Quantum Integrability of Certain Boundary Conditions

TL;DR

This paper investigates the quantum integrability of the O(N) nonlinear sigma and Gross-Neveu models on a half-line, identifying specific boundary conditions under which these models remain integrable.

Contribution

It demonstrates the integrability of these models with particular boundary conditions and clarifies the boundary conditions for the O(3) nonlinear sigma model.

Findings

NLS model is integrable with Neumann, Dirichlet, and mixed boundary conditions.

GN model is integrable when boundary fermion conditions are satisfied.

Comments on boundary conditions for the O(3) NLS model by Corrigan and Sheng.

Abstract

We study the quantum integrability of the O(N) nonlinear $\sigma$ (nls) model and the O(N) Gross-Neveu (GN) model on the half-line. We show that the \nls model is integrable with Neumann, Dirichlet and a mixed boundary condition, and that the GN model is integrable if $\psi_+^a\x=\pm\psi_-^a\x$. We also comment on the boundary condition found by Corrigan and Sheng for the O(3) nls model.