On integrable boundaries in the 2 dimensional $O(N)$ $\sigma$-models

Abstract

We make an attempt to map the integrable boundary conditions for 2 dimensional non-linear O(N) $\sigma$-models. We do it at various levels: classically, by demanding the existence of infinitely many conserved local charges and also by constructing the double row transfer matrix from the Lax connection, which leads to the spectral curve formulation of the problem; at the quantum level, we describe the solutions of the boundary Yang-Baxter equation and derive the Bethe-Yang equations. We then show how to connect the thermodynamic limit of the boundary Bethe-Yang equations to the spectral curve.

Dedicated to the memory of Petr Kulish, 31 pages, 1 figure, v2: conformality and integrability of the boundary conditions are distinguished

References in corpus (19)

• Review of AdS/CFT Integrability: An Overview
• Boundary S-Matrix and Boundary State in Two-Dimensional Integrable Quantum Field Theory
• The Algebraic Curve of Classical Superstrings on AdS_5xS^5
• Algebraic Curve for the SO(6) sector of AdS/CFT
• Review of AdS/CFT Integrability, Chapter IV.2: Deformations, Orbifolds and Open Boundaries
• Strings as Multi-Particle States of Quantum Sigma-Models
• Integrability of Green-Schwarz Sigma Models with Boundaries
• Boundary scattering, symmetric spaces and the principal chiral model on the half-line
• Commuting charges and symmetric spaces
• Classification of reflection matrices related to (super) Yangians and application to open spin chain models
• Boundary S-matrix of the $O(N)$-symmetric Non-linear Sigma Model
• Integrable Boundary Conditions and Reflection Matrices for the O(N) Nonlinear Sigma Model
• Classical integrability of the O(N) nonlinear Sigma model on a half-line
• Boundary finite size corrections for multiparticle states and planar AdS/CFT
• Classically integrable boundary conditions for symmetric-space sigma models
• Classical O(N) nonlinear sigma model on the half line: a study on consistent Hamiltonian description
• Spectral curve for open strings attached to the Y=0 brane
• Quantum Integrability of Certain Boundary Conditions
• Algebraic Bethe Ansatz for O(2N) sigma models with integrable diagonal boundaries

Cited by in corpus (6)

• Boundary states, overlaps, nesting and bootstrapping AdS/dCFT
• String integrability of defect CFT and dynamical reflection matrices
• The R-matrix bootstrap for the 2d O(N) bosonic model with a boundary
• Integrable crosscaps in classical sigma models
• New boundary monodromy matrices for classical sigma models
• Quantum Integrability and Quantum Groups: a special issue in memory of Petr P. Kulish