Integrable Boundary Conditions and Reflection Matrices for the O(N) Nonlinear Sigma Model

TL;DR

This paper introduces new integrable nondiagonal boundary conditions for the O(N) nonlinear sigma model, derived from a microscopic Lagrangian, and explores their integrability and associated flows.

Contribution

It presents novel boundary conditions depending on a free parameter, derived from a microscopic Lagrangian, and connects these to solutions of the boundary Yang-Baxter equation.

Findings

Derived new boundary conditions for the O(N) model

Connected boundary conditions to solutions of the boundary Yang-Baxter equation

Explored integrable flows between different boundary conditions

Abstract

We find new integrable boundary conditions, depending on a free parameter $g$, for the O(N) nonlinear $\sigma$ model, which are of nondiagonal type, that is, particles can change their ``flavor'' through scattering off the boundary. These boundary conditions are derived from a microscopic boundary lagrangian, which is used to establish their integrability, and exhibit integrable flows between diagonal boundary conditions investigated earlier. We solve the boundary Yang-Baxter equation, connect these solutions to the boundary conditions, and examine the corresponding integrable flows.