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.
Highlights
The emergence of classical physics at large quantum numbers is a concept familiar since the early developments of quantum mechanics [1]
The connection between semiclassics and large quantum number has provided a useful inspiration in the study of operators carrying a large conserved internal charge in conformal field theories
II we briefly review the structure of the effective field theory (EFT) and explain how to use it to compute flat space correlators in the large charge regime
Summary
The emergence of classical physics at large quantum numbers is a concept familiar since the early developments of quantum mechanics [1]. Well-known examples include the rigid rotor and the hydrogen atom In both these cases, the path integral computing the wave function of states with large angular momentum l ≫ 1 is dominated by a classical saddle-point trajectory. The connection between semiclassics and large quantum number has provided a useful inspiration in the study of operators carrying a large conserved internal charge in conformal field theories The interest toward this problem stems from the remarkable fact that the large charge sector of many, otherwise nearly intractable, strongly coupled CFTs has been argued to admit a universal weakly coupled description in terms of a certain number of hydrodynamic Goldstone modes [8]. As we will argue in this paper, the EFT allows for the controlled calculation of three- and higher-point function of large charge operators. The Appendix contains a formal discussion of three-point functions of large charge operators in the weakly coupled Uð1Þ tricritical model in 3 − ε dimensions
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