Matrix models vs. Seiberg-Witten/Whitham theories

Details Matrix models vs. Seiberg-Witten/Whitham theories Matrix models vs. Seiberg-Witten/Whitham theories

2002-09-10

arxiv.org/abs/hep-th/0209085v2

Phys.Lett. B552 (2003) 293-302

Physics

High Energy Physics

High Energy Physics - Theory

8 pages in LaTeX, 1 LaTeX figure, reference added

Scientific paper

10.1016/S0370-2693(02)03163-5

We discuss the relation between matrix models and the Seiberg--Witten type (SW) theories, recently proposed by Dijkgraaf and Vafa. In particular, we prove that the partition function of the Hermitean one-matrix model in the planar (large $N$) limit coincides with the prepotential of the corresponding SW theory. This partition function is the logarithm of a Whitham $\tau$-function. The corresponding Whitham hierarchy is explicitly constructed. The double-point problem is solved.

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