Instanton calculus in R-R background and the topological string

We study a system of fractional D3 and D(-1) branes in a Ramond-Ramond closed string background and show that it describes the gauge instantons of N=2 super Yang-Mills theory and their interactions with the graviphoton of N=2 supergravity. In particular, we analyze the instanton moduli space using string theory methods and compute the prepotential of the effective gauge theory exploiting the localization methods of the instanton calculus showing that this leads to the same information given by the topological string. We also comment on the relation between our approach and the so-called Omega-background.