Semiclassics, Goldstone Bosons and CFT data

TL;DR

This paper explores the semiclassical analysis of large charge operators in conformal field theories, emphasizing Goldstone modes and coset constructions, with results on universal scaling laws for correlation functions.

Contribution

It extends the semiclassical large charge framework to non-abelian groups and higher-rank symmetries, providing systematic methods and new insights into correlation functions.

Findings

Goldstone boson dynamics dominate large charge spectra.

Universal scaling laws for three-point function coefficients.

Systematic coset construction for non-linear symmetries.

Abstract

Hellerman et al. (arXiv:1505.01537) have shown that in a generic CFT the spectrum of operators carrying a large U(1) charge can be analyzed semiclassically in an expansion in inverse powers of the charge. The key is the operator state correspondence by which such operators are associated with a finite density superfluid phase for the theory quantized on the cylinder. The dynamics is dominated by the corresponding Goldstone hydrodynamic mode and the derivative expansion coincides with the inverse charge expansion. We illustrate and further clarify this situation by first considering simple quantum mechanical analogues. We then systematize the approach by employing the coset construction for non-linearly realized space-time symmetries. Focussing on CFT3 we illustrate the case of higher rank and non-abelian groups and the computation of higher point functions. Three point function coefficients turn out to satisfy universal scaling laws and correlations as the charge and spin are varied.