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

TL;DR

This paper calculates exact quantum particle reflection amplitudes in a_n^(1) affine Toda theories with integrable boundary conditions, revealing a rich spectrum of boundary states and explaining pole structures.

Contribution

It introduces a method to derive particle reflection amplitudes from breather reflection amplitudes using analytic continuation and bootstrap techniques, covering all known vacua.

Findings

Uncovered a rich spectrum of excited boundary states.

Calculated reflection amplitudes for a_2^(1) and a_4^(1) Toda theories.

Explained all physical poles via boundary bound states or Coleman-Thun mechanism.

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.