Improving 3d Ising OPE Coefficients with Fuzzy Sphere Conformal Generators

TL;DR

This paper employs the Fuzzy sphere approach and special conformal generators to identify primary states in the Ising CFT, improving the extrapolation of OPE coefficients and revealing new primaries, including in the parity-odd sector.

Contribution

It introduces a novel method using the $K$ generator in the Fuzzy sphere setup to identify primaries and compute OPE coefficients with enhanced accuracy.

Findings

Recovered known primaries for $$ and found new ones.

Primaries constructed from special-$K$ improve OPE extrapolation.

Existence of an $O(1)$ gap protects primaries from mixing.

Abstract

We use the $K$ special conformal generator in the Fuzzy sphere setup of the Ising CFT to determine primary states. For $\Delta \lesssim 8$, 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 $|K|^2$ which protects the primaries from strongly mixing with descendants. We compare the CFT data we obtain with the Eigenstate Thermalization Hypothesis.