Extended N=1 super Yang-Mills theory

TL;DR

This paper explores a generalized N=1 super Yang-Mills theory with arbitrary superpotential and gauge kinetic terms, demonstrating the equivalence of macroscopic and microscopic approaches and deriving non-perturbative dynamics.

Contribution

It introduces a comprehensive analysis of extended N=1 super Yang-Mills theory using two distinct formalisms and proves their equivalence, advancing understanding of non-perturbative gauge dynamics.

Findings

Macroscopic and microscopic formalisms yield identical gauge correlators.

The work establishes a link between anomaly equations, matrix models, and Nekrasov's partitions.

A microscopic derivation of non-perturbative N=1 gauge dynamics is provided.

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}\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.