Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2007-09-04
JHEP 0711:001,2007
Physics
High Energy Physics
High Energy Physics - Theory
47 pages, 3 figures, 2 appendices; v2: typos and references corrected, published in JHEP
Scientific paper
10.1088/1126-6708/2007/11/001
We solve a generalization of ordinary N=1 super Yang-Mills theory with gauge group U(N) and an adjoint chiral multiplet X for which we turn on both an arbitrary tree-level superpotential term \int d^{2}\theta Tr W(X) and an arbitrary field-dependent gauge kinetic term \int d^{2}\theta Tr V(X)W^{\alpha}W_{\alpha}. When W=0, the model reduces to the extended Seiberg-Witten theory recently studied by Marshakov and Nekrasov. We use two different points of view: a ''macroscopic'' approach, using generalized anomaly equations, the Dijkgraaf-Vafa matrix model and the glueball superpotential; and the recently proposed ''microscopic'' approach, using Nekrasov's sum over colored partitions and the quantum microscopic superpotential. The two formalisms are based on completely different sets of variables and statistical ensembles. Yet it is shown that they yield precisely the same gauge theory correlators. This beautiful mathematical equivalence is a facet of the open/closed string duality. A full microscopic derivation of the non-perturbative N=1 gauge dynamics follows.
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