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arXiv · hep-th/0207106

On Geometry and Matrix Models

Robbert Dijkgraaf·Cumrun Vafa
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Abstract

We point out two extensions of the relation between matrix models, topological strings and N=1 supersymmetric gauge theories. First, we note that by considering double scaling limits of unitary matrix models one can obtain large N duals of the local Calabi-Yau geometries that engineer N=2 gauge theories. In particular, a double scaling limit of the Gross-Witten one-plaquette lattice model gives the SU(2) Seiberg-Witten solution, including its induced gravitational corrections. Secondly, we point out that the effective superpotential terms for N=1 ADE quiver gauge theories is similarly computed by large multi-matrix models, that have been considered in the context of ADE minimal models on random surfaces. The associated spectral curves are multiple branched covers obtained as Virasoro and W-constraints of the partition function.

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Robbert Dijkgraaf, Cumrun Vafa. 2002-07-11. On Geometry and Matrix Models. https://doi.org/10.1016/s0550-3213(02)00764-2

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