The case of asymptotic supersymmetry

TL;DR

This paper explores the possibility that supersymmetry (SUSY) could emerge as an asymptotic state at high energies in gauge theories, analyzing the renormalization group flow of couplings and their ratios.

Contribution

It provides a systematic analysis of the conditions under which SUSY can be asymptotically realized, showing that Yukawa couplings do not reach supersymmetric fixed points, and investigates SUSY restoration scenarios.

Findings

Yukawa coupling fixed points are not supersymmetric.

SUSY can be broken in the scalar sector.

SUSY restoration is possible in specific models.

Abstract

We start a systematic investigation of the possibility to have supersymmetry (SUSY) to be an asymptotic state of the gauge theory in the high energy (UV) limit, due to the renormalization group running of coupling constants of the theory. The answer on whether this situation takes place or not, can be resolved by dealing with the running of the ratios between Yukawa and scalar couplings to the gauge coupling. The behavior of these ratios does not depend too much on whether gauge coupling is asymptotically free (AF) or not. It can be shown that the UV stable fixed point for the Yukawa coupling is not supersymmetric. Taking this into account, one can break down SUSY only in the scalar coupling sector. We consider two simplest examples of such breaking, namely N=1 supersymmetric QED and QCD. In one of the cases one can construct an example of SUSY being restored in the UV regime.