The uses of the refined matrix model recursion

Abstract: We study matrix models in the beta ensemble by building on the refined recursion relation proposed by Chekhov and Eynard. We present explicit results for the first beta-deformed corrections in the one-cut and the two-cut cases, as well as two applications to supersymmetric gauge theories: the calculation of superpotentials in N=1 gauge theories, and the calculation of vevs of surface operators in superconformal N=2 theories and their Liouville duals. Finally, we study the beta deformation of the Chern-Simons matrix model. Our results indicate that this model does not provide an appropriate description of the Omega-deformed topological string on the resolved conifold, and therefore that the beta-deformation might provide a different generalization of topological string theory in toric Calabi-Yau backgrounds.