Extended N=1 super Yang-Mills theory

Abstract

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}θTr W(X) and an arbitrary field-dependent gauge kinetic term \int d^{2}θTr V(X)W^αW_α. 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.

47 pages, 3 figures, 2 appendices; v2: typos and references corrected, published in JHEP

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• Developments of theory of effective prepotential from extended Seiberg-Witten system and matrix models
• Consistency conditions in the chiral ring of super Yang-Mills theories
• On the Geometry of Super Yang-Mills Theories: Phases and Irreducible Polynomials
• Low Energy Processes Associated with Spontaneously Broken N=2 Supersymmetry
• Quiver Gauge Theory and Extended Electric-magnetic Duality
• Instanton Calculus and Loop Operator in Supersymmetric Gauge Theory
• Glueball operators and the microscopic approach to N=1 gauge theories
• SUSY/Non-SUSY Duality in U(N) Gauge Model with Partially Broken N=2 Supersymmetry
• Flavors in the microscopic approach to N=1 gauge theories
• A Nonperturbative Proof of Dijkgraaf-Vafa Conjecture
• On the Chiral Ring and Vacua of $\mathcal{N}=1$ Adjoint SQCD