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

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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 $d=6-\epsilon$ 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 6 dimensions.