Boundary Bound States in Affine Toda Field Theory

TL;DR

This paper extends the Coleman-Thun mechanism to boundary scattering in affine Toda field theories, revealing that boundary bound states have energies related to the sum of certain masses, and explicitly computes the spectrum for E6.

Contribution

It introduces a generalized boundary bootstrap approach for affine Toda theories and explicitly determines the boundary bound state spectrum for E6.

Findings

Boundary bound state energies are half the sum of masses with the same colour.

The boundary spectrum for E6 is fully computed and forms a closed bootstrap.

The generalized Coleman-Thun mechanism applies to boundary scattering in these theories.

Abstract

We demonstrate that the generalization of the Coleman-Thun mechanism may be applied to the situation, when considering scattering processes in 1+1-dimensions in the presence of reflecting boundaries. For affine Toda field theories we find that the binding energies of the bound states are always half the sum over a set of masses having the same colour with respect to the bicolouration of the Dynkin diagram. For the case of $E_6$-affine Toda field theory we compute explicitly the spectrum of all higher boundary bound states. The complete set of states constitutes a closed bootstrap.