Comments on scale invariant but non-conformal supersymmetric field theories

TL;DR

This paper examines whether scale invariant but non-conformal supersymmetric field theories can exist, using perturbative methods, and finds strong evidence against their existence at two-loop order.

Contribution

It provides a perturbative analysis showing the non-existence of such theories at two-loop order and critiques previous claims based on scheme changes.

Findings

Existence of a monotonically decreasing a-function at two-loop order

Obstruction to scale invariant non-conformal theories in supersymmetric models

Critique of scheme change arguments in (4- extepsilon) dimensions

Abstract

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.