More on the cubic versus quartic interaction equivalence in the O (N) model

We compute the scaling dimensions of a family of fixed-charge operators at the infrared fixed point of the O(N) model featuring cubic interactions in d=6-ϵ for arbitrary N to leading and subleading order in the charge but to all orders in the couplings. The results are used to analyze the conjectured equivalence with the O(N) model displaying quartic interactions at its ultraviolet fixed point. This is performed by comparing the cubic model scaling dimensions against the known large N results for the quartic model and demonstrating that they match. Our results reinforce the conjectured equivalence and further provide novel information on the finite N physics stemming from the computations in the cubic model just below six dimensions.