2D CFTs - Large Charge is not enough

TL;DR

This paper investigates the limitations of large-charge expansions in two-dimensional conformal field theories, highlighting the need for additional parameters to achieve a meaningful effective field theory description.

Contribution

It demonstrates that large charge alone does not control dynamics in 2D CFTs and proposes a double-scaling limit involving an extra parameter for better analysis.

Findings

Large-charge sector decouples from dynamics in 2D CFTs.

A double-scaling limit can be used when an additional parameter is present.

Analysis of the $SU(2)_k$ WZW model illustrates applicability regimes.

Abstract

In this note we study two-dimensional CFTs at large global charge. Since the large-charge sector decouples from the dynamics, it does not control the dynamics and an EFT construction that works in higher-dimensional theories fails. It is however possible to use large charge in a double-scaling limit when another controlling parameter is present. We find some general features of the spectrum of models that admit an NLSM description in a WKB approximation and use the large-charge sector of the solvable $SU(2)_k$ WZW model to argue the regimes of applicability of both the large-Q expansion and the double-scaling limit.