# A functional perspective on emergent supersymmetry

## TL;DR

This paper demonstrates that three-dimensional parity-symmetric Yukawa systems naturally develop ${
m N}=1$ supersymmetry at long distances, using a renormalization approach that preserves supersymmetry and shows supersymmetry-breaking operators are irrelevant.

## Contribution

It introduces a renormalization method that maintains supersymmetry explicitly and proves the irrelevance of supersymmetry-breaking operators in the infrared regime.

## Key findings

- Supersymmetry emerges in the long-range behavior of the studied systems.
- Supersymmetry-breaking operators are shown to be irrelevant in the infrared.
- Numerical estimates of critical exponents are provided using non-perturbative methods.

## Abstract

We investigate the emergence of ${\cal N}=1$ supersymmetry in the long-range behavior of three-dimensional parity-symmetric Yukawa systems. We discuss a renormalization approach that manifestly preserves supersymmetry whenever such symmetry is realized, and use it to prove that supersymmetry-breaking operators are irrelevant, thus proving that such operators are suppressed in the infrared. All our findings are illustrated with the aid of the $\epsilon$-expansion and a functional variant of perturbation theory, but we provide numerical estimates of critical exponents that are based on the non-perturbative functional renormalization group.