Emergence of 3D Superconformal Ising Criticality on the Fuzzy Sphere

TL;DR

This paper presents a non-perturbative realization of a 3D superconformal Ising critical point using fuzzy sphere regularization, revealing emergent spacetime supersymmetry and operator spectrum evolution.

Contribution

It introduces a microscopic, non-perturbative approach to realize and study 3D superconformal field theories with emergent supersymmetry.

Findings

Identification of conformal multiplet structure at criticality

Observation of emergent spacetime supersymmetry relations

Tracking of operator spectrum evolution along RG flow

Abstract

Supersymmetric conformal field theories (SCFTs) form a unique subset of quantum field theories which provide powerful insights into strongly coupled critical phenomena. Here, we present a microscopic and non-perturbative realization of the three-dimensional $\mathcal{N}=1$ superconformal Ising critical point, based on a Yukawa-type coupling between a 3D Ising CFT and a gauged Majorana fermion. Using the recently developed fuzzy sphere regularization, we directly extract the scaling dimensions of low-lying operators via the state-operator correspondence. At the critical point, we demonstrate conformal multiplet structure together with the hallmark of emergent spacetime supersymmetry through characteristic relations between fermionic and bosonic operators. Moreover, by tuning the Yukawa coupling, we explicitly track the evolution of operator spectra from the decoupled Ising-Majorana fixed point to the interacting superconformal fixed point, revealing renormalization-group flow at the operator level. Our results establish a controlled, non-perturbative microscopic route to 3D SCFTs.