Comments on scale invariant but non-conformal supersymmetric field theories

Understand

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-\epsilon) dimension proposed in literatures.