Aspects of affine Toda field theory on a half line

Abstract

The question of the integrability of real-coupling affine toda field theory on a half line is discussed. It is shown, by examining low-spin conserved charges, that the boundary conditions preserving integrability are strongly constrained. In particular, among the cases treated so far, $e_6^{(1)}$, $d_n^{(1)}$ and $a_n^{(1)},n\ge 2$, there can be no free parameters introduced by such boundary conditions; indeed the only remaining freedom (apart from choosing the simple condition ${\partial }_1\varphi =0$), resides in a choice of signs. For a special case of the boundary condition, accessible only for $a_n^{(1)}$, it is pointed out that the classical boundary bound state spectrum may be related to a set of reflection factors in the quantum field theory. Some preliminary calculations are reported for other boundary conditions, demonstrating that the classical scattering data satisfies the weak coupling limit of the reflection bootstrap equation. (Invited talk at \lq Quantum field theory, integrable models and beyond', Yukawa Institute for Theoretical Physics, Kyoto University, 14-18 February 1994.)

27 pages, harvmac, DTP-94/29

References in corpus (8)

• Quantum Solitons in Affine Toda Field Theories
• Classically integrable boundary conditions for affine Toda field theories
• Affine Toda field theory on a half line
• Factorized Scattering in the Presence of Reflecting Boundaries
• Statistical Models with a Line of Defect
• Affine Toda Field Theory in the Presence of Reflecting Boundaries
• Quantum Soliton Mass Corrections in SL(N) Affine Toda Theory
• Reflection Bootstrap Equations for Toda Field Theory

Cited by in corpus (35)

• Classically integrable boundary conditions for affine Toda field theories
• Scattering Theory and Correlation Functions in Statistical Models with a Line of Defect
• Classically integrable field theories with defects
• Reflection-Transmission Algebras
• Affine Toda field theories with defects
• Boundary Exchange Algebras and Scattering on the Half Line
• Generalisations of the Coleman-Thun mechanism and boundary reflection factors
• Reflection factors and a two-parameter family of boundary bound states in the sinh-Gordon model
• On duality and reflection factors for the sinh-Gordon model
• Boundary Reflection Matrix in Perturbative Quantum Field Theory
• Particle Reflection Amplitudes in a_n^(1) Toda Field Theories
• Reflection factors and exact g-functions for purely elastic scattering theories
• On a_2^(1) Reflection Matrices and Affine Toda Theories
• Quantum mass corrections for affine Toda solitons
• Soliton-preserving boundary condition in affine Toda field theories
• Reflection-Transmission Quantum Yang-Baxter Equations
• Background field boundary conditions for affine Toda field theories
• Solving the quantum non-linear Schrodinger equation with delta-type impurity
• Boundary breathers in the sinh-Gordon model
• Quantum corrections to the classical reflection factor in A2(1) Toda Field Theory
• Form factors of boundary fields for A(2)-affine Toda field theory
• Interplay between Zamolodchikov-Faddeev and Reflection-Transmission algebras
• Boundary Reflection Matrix for $ade$ Affine Toda Field Theory
• Universal boundary reflection amplitudes
• Integrable field theory with boundary conditions
• On the quantum reflection factor for the sinh-Gordon model with general boundary conditions
• Quantum anomalies in A^{(1)}_r Toda theories with defects
• Aspects of classical backgrounds and scattering for affine Toda theory on a half-line
• Boundary Quantum Field Theories Perturbed by $\mathrm{T}\bar{\mathrm{T}}$: Towards a Form Factor Program
• On the elliptic sinh-Gordon equation with Durham boundary conditions
• Second order quantum corrections to the classical reflection factor of the sinh-Gordon model
• First order quantum corrections to the classical reflection factor of the sinh-Gordon model
• Square Root Singularity in Boundary Reflection Matrix
• Boundary Reflection Matrix for $D_4^{(1)}$ Affine Toda Field Theory
• Linearizable Initial-Boundary Value Problems for the sine-Gordon Equation on the Half-Line