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Unoriented Strings, Loop Equations, and N=1 Superpotentials from Matrix Models

Sujay K. Ashok·Richard Corrado·Nick Halmagyi·Kristian D. Kennaway·Christian Romelsberger
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Abstract

We apply the proposal of Dijkgraaf and Vafa to analyze N=1 gauge theory with SO(N) and Sp(N) gauge groups with arbitrary tree-level superpotentials using matrix model techniques. We derive the planar and leading non-planar contributions to the large M SO(M) and Sp(M) matrix model free energy by applying the technology of higher-genus loop equations and by straightforward diagrammatics. The loop equations suggest that the RP^2 free energy is given as a derivative of the sphere contribution, a relation which we verify diagrammatically. With a refinement of the proposal of Dijkgraaf and Vafa for the effective superpotential, we find agreement with field theory expectations.

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Sujay K. Ashok, Richard Corrado, Nick Halmagyi, Kristian D. Kennaway, Christian Romelsberger. 2002-12-16. Unoriented Strings, Loop Equations, and N=1 Superpotentials from Matrix Models. https://doi.org/10.1103/physrevd.67.086004

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