Year: 2003
Type: article
Abstract: We apply the proposal of Dijkgraaf and Vafa to analyze $\mathcal{N}=1$ gauge theory with $\mathrm{SO}(N)$ and $\mathrm{Sp}(N)$ gauge groups with arbitrary tree-level superpotentials using matrix model techniques. We derive the planar and leading nonplanar contributions to the large M $\mathrm{SO}(M)$ and $\mathrm{Sp}(M)$ matrix model free energy by applying the technology of higher-genus loop equations and by straightforward diagrammatics. The loop equations suggest that the $R{P}^{2}$ 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.
Language: Latvian
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2098712482