Correlation functions in scalar field theory at large charge

Abstract

We compute general higher-point functions in the sector of large charge operators ϕn,ϕ¯ n at large charge in O(2) (ϕ¯ ϕ) 2 theory. We find that there is a special class of “extremal” correlators having only one insertion of ϕ¯ n that have a remarkably simple form in the double-scaling limit n →∞ at fixed g n2 ≡ λ, where g ~ ϵ is the coupling at the O(2) Wilson-Fisher fixed point in 4 − ϵ dimensions. In this limit, also non-extremal correlators can be computed. As an example, we give the complete formula for 〈ϕ(x1)nϕ(x2)nϕ¯(x3)nϕ¯(x4)n〉, which reveals an interesting structure.