Singularity analysis in $A_n$ Affine Toda Theories

TL;DR

This paper investigates the singularity structures in $A_n$ affine Toda field theories, providing explicit formulae for subleading poles and testing the conjectured exact S-matrices against one-loop amplitude singularities.

Contribution

It offers a new explicit formula for subleading singularities and validates the conjectured S-matrices at one-loop level, independent of renormalization details.

Findings

Conjectured S-matrices reproduce correct singularity structures at one-loop.

Explicit formulae for subleading pole structures are derived.

The test confirms the S-matrices' validity without relying on renormalization details.

Abstract

The leading and the subleading Landau singularities in affine Toda field theories are examined in some detail. Formulae describing the subleading simple pole structure of box diagrams are given explicitly. This leads to a new and nontrivial test of the conjectured exact S-matrices for these theories. We show that to the one-loop level the conjectured S-matrices of the $A_n$ Toda family reproduce the correct singularity structure, leading as well as subleading, of the field theoretical amplitudes. The present test has the merit of being independent of the details of the renormalisations.