Particle Reflection Amplitudes in a_n^(1) Toda Field Theories

Abstract

We determine the exact quantum particle reflection amplitudes for all known vacua of a_n^(1) affine Toda theories on the half-line with integrable boundary conditions. (Real non-singular vacuum solutions are known for about half of all the classically integrable boundary conditions.) To be able to do this we use the fact that the particles can be identified with the analytically continued breather solutions, and that the real vacuum solutions are obtained by analytically continuing stationary soliton solutions. We thus obtain the particle reflection amplitudes from the corresponding breather reflection amplitudes. These in turn we calculate by bootstrapping from soliton reflection matrices which we obtained as solutions of the boundary Yang-Baxter equation (reflection equation). We study the pole structure of the particle reflection amplitudes and uncover an unexpectedly rich spectrum of excited boundary states, created by particles binding to the boundary. For a_2^(1) and a_4^(1) Toda theories we calculate the reflection amplitudes for particle reflection off all these excited boundary states. We are able to explain all physical strip poles in these reflection factors either in terms of boundary bound states or a generalisation of the Coleman-Thun mechanism.

minor corrections, 42 pages, 1 eps figure, see http://www.mth.kcl.ac.uk/~delius/pub/reflect.html for animated plot and further information

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• Form factors of boundary fields for A(2)-affine Toda field theory
• Reflection Amplitudes of Boundary Toda Theories and Thermodynamic Bethe Ansatz
• Boundary One-Point Functions, Scattering Theory and Vacuum Solutions in Integrable Systems
• Quantum complex sine-Gordon model on a half line
• Universal boundary reflection amplitudes
• On the quantum reflection factor for the sinh-Gordon model with general boundary conditions
• Boundary bootstrap principle in two-dimensional integrable quantum field theories
• N=1 Supersymmetric Boundary Bootstrap
• First order quantum corrections to the classical reflection factor of the sinh-Gordon model
• Aspects of classical backgrounds and scattering for affine Toda theory on a half-line
• Second order quantum corrections to the classical reflection factor of the sinh-Gordon model
• Boundary effects in two-dimensional critical and off-critical systems