OPE meets semiclassics

We show that the correlator of three large charge operators with minimal scaling dimension can be computed semiclassically in conformal field theories (CFTs) with a U(1) symmetry for arbitrary fixed values of the ratios of their charges. We obtain explicitly the operator product expansion coefficient from the numerical solution of a nonlinear boundary value problem in the conformal superfluid effective field theory in 3d. The result applies in all three-dimensional CFTs with a U(1) symmetry whose large charge sector is a superfluid.