Scaling dimensions at large charge for cubic phi(3) theory in six dimensions

The O(N) model with scalar quartic interactions at its ultraviolet fixed point, and the O(N) model with scalar cubic interactions at its infrared fixed point are conjectured to be equivalent. This has been checked by comparing various features of the two models at their respective fixed points. Recently, the scaling dimensions of a family of operators of fixed charge Q have been shown to match at the FPs up to O(1N2) at leading order (LO) and next-to-leading order (NLO) in Q using a semiclassical computation which is valid to all orders in the coupling. Here we perform a complementary but overlapping comparison using a perturbative calculation in six dimensions, up to three-loop order in the coupling, to compare these critical scaling dimensions beyond NLO in Q, in fact to all relevant orders in Q. We also obtain the corresponding results at O(1N3) for the cubic theory