Mixed five-point correlators in the 3d Ising model

Abstract

We study five-point correlators of the $\ddot{I}ƒ$, $\hat{I}\mu$, and $\hat{I}{\mu }^{\prime }$ operators in the critical 3d Ising model. We consider the $\ddot{I}ƒ\times \ddot{I}ƒ$ and $\ddot{I}ƒ\times \hat{I}\mu$ operator product expansions (OPEs) and truncate them by including a finite set of exchanged operators. We approximate the truncated operators by the corresponding contributions in appropriate disconnected five-point correlators. We compute a number of OPE coefficients that were previously unknown and show that these are consistent with predictions obtained using the fuzzy sphere regularization of the critical 3d Ising model.

v1: 37 pages, v2: small adjustments, references added