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.
Keywords
Cite
@article{arxiv.1010.1210,
title = {The uses of the refined matrix model recursion},
author = {Andrea Brini and Marcos Marino and Sebastien Stevan},
journal= {arXiv preprint arXiv:1010.1210},
year = {2014}
}
Comments
29 pages, 2 figures; v2: minor changes, references added; v3: few misprints fixed, to appear on JMP; v4: we correct a mistake in Eq. (2.60) (now (2.63))