Bootstrapping the minimal $$ \mathcal{N} $$ = 1 superconformal field theory in three dimensions

Abstract

Abstract We develop the numerical bootstrap technique to study the 2 + 1 dimensional $$ \mathcal{N} $$ N = 1 superconformal field theories (SCFTs). When applied to the minimal $$ \mathcal{N} $$ N = 1 SCFT, it allows us to determine its critical exponents to high precision. This model was argued in [1] to describe a quantum critical point (QCP) at the boundary of a 3 + 1D topological superconductor. More interestingly, this QCP can be reached by tuning a single parameter, where supersymmetry (SUSY) is realized as an emergent symmetry. We show that the emergent SUSY condition also plays an essential role in bootstrapping this SCFT. But performing a “two-sided” Padé re-summation of the large N expansion series, we calculate the critical exponents for Gross-Neveu-Yukawa models at N =4 and N =8.