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

Abstract

A bstract We study large charge sectors in the O( N ) model in 6 − ϵ 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 “extremal” higher-point correlation functions for large charge operators and find a precise equivalence between both pictures. Instanton instabilities are found to be exponentially suppressed at large charge. We also consider correlation function of U(1)-invariant meson operators in the O(2 N ) ⊃ U(1) × SU( N ) theory, as a first step towards tests of (higher spin) AdS / CFT.