String theory on the Omega background

My Thesis deals with the dynamics of four-dimensional gauge theories with N=2 supersymmetry and its description within string theory. In particular, we aim at computing the perturbative part of the holomorphic prepotential of pure Super-Yang-Mills theories with unitary gauge group in the infrared region on the Omega background. In order to do, so we consider type I strings on a Melvin background and compute radiative corrections to the gauge coupling. We employ the background field method and construct the one-loop cylinder amplitude of open strings on the Melvin background coupled to an external magnetic field.