Microscopic quantum superpotential in N=1 gauge theories

TL;DR

This paper introduces a microscopic quantum superpotential for N=1 gauge theories that uniquely captures all quantum vacua and unifies solutions with different gauge group ranks, advancing the understanding of these theories.

Contribution

It provides a novel microscopic superpotential for N=1 gauge theories that accurately reflects all quantum vacua and differs from existing superpotentials by its comprehensive vacuum correspondence.

Findings

The superpotential W_mic's critical points match all quantum vacua.

W_mic offers a unified picture of vacua with different gauge group ranks.

This approach extends Nekrasov's methods from N=2 to N=1 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.