SUSY Glue-Balls, Dynamical Symmetry Breaking and Non-Holomorphic Potentials

TL;DR

This paper extends the Veneziano-Yankielowicz effective action for supersymmetric Yang-Mills theory to include higher derivative terms, leading to stable dynamics, the formation of glueballs, and dynamical supersymmetry breaking beyond semi-classical approximations.

Contribution

It introduces a non-holomorphic extension of the effective action that stabilizes the ground state and reveals new dynamical effects such as glueball formation and supersymmetry breaking.

Findings

Stable non-perturbative ground state achieved

Formation of massive glueball states demonstrated

Dynamical supersymmetry breaking identified

Abstract

We discuss the instability of the Veneziano-Yankielowicz effective action (or its supersymmetric ground-state) with respect to higher order derivative terms. As such terms must be present in an effective action, the V-Y action alone cannot describe the dynamics of SYM consistently. We introduce an extension of this action, where all instabilities are removed by means of a much richer structure of the Kaehler potential. We demonstrate that the dominant contributions to the effective potential are determined by the non-holomorphic part of the action and we prove that the non-perturbative ground-state can be equipped with stable dynamics. Making an expansion near the resulting ground-state to second order in the derivatives never leads back to the result by Veneziano and Yankielowicz. As a consequence new dynamical effects arise, which are interpreted as the formation of massive states in the boson sector (glueballs) and are accompanied by dynamical supersymmetry breaking. As this regime of the dynamics is not captured by standard semi-classical analysis (instantons etc.), our results do not contradict these calculations but investigate the physics of the system beyond these approximations.