Calculating Gluino-Condensate Prepotential

TL;DR

This paper explores the derivation of the prepotential in N=1 supersymmetric Yang-Mills theory using matrix models, revealing structures and providing a non-perturbative cubic contribution for arbitrary parameters.

Contribution

It introduces a method to derive the CIV-DV prepotential for arbitrary powers of the superpotential in N=1 SUSY YM theory, highlighting emerging structures and calculating a non-perturbative cubic term.

Findings

Derived the prepotential for arbitrary superpotential powers.

Identified structures reminiscent of representation theory.

Obtained a cubic non-perturbative contribution for any n.

Abstract

We discuss the derivation of the CIV-DV prepotential for arbitrary power n+1 of the original superpotential in the N=1 SUSY YM theory (for arbitrary number n of cuts in the solution of the planar matrix model in the Dijkgraaf-Vafa interpretation). The goal is to hunt for structures, not so much for exact formulas, which are necessarily complicated, before the right language is found to represent them. Some entities, reminiscent of representation theory, clearly emerge, but a lot of work remains to be done to identify the relevant ones. As a practical application, we obtain a cubic (first non-perturbative) contribution to the prepotential for any n.