From tree- to loop-simplicity in affine Toda theories II: higher-order poles and cut decompositions

TL;DR

This paper extends a cutting method for scalar theories to higher loops in affine Toda models, simplifying complex diagrams and confirming consistency with bootstrap results through cancellation mechanisms.

Contribution

It generalizes the cut method to multi-loop diagrams in affine Toda theories, revealing a simplification mechanism and confirming bootstrap predictions.

Findings

Most cut diagrams cancel out, leaving only a few contributing to the result.

The method confirms the Laurent expansion coefficients match bootstrap results.

A cancellation mechanism akin to Gauss's theorem explains diagram simplifications.

Abstract

Recently we showed how, in two-dimensional scalar theories, one-loop threshold diagrams can be cut into the product of one or more tree-level diagrams arXiv:2206.09368. Using this method on the ADE series of Toda models, we computed the double- and single-pole coefficients of the Laurent expansion of the S-matrix around a pole of arbitrary even order, finding agreement with the bootstrapped results. Here we generalise the cut method explained in arXiv:2206.09368 to multiple loops and use it to simplify large networks of singular diagrams. We observe that only a small number of cut diagrams survive and contribute to the expected bootstrapped result, while most of them cancel each other out through a mechanism inherited from the tree-level integrability of these models. The simplification mechanism between cut diagrams inside networks is reminiscent of Gauss's theorem in the space of Feynman diagrams.