On the UV completion of the $O(N)$ model in $6-\epsilon$ dimensions: a stable large-charge sector

Understand

We study large charge sectors in the $O(N)$ model in $6-\epsilon $ dimensions.

• For $4<d<6$, in perturbation theory, the quartic $O(N)$ theory has a UV stable fixed point at large $N$.
• It was recently argued that this fixed point can be described in terms of an IR fixed point of a cubic $O(N)$ model.
• By considering a double scaling limit of large charge and weak couplings, we compute two-point and all &#34;extremal&#34; higher-point correlation functions for large charge operators and find a precise equivalence between both pictures.