Quantum Integrability of Certain Boundary Conditions

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 $ψ_+^a\x=\pmψ_-^a\x$. We also comment on the boundary condition found by Corrigan and Sheng for the O(3) nls model.

11 pages, Latex file, minor changes, one reference added

References in corpus (6)

• Boundary S-Matrix and Boundary State in Two-Dimensional Integrable Quantum Field Theory
• Classically integrable boundary conditions for affine Toda field theories
• Boundary S-matrix of the $O(N)$-symmetric Non-linear Sigma Model
• Classical integrability of the O(N) nonlinear Sigma model on a half-line
• Non-decoupling Effects of Heavy Particles in Triple Gauge Boson Vertices
• Fusion of SO(N) reflection matrices

Cited by in corpus (6)

• Integrable Boundary Conditions and Reflection Matrices for the O(N) Nonlinear Sigma Model
• The R-matrix bootstrap for the 2d O(N) bosonic model with a boundary
• Classical O(N) nonlinear sigma model on the half line: a study on consistent Hamiltonian description
• On integrable boundaries in the 2 dimensional $O(N)$ $\sigma$-models
• Algebraic Bethe Ansatz for O(2N) sigma models with integrable diagonal boundaries
• Supersymmetric WZW $\sigma$ Model on Full and Half Plane