Extending the Veneziano-Yankielowicz Effective Theory

TL;DR

This paper extends the Veneziano-Yankielowicz effective theory to include glueball states by proposing a new superpotential, connecting it with geometric approaches, and analyzing supersymmetry breaking effects.

Contribution

A new superpotential form incorporating glueball degrees of freedom is introduced, linking the VY theory with geometric methods and supersymmetry breaking.

Findings

The new superpotential reproduces the VY vacua.

The approach connects glueball states with underlying degrees of freedom.

The glueball effective potential matches ordinary Yang-Mills results.

Abstract

We extend the Veneziano Yankielowicz (VY) effective theory in order to account for ordinary glueball states. We propose a new form of the superpotential including a chiral superfield for the glueball degrees of freedom. When integrating it ``out'' we obtain the VY superpotential while the N vacua of the theory naturally emerge. This fact has a counterpart in the Dijkgraaf and Vafa geometric approach. We suggest a link of the new field with the underlying degrees of freedom which allows us to integrate it ``in'' the VY theory. We finally break supersymmetry by adding a gluino mass and show that the Kahler independent part of the ``potential'' has the same form of the ordinary Yang-Mills glueball effective potential.