Comments on scale invariant but non-conformal supersymmetric field theories

We investigate a possibility of scale invariant but non-conformal supersymmetric field theories from a perturbative approach. The explicit existence of monotonically decreasing a-function that generates beta-functions as a gradient flow provides a strong obstruction for such a possibility at two-loop order. We comment on the "discovery" of scale invariant but non-conformal renormalization group trajectories via a "change of scheme" in (4-ε) dimension proposed in literatures.

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