Unoriented Strings, Loop Equations, and N=1 Superpotentials from Matrix Models
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.
Cite
@article{arxiv.hep-th/0211291,
title = {Unoriented Strings, Loop Equations, and N=1 Superpotentials from Matrix Models},
author = {Sujay K. Ashok and Richard Corrado and Nick Halmagyi and Kristian D. Kennaway and Christian Romelsberger},
journal= {arXiv preprint arXiv:hep-th/0211291},
year = {2010}
}
Comments
LaTeX, 41 pages, 1 figure, 1 C source file. References added. Derivation of loop equation corrected; result for free energy unchanged