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It is shown that integrability is an accidental property of generictwo-dimensional $O(2)$-symmetric asymptotically-free theories in the regimewhere the charge density is much larger than the dynamical scale. We show thisby constructing an infinite tower of higher-spin conserved currents in the mostgeneric effective Lagrangian at large chemical potential to all orders inperturbative expansion in the renormalization-group invariant couplingconstant.

Integrability of Large-Charge Sectors in Generic 2D EFTs