We compute general higher-point functions in the sector of large charge operators $\phi^n$, $\bar\phi^n$ at large charge in $O(2)$ $(\bar \phi\phi)^2$ theory.
We find that there is a special class of "extremal" correlators having only one insertion of $\bar \phi^n$ that have a remarkably simple form in the double-scaling limit $n\to \infty $ at fixed $g\,n^2\equiv \lambda$, where $g\sim\epsilon $ is the coupling at the $O(2)$ Wilson-Fisher fixed point in $4-\epsilon$ dimensions.
In this limit, also non-extremal correlators can be computed.
As an example, we give the complete formula for $ \langle \phi(x_1)^{n}\,\phi(x_2)^{n}\,\bar{\phi}(x_3)^{n}\,\bar{\phi}(x_4)^{n}\rangle$, which reveals an interesting structure.
Correlation functions in scalar field theory at large charge · Around
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