Improving 3d Ising OPE coefficients with fuzzy sphere conformal generators

We use the K K special conformal generator in the Fuzzy sphere setup of the Ising CFT to determine primary states. For \Delta ≲ 8 Δ ≲ 8 , we recover the known primaries and find several new ones, including in the parity-odd sector. We then use these primaries to compute OPE coefficients. We find that using primaries constructed from special- K K allows for better extrapolation of OPE coefficients to the CFT limit, because of the existence of an O(1) O ( 1 ) gap between primaries and descendants in the spectrum of eigenvalues of |K|^2 | K | 2 which protects the primaries from strongly mixing with descendants. We compare the CFT data we obtain with the Eigenstate Thermalization Hypothesis.