Emergence of 3D Superconformal Ising Criticality on the Fuzzy Sphere

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.