A Perturbative Window into Non-Perturbative Physics

TL;DR

This paper demonstrates that for a broad class of N=1 supersymmetric gauge theories, the effective superpotential can be computed exactly through perturbative planar diagrams, linking it to matrix models and enabling systematic instanton effect calculations.

Contribution

It provides a perturbative method to compute non-perturbative effects in N=1 supersymmetric gauge theories without relying on dualities or conjectures.

Findings

Effective superpotential equals sum of planar diagrams.

Perturbative corrections up to n-th loop yield up to n-instanton effects.

Method applies to theories embedded in string theory and beyond.

Abstract

We argue that for a large class of N=1 supersymmetric gauge theories the effective superpotential as a function of the glueball chiral superfield is exactly given by a summation of planar diagrams of the same gauge theory. This perturbative computation reduces to a matrix model whose action is the tree-level superpotential. For all models that can be embedded in string theory we give a proof of this result, and we sketch an argument how to derive this more generally directly in field theory. These results are obtained without assuming any conjectured dualities and can be used as a systematic method to compute instanton effects: the perturbative corrections up to n-th loop can be used to compute up to n-instanton corrections. These techniques allow us to see many non-perturbative effects, such as the Seiberg-Witten solutions of N=2 theories, the consequences of Montonen-Olive S-duality in N=1* and Seiberg-like dualities for N=1 theories from a completely perturbative planar point of view in the same gauge theory, without invoking a dual description.