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Critical Points of Glueball Superpotentials and Equilibria of Integrable Systems

Timothy J. Hollowood
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Abstract

We compare the matrix model and integrable system approaches to calculating the exact vacuum structure of general N=1 deformations of either the basic N=2 theory or its generalization with a massive adjoint hypermultiplet, the N=2* theory. We show that there is a one-to-one correspondence between arbitrary critical points of the Dijkgraaf-Vafa glueball superpotential and equilibrium configurations of the associated integrable system. The latter being either the periodic Toda chain, for N=2, or the elliptic Calogero-Moser system, for N=2*. We show in both cases that the glueball superpotential at the crtical point equals the associated Hamiltonian. Our discussion includes an analysis of the vacuum structure of the N=1* theory with an arbitrary tree-level superpotential for one of the adjoint chiral fields.

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Timothy J. Hollowood. 2003-07-22. Critical Points of Glueball Superpotentials and Equilibria of Integrable Systems. https://doi.org/10.1088/1126-6708%2F2003%2F10%2F051

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