Microscopic quantum superpotential in N=1 gauge theories

Abstract

We consider the N=1 super Yang-Mills theory with gauge group U(N), adjoint chiral multiplet X and tree-level superpotential Tr W(X). We compute the quantum effective superpotential W_mic as a function of arbitrary off-shell boundary conditions at infinity for the scalar field X. This effective superpotential has a remarkable property: its critical points are in one-to-one correspondence with the full set of quantum vacua of the theory, providing in particular a unified picture of solutions with different ranks for the low energy gauge group. In this sense, W_mic is a good microscopic effective quantum superpotential for the theory. This property is not shared by other quantum effective superpotentials commonly used in the literature, like in the strong coupling approach or the glueball superpotentials. The result of this paper is a first step in extending Nekrasov's microscopic derivation of the Seiberg-Witten solution of N=2 super Yang-Mills theories to the realm of N=1 gauge theories.

23 pages, 1 figure; typos corrected, version to appear in JHEP

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Cited by in corpus (6)

• Extended N=1 super Yang-Mills theory
• Consistency conditions in the chiral ring of super Yang-Mills theories
• On the Geometry of Super Yang-Mills Theories: Phases and Irreducible Polynomials
• Instanton Calculus and Loop Operator in Supersymmetric Gauge Theory
• Partition Functions of $\mathcal{N}=1$ Gauge Theories on $S^2\times {\mathbb{R}}_{\epsilon }^2$ and Duality
• Flavors in the microscopic approach to N=1 gauge theories