Effective Gauge Degrees of Freedom and the (Non)existence of the Glueball Superpotential

TL;DR

The paper introduces a method to accurately determine the glueball superpotential in certain supersymmetric theories, revealing that some theories lack such a superpotential despite having isolated vacua.

Contribution

It presents a novel approach to compute the Veneziano-Yankielowicz integration constant, clarifying the existence of the superpotential in massless supersymmetric theories.

Findings

Some $ abla$ theories do not possess an effective glueball superpotential.

The method accurately determines the superpotential even in massless cases.

In certain theories, the glueball superfield $S$ is zero, indicating no superpotential.

Abstract

We propose an efficient way to obtain a correct Veneziano-Yankielowicz type integration constant of the effective glueball superpotential $W_{eff}(S,g,\Lambda)$, even for massless theories. Applying our method, we show some $\mathcal{N} = 1$ theories do not have such an effective glueball superpotential, even though they have isolated vacua. In these cases, $S = 0$ typically.