Conformality of supersymmetric gauge theory

We show that the 4-dimensional N = 1, 2 supersymmetric gauge theories are conformal provided that the anomalous breaking of chiral symmetry is unobservable. In supersymmetric gauge theories, the trace anomaly which controls the scale evolution of the coupling constant and the axial anomaly of the R-symmetry belong to the same multiplet, so that the irrelevance of the latter leads to the conformality. For the N = 1 case, this also automatically resolves the ``anomaly puzzle'' since both anomalous violations are unphysical. We also show that the anomaly mediated supersymmetry breaking does not happen for the same reason. We then conclude that any extensions of the standard model which restore the supersymmetry below the grand unification scale are excluded.