A Note on effective N=1 Super Yang-Mills Theories versus Lattice Results

TL;DR

This paper compares the glueball mass spectrum of an effective N=1 super Yang-Mills theory with lattice data, revealing partial agreement and predicting additional masses and mixing angles, while introducing a new Fayet-Iliopoulos term.

Contribution

It provides a detailed comparison between an effective super Yang-Mills model and lattice results, and introduces a Fayet-Iliopoulos term for the three-form multiplet.

Findings

Confirmation of four scalars and two Majorana fermions in lattice data

Mass of the three-form dominates over the Veneziano-Yankielowicz-Dijkgraaf-Vafa term

Fayet-Iliopoulos term generates a glueball condensate

Abstract

We compare the glueball mass spectrum of an effective N=1 pure super Yang-Mills theory formulated in terms of a three-form supermultiplet with the available lattice data. These confirm the presence of four scalars and two Majorana fermions but the detailed mass spectrum is difficult to reconcile with the effective supersymmetric theory. By imposing supersymmetry and using two of four bosonic masses we get a prediction for the remaining masses as well as the mixing angles. We find that the mass of the three-form dominates over the contribution of the Veneziano-Yankielowicz-Dijkgraaf-Vafa term. As a byproduct we introduce a Fayet-Iliopoulos term for the three-form multiplet and show that it generates a glueball condensate.