Conformal field theory (CFT) plays a crucial role in the study of various critical phenomena. While much attention has been paid to the critical exponents of different universalities, which correspond to the conformal dimensions of CFT primary fields, other important and intricate data such as operator product expansion (OPE) coefficients governing the fusion of two primary fields, have remained largely unexplored, especially in dimensions higher than 2D (or equivalently, $1+1\mathrm{D}$). Motivated by the recently proposed fuzzy sphere regularization, we investigate the operator content of 3D Ising criticality from a microscopic perspective. We first outline the procedure for extracting OPE coefficients on the fuzzy sphere and then compute 13 OPE coefficients of low-lying CFT primary fields. Our results are highly accurate and in agreement with the numerical conformal bootstrap data of 3D Ising CFT. Moreover, we were able to obtain 4 OPE coefficients, including $f_{T_{\mu \nu }{T}_{\rho \eta }\epsilon }$, which were previously unknown, thus demonstrating the superior capabilities of our scheme. Expanding the horizon of the fuzzy sphere regularization from the state perspective to the operator perspective opens up new avenues for exploring a wealth of new physics.

• Received 26 March 2023
• Accepted 21 June 2023

DOI:https://doi.org/10.1103/PhysRevLett.131.031601