Correlation functions in scalar field theory at large charge

Abstract

We compute general higher-point functions in the sector of large charge operators ${\varphi }^n$, ${\bar{\varphi }}^n$ at large charge in $O(2)$ $(\bar{\varphi }\varphi {)}^2$ theory. We find that there is a special class of "extremal" correlators having only one insertion of ${\bar{\varphi }}^n$ 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 $⟨\varphi (x_1{)}^n\varphi (x_2{)}^n\bar{\varphi }(x_3{)}^n\bar{\varphi }(x_4{)}^n⟩$, which reveals an interesting structure.

13 pages

References in corpus (1)

• Feynman diagrams and the large charge expansion in $3-\epsilon$ dimensions

Cited by in corpus (1)

• The OPE meets semiclassics