On a generalised bootstrap principle

TL;DR

This paper explores a generalized bootstrap principle for non-simply-laced affine Toda field theories, analyzing their S-matrices and pole structures across dual algebra pairs, proposing criteria for physical poles and explaining others via a Coleman-Thun mechanism.

Contribution

It introduces a generalized bootstrap framework for affine Toda S-matrices, including new cases and criteria for physical poles based on algebraic and pole order considerations.

Findings

Only odd order poles with positive coefficients are physically relevant.

The generalized Coleman-Thun mechanism explains non-physical singularities.

New examples of pole generation are provided for specific algebra cases.

Abstract

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.