Emergence of supersymmetry at a critical point of a lattice model

Supersymmetry is a symmetry between a boson and a fermion. Although there is no apparent supersymmetry in nature, its mathematical consistency and appealing properties 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 nonsupersymmetric condensed matter system. We propose a $(2+1)$-dimensional 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 $ϵ$ expansion and the critical theory is the two copies of the Wess-Zumino theory with four supercharges. Exact critical exponents are predicted.