Emergence of supersymmetry at a critical point of a lattice model

TL;DR

This paper demonstrates that supersymmetry can dynamically emerge at a quantum critical point in a 2+1D lattice model, providing a new perspective on how supersymmetry might manifest in condensed matter systems.

Contribution

It introduces a 2+1D lattice model where supersymmetry emerges at a critical point, with exact critical exponents and a connection to Wess-Zumino theory.

Findings

Emergent supersymmetry at a quantum critical point

Only one relevant perturbation at the critical point

Critical theory corresponds to two copies of Wess-Zumino model

Abstract

Supersymmetry is a symmetry between a boson and a fermion. Although there is no apparent supersymmetry in nature, its mathematical consistency and appealing property have led many people to believe that supersymmetry may exist in nature in the form of a spontaneously broken symmetry. In this paper, we explore an alternative possibility by which supersymmetry is realized in nature, that is, supersymmetry dynamically emerges in the low energy limit of a non-supersymmetric condensed matter system. We propose a 2+1D lattice model which exhibits an emergent space-time supersymmetry at a quantum critical point. It is shown that there is only one relevant perturbation at the supersymmetric critical point in the $\epsilon$-expansion and the critical theory is the two copies of the Wess-Zumino theory with four supercharges. Exact critical exponents are predicted.