  Conformal field theory (CFT) is the key to various critical phenomena. So
far, most of studies focus on the critical exponents of various universalities,
corresponding to conformal dimensions of CFT primary fields. However, other
important yet intricate data such as the operator product expansion (OPE)
coefficients governing the fusion of two primary fields, is largely unexplored
before, specifically in dimensions higher than 2D (or equivalently $1+1$D).
Here, motivated by the recently-proposed fuzzy sphere regularization, we
investigate the operator content of 3D Ising criticality starting from a
microscopic description. We first outline the procedure of extracting OPE
coefficients on the fuzzy sphere, and then compute 13 OPE coefficients of
low-lying CFT primary fields. The obtained results are in agreement with the
numerical conformal bootstrap data of 3D Ising CFT within a high accuracy. In
addition, we also manage to obtain 4 OPE coefficients including $f_{T_{\mu\nu}
T_{\rho\eta} \epsilon}$ that were not available before, which demonstrates the
superior capabilities of our scheme. By expanding the horizon of the fuzzy
sphere regularization from the state perspective to the operator perspective,
we expect a lot of new physics ready for exploration.
