The OPE meets semiclassics

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.

6 pages+appendices, 4 figures v2 journal version

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• Spin Impurities, Wilson Lines and Semiclassics
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• Yukawa interactions at Large Charge
• Nonrelativistic CFTs at Large Charge: Casimir Energy and Logarithmic Enhancements
• Numerical tests of the large charge expansion
• Operator spectrum of nonrelativistic CFTs at large charge
• Long Range, Large Charge, Large $N$
• Spinning correlators in large-charge CFTs
• The analytic structure of the fixed charge expansion
• Large R-charge EFT correlators in N=2 SQCD
• The Breakdown of Resummed Perturbation Theory at High Energies
• On the exponentially small corrections to $\mathcal{N}=2$ superconformal correlators at large R-charge
• Identifying Large Charge Operators