On the Integrability of the Bukhvostov-Lipatov Model

TL;DR

This paper examines the classical and quantum integrability of the Bukhvostov-Lipatov model, revealing classical conservation laws but suggesting quantum non-integrability due to broken conservation at the quantum level.

Contribution

It demonstrates the presence of a classical conserved current of Lorentz spin 3 and shows that quantum effects break this conservation, challenging previous assumptions about quantum integrability.

Findings

Classical model has a conserved Lorentz spin 3 current.

Quantum conservation law is broken, indicating non-integrability.

Quantum effects may prevent the model from being integrable as previously believed.

Abstract

The integrability of the Bukhvostov-Lipatov four-fermion model is investigated. It is shown that the classical model possesses a current of Lorentz spin 3, conserved both in the bulk and on the half-line for specific types of boundary actions. It is then established that the conservation law is spoiled at the quantum level -- a fact that might indicate that the quantum Bukhvostov-Lipatov model is not integrable, contrary to what was previously believed.