On a generalised bootstrap principle

The S-matrices for non-simply-laced affine Toda field theories are considered in the context of a generalised bootstrap principle. The S-matrices, and in particular their poles, depend on a parameter whose range lies between the Coxeter numbers of dual pairs of the corresponding non-simply-laced algebras. It is proposed that only odd order poles in the physical strip with positive coefficients throughout this range should participate in the bootstrap. All other singularities have an explanation in principle in terms of a generalised Coleman-Thun mechanism. Besides the S-matrices introduced by Delius, Grisaru and Zanon, the missing case ($f_4^{(1)},e_6^{(2)}$), is also considered and provides many interesting examples of pole generation.