Identifying Large Charge Operators

TL;DR

This paper analyzes the spectrum of large charge operators in U(1) invariant CFTs, using semiclassical methods to connect superfluid excitations with conformal multiplets and compute correlation functions.

Contribution

It provides a detailed semiclassical analysis of spinning large charge operators, including their organization into conformal multiplets and the computation of correlation functions.

Findings

Phonon excitations describe low-spin states at large charge.

Semiclassical approach breaks down for spins of order n^{1/2}.

Computed conformal 3- and 4-point functions and analyzed their conformal block decomposition.

Abstract

The Large Charge sector of Conformal Field Theory (CFT) can generically be described through a semiclassical expansion around a superfluid background. In this work, focussing on $U(1)$ invariant Wilson-Fisher fixed points, we study the spectrum of spinning large charge operators. For sufficiently low spin these correspond to the phonon excitations of the superfluid state. We discuss the organization of these states into conformal multiplets and the form of the corresponding composite operators in the free field theory limit. The latter entails a mapping, built order-by-order in the inverse charge $n^{-1}$, between the Fock space of vacuum fluctuations and the Fock space of fluctuations around the superfluid state. We discuss the limitations of the semiclassical method, and find that the phonon description breaks down for spins of order $n^{1/2}$ while the computation of observables is valid up to spins of order $n$. Finally, we apply the semiclassical method to compute some conformal 3-point and 4-point functions, and analyze the conformal block decomposition of the latter with our knowledge of the operator spectrum.