Bootstrapping the Three-Dimensional Supersymmetric Ising Model

Abstract

We implement the conformal bootstrap program for three-dimensional CFTs with $\mathcal{N}=2$ supersymmetry and find universal constraints on the spectrum of operator dimensions in these theories. By studying the bounds on the dimension of the first scalar appearing in the OPE of a chiral and an anti-chiral primary, we find a kink at the expected location of the critical three-dimensional $\mathcal{N}=2$ Wess-Zumino model, which can be thought of as a supersymmetric analog of the critical Ising model. Focusing on this kink, we determine, to high accuracy, the low-lying spectrum of operator dimensions of the theory.