Improving 3d Ising OPE Coefficients with Fuzzy Sphere Conformal Generators

We use the $K$ special conformal generator in the Fuzzy sphere setup of the Ising CFT to determine primary states. For $\mathrm{\Delta }\lesssim 8$, 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-$K$ allows for better extrapolation of OPE coefficients to the CFT limit, because of the existence of an $O(1)$ gap between primaries and descendants in the spectrum of eigenvalues of $\mathrm{\mid }K{\mathrm{\mid }}^2$ which protects the primaries from strongly mixing with descendants. We compare the CFT data we obtain with the Eigenstate Thermalization Hypothesis.