations in RNS open string theory with insertions of closed string Ramond-Ramond vertices. We also study instanton configurations in this gauge theory and their ADHM moduli space, using systems of D3 and D(−1) branes in a R-R background.