Integrable boundary conditions and reflection matrices for the O( N) nonlinear sigma model

Abstract

We find new integrable boundary conditions, depending on a free parameter g, for the O( N) nonlinear σ 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 previously. We solve the boundary Yang–Baxter equation, connect these solutions to the boundary conditions, and examine the corresponding integrable flows.