Comments on asymptotic safety in four-dimensional $\mathcal{N} = 1$ supersymmetric gauge theories

TL;DR

This paper critically examines the possibility of asymptotic safety in four-dimensional $\\mathcal{N} = 1$ supersymmetric gauge theories, concluding that controlled examples are lacking and it likely does not occur.

Contribution

The paper provides a critical analysis showing that asymptotic safety is unlikely in these theories, challenging previous assumptions.

Findings

No controlled examples of asymptotic safety found.

Reasons suggest asymptotic safety does not occur in these theories.

Provides a reasoned argument against the existence of asymptotic safety.

Abstract

We discuss asymptotic safety in four-dimensional $\mathcal{N} = 1$ supersymmetric gauge theories. Our main conclusion is that in a reasonable definition of this phenomenon there are currently no controlled examples of it; there are reasons to believe that it does not occur.