The uses of the refined matrix model recursion

Abstract

We study matrix models in the β-ensemble by building on the refined recursion relation proposed by Chekhov and Eynard. We present explicit results for the first β-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 \documentclass[12pt]{minimal}\begin{document}${\cal N}=1$\end{document}N=1 gauge theories, and the calculation of vevs of surface operators in superconformal \documentclass[12pt]{minimal}\begin{document}${\cal N}=2$\end{document}N=2 theories and their Liouville duals. Finally, we study the β-deformation of the Chern–Simons matrix model. Our results indicate that this model does not provide an appropriate description of the Ω-deformed topological string on the resolved conifold, and therefore that the β-deformation might provide a different generalization of topological string theory in toric Calabi–Yau backgrounds.