The OPE meets semiclassics

TL;DR

This paper demonstrates a semiclassical method to compute three-point correlators of large charge operators in 3D conformal field theories with a $U(1)$ symmetry, revealing explicit OPE coefficients via boundary value problem solutions.

Contribution

It introduces a semiclassical approach to calculate three-point functions of large charge operators in 3D CFTs with $U(1)$ symmetry, connecting superfluid EFT to conformal correlators.

Findings

Explicit OPE coefficients obtained from boundary value problem solutions.

Method applicable to all 3D $U(1)$ symmetric CFTs with superfluid large charge sectors.

Provides a bridge between semiclassical superfluid EFT and conformal correlator computations.

Abstract

We show that the correlator of three large charge operators with minimal scaling dimension can be computed semiclassically in CFTs with a $U(1)$ symmetry for arbitrary fixed values of the ratios of their charges. We obtain explicitly the OPE coefficient from the numerical solution of a nonlinear boundary value problem in the conformal superfluid EFT in $3d$. The result applies in all three-dimensional CFTs with a $U(1)$ symmetry whose large charge sector is a superfluid.