Improving 3d Ising OPE coefficients with fuzzy sphere conformal generators

We use the

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.