Correlation functions in scalar field theory at large charge

A bstract We compute general higher-point functions in the sector of large charge operators ϕ n , 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 n 2 ≡ 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 x 1 n ϕ x 2 n ϕ ¯ x 3 n ϕ ¯ x 4 n , which reveals an interesting structure.