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.

arXiv comment13 pages

References in corpus (14)

• Conformal Four Point Functions and the Operator Product Expansion
• Semiclassics, Goldstone Bosons and CFT data
• Compensating strong coupling with large charge
• The Epsilon Expansion Meets Semiclassics
• Semiclassical approach for multiparticle production in scalar theories
• A limit for large $R$-charge correlators in $\mathcal{N}=2$ theories
• Exponentiation of Multiparticle Amplitudes in Scalar Theories
• Implications of N=1 Superconformal Symmetry for Chiral Fields
• Feynman diagrams and the large charge expansion in $3-\epsilon$ dimensions
• On the large R-charge $\mathcal{N}=2$ chiral correlators and the Toda equation
• The large charge limit of scalar field theories and the Wilson-Fisher fixed point at $\epsilon =0$
• Exponentiation of multiparticle amplitudes in scalar theories. II. Universality of the exponent
• Double scaling limit of N=2 chiral correlators with Maldacena-Wilson loop
• Asymptotic expansions of the hypergeometric function with two large parameters $-$ application to the partition function of a lattice gas in a field of traps

Cited by in corpus (10)

• Selected Topics in the Large Quantum Number Expansion
• Correlation functions in finite temperature CFT and black hole singularities
• $\mathcal{N}=2$ conformal gauge theories at large R-charge: the $SU(N)$ case
• Resurgence of the large-charge expansion
• Charging the Conformal Window
• Untangling scaling dimensions of fixed charge operators in Higgs Theories
• The OPE meets semiclassics
• Transition of Large $R$-Charge Operators on a Conformal Manifold
• Nonrelativistic CFTs at Large Charge: Casimir Energy and Logarithmic Enhancements
• Identifying Large Charge Operators