Integrability of Large-Charge Sectors in Generic 2D EFTs

It is shown that integrability is an accidental property of generic two-dimensional $O(2)$-symmetric asymptotically-free theories in the regime where the charge density is much larger than the dynamical scale. We show this by constructing an infinite tower of higher-spin conserved currents in the most generic effective Lagrangian at large chemical potential to all orders in perturbative expansion in the renormalization-group invariant coupling constant.