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

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

2002-11-29

arxiv.org/abs/hep-th/0211291v3

Phys.Rev.D67:086004,2003

Physics

High Energy Physics

High Energy Physics - Theory

LaTeX, 41 pages, 1 figure, 1 C source file. References added. Derivation of loop equation corrected; result for free energy un

Scientific paper

10.1103/PhysRevD.67.086004

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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