Massive Vacua of N=1* Theory and S-duality from Matrix Models

TL;DR

This paper demonstrates how matrix models can describe all massive vacua of the N=1* theory, revealing modular invariance and S-duality properties consistent with N=4 supersymmetry.

Contribution

It extends the Dijkgraaf-Vafa matrix model approach to encompass all massive vacua of the N=1* theory, including the Higgs vacuum, and shows their modular relations.

Findings

Matrix model superpotentials are modular functions of the effective coupling.

Different vacua are related by SL(2,Z) transformations, indicating S-duality.

Results support the modular invariance of the underlying N=4 theory.

Abstract

In this note we show how Dijkgraaf and Vafa's hypothesis relating the exact superpotential of an N=1 theory to a matrix model can be used to describe all the massive vacua of the N=1*, or mass deformed N=4, theory including the Higgs vacuum. The matrix model computation of the superpotential for each massive vacuum independently yields a modular function of the associated effective coupling in that vacuum which agrees with previously derived results up to a vacuum-independent additive constant. The results in the different massive vacua can be related by the action of SL(2,Z) on the N=4 coupling, thus providing evidence for modular invariance of the underlying N=4 theory.