Supersymmetric asymptotic safety is not guaranteed

TL;DR

This paper investigates whether supersymmetric theories can exhibit UV asymptotic safety and concludes that, using unitarity bounds and the a-theorem, such behavior is generally not possible without additional degrees of freedom.

Contribution

It provides a non-perturbative argument ruling out supersymmetric asymptotic safety in broad classes of theories, highlighting the necessity of extra degrees of freedom for UV completion.

Findings

Supersymmetric theories do not generally exhibit asymptotic safety.

Unitarity bounds and the a-theorem constrain UV behavior of susy theories.

Additional degrees of freedom are required for UV completion of non-asymptotically free susy theories.

Abstract

It was recently shown that certain perturbatively accessible, non-supersymmetric gauge-Yukawa theories have UV asymptotic safety, without asymptotic freedom: the UV theory is an interacting RG fixed point, and the IR theory is free. We here investigate the possibility of asymptotic safety in supersymmetric theories, and use unitarity bounds, and the a-theorem, to rule it out in broad classes of theories. The arguments apply without assuming perturbation theory. Therefore, the UV completion of a non-asymptotically free susy theory must have additional, non-obvious degrees of freedom, such as those of an asymptotically free (perhaps magnetic dual) extension.