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

Abstract

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.

21 pages, 2 figures, 1 table

References in corpus (7)

• Critical $O(N)$ Models in $6-\epsilon$ Dimensions
• Three Loop Analysis of the Critical $O(N)$ Models in $6-\epsilon$ Dimensions
• Bootstrapping $O(N)$ Vector Models in $4<d<6$
• On the Large $R$-charge Expansion in $\mathcal{N}=2$ Superconformal Field Theories
• Triviality from the Exact Renormalization Group
• Are there scaling solutions in the O(N)-models for large N in d>4?
• The OPE meets semiclassics