Breathers in the elliptic sine-Gordon model

TL;DR

This paper derives new scattering amplitudes for the elliptic sine-Gordon model, revealing breather states and their interactions, and introduces an elliptic version of minimal affine Toda field theory.

Contribution

It provides explicit expressions for the S-matrix in the elliptic sine-Gordon model, including breathers and their scattering, and introduces a novel elliptic affine Toda theory.

Findings

New expressions for scattering amplitudes using q-deformed gamma functions

Identification of breather bound states and their unavoidably associated Tachyons

Introduction of an elliptic version of minimal D(n+1)-affine Toda field theory

Abstract

We provide new expressions for the scattering amplitudes in the soliton-antisoliton sector of the elliptic sine-Gordon model in terms of cosets of the affine Weyl group corresponding to infinite products of q-deformed gamma functions. When relaxing the usual restriction on the coupling constants, the model contains additional bound states which admit an interpretation as breathers. These breather bound states are unavoidably accompanied by Tachyons. We compute the complete S-matrix describing the scattering of the breathers amonst themselves and with the soliton-antisoliton sector. We carry out various reductions of the model, one of them leading to a new type of theory, namely an elliptic version of the minimal D(n+1)-affine Toda field theory.