Integrability of Large-Charge Sectors in Generic 2D EFTs

TL;DR

This paper demonstrates that integrability in large-charge sectors of generic 2D $O(2)$-symmetric asymptotically-free theories is an accidental feature, established through the construction of an infinite set of conserved currents at large chemical potential.

Contribution

It constructs an infinite tower of higher-spin conserved currents in generic 2D $O(2)$-symmetric theories at large charge density, showing integrability is accidental.

Findings

Integrability appears only at large charge density.

Infinite tower of conserved currents constructed to all orders.

Integrability is not a generic feature at all scales.

Abstract

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.