Quantum integrability in two-dimensional systems with boundary

Abstract

In this paper we consider affine Toda systems defined on the half-plane and study the issue of integrability, i.e. the construction of higher-spin conserved currents in the presence of a boundary perturbation. First at the classical level we formulate the problem within a Lax pair approach which allows to determine the general structure of the boundary perturbation compatible with integrability. Then we analyze the situation at the quantum level and compute corrections to the classical conservation laws in specific examples. We find that, except for the sinh-Gordon model, the existence of quantum conserved currents requires a finite renormalization of the boundary potential.

latex file, 18 pages, 1 figure

References in corpus (4)

• Boundary S-Matrix and Boundary State in Two-Dimensional Integrable Quantum Field Theory
• Classically integrable boundary conditions for affine Toda field theories
• Affine Toda field theory on a half line
• Boundary Effects in Integrable Field Theory on a Half Line

Cited by in corpus (18)

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• Quantum corrections to the classical reflection factor in A2(1) Toda Field Theory
• $A_n^{(1)}$ affine Toda field theories with integrable boundary conditions revisited
• Classical Versus Quantum Symmetries for Toda Theories with a Nontrivial Boundary Perturbation
• A Collection of Exercises in Two-Dimensional Physics, Part 1
• Boundary Reflection Matrix for $ade$ Affine Toda Field Theory
• Quantum complex sine-Gordon model on a half line
• Quantum boundary currents for nonsimply-laced Toda theories
• Quantum anomalies in A^{(1)}_r Toda theories with defects
• Boundary Reflection Matrix for $D_4^{(1)}$ Affine Toda Field Theory
• Boundary form factors in the Smirnov--Fateev model with a diagonal boundary $S$ matrix
• First order quantum corrections to the classical reflection factor of the sinh-Gordon model
• Square Root Singularity in Boundary Reflection Matrix
• Quantum group symmetry of integrable models on the half-line