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

${\cal N}=1$
N=1 gauge theories, and the calculation of vevs of surface operators in superconformal
${\cal N}=2$
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.

Topics
Free energy, Integral calculus, Probability theory, Calabi Yau theory, Complex analysis, Gauge symmetry, String theory, Supersymmetric gauge theory, Gauge group, Statistical thermodynamics
© 2011 American Institute of Physics.
2011
American Institute of Physics
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