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

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.