# Absence of emergent supersymmetry at superconducting quantum critical points in Dirac and Weyl semimetals

## TL;DR

This study investigates the possibility of emergent supersymmetry at superconducting quantum critical points in Dirac and Weyl semimetals, concluding that such supersymmetry does not manifest due to dynamical generation of non-supersymmetric terms.

## Contribution

The paper demonstrates that Yukawa coupling at these critical points prevents the emergence of space-time supersymmetry by generating non-supersymmetric terms.

## Key findings

- No emergent supersymmetry at superconducting quantum critical points.
- Yukawa coupling induces non-supersymmetric terms.
- Constraints on realizing supersymmetry in condensed matter systems.

## Abstract

Supersymmetry plays a crucial role in superstring theory and high-energy physics, but has never been observed in experiments. Recently, an effective space-time supersymmetry was argued to emerge in the low-energy region by tuning Dirac or Weyl semimetal to approach a superconducting quantum critical point, at which the Dirac or Weyl fermion and the bosonic order parameter are both massless. Here, we study under what circumstances can space-time supersymmetry be realized at a quantum critical point. We demonstrate that the Yukawa-type coupling between the massless fermion and massless boson can dynamically generate an infinite number of non-supersymmetric terms in the effective field theory of the boson. Owing to these terms, no space-time supersymmetry emerges at the superconducting quantum critical points. The results provide important constraint on the exploration of emergent space-time supersymmetry in condensed matter systems.