Bootstrapping the Three-Dimensional Supersymmetric Ising Model

TL;DR

This paper applies the conformal bootstrap to 3D $ abla=2$ supersymmetric theories, identifying a critical kink that corresponds to the supersymmetric Ising model and accurately determining its operator spectrum.

Contribution

It introduces a bootstrap approach for 3D $ abla=2$ supersymmetric CFTs and pinpoints the critical supersymmetric Ising model through a distinctive spectral kink.

Findings

Identified a kink at the expected location of the supersymmetric Ising model.

Determined the low-lying operator dimensions with high precision.

Established universal bounds on operator spectra in $ abla=2$ supersymmetric theories.

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.