2D CFTs - Large Charge is not enough


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)​ WZW model to argue the regimes of applicability of both the large-Q expansion and the double-scaling limit.

Phys.Rev.D 105 (2022) 8, 086029