Tree level integrability in 2d quantum field theories and affine Toda models

Dorey, Patrick; Polvara, Davide

doi:10.1007/jhep02(2022)199

Tree level integrability in 2d quantum field theories and affine Toda models

Dorey, Patrick; Polvara, Davide

Authors

Professor Patrick Dorey p.e.dorey@durham.ac.uk
Professor

Davide Polvara

Abstract

We investigate the perturbative integrability of massive (1+1)-dimensional bosonic quantum field theories, focusing on the conditions for them to have a purely elastic S-matrix, with no particle production and diagonal scattering, at tree level. For theories satisfying what we call ‘simply-laced scattering conditions’, by which we mean that poles in inelastic 2 to 2 processes cancel in pairs, and poles in allowed processes are only due to one on-shell propagating particle at a time, the requirement that all inelastic amplitudes must vanish is shown to imply the so-called area rule, connecting the 3-point couplings C(3)abc to the masses ma, mb, mc of the coupled particles in a universal way. We prove that the constraints we find are universally satisfied by all affine Toda theories, connecting pole cancellations in amplitudes to properties of the underlying root systems, and develop a number of tools that we expect will be relevant for the study of loop amplitudes.

Citation

Dorey, P., & Polvara, D. (2022). Tree level integrability in 2d quantum field theories and affine Toda models. Journal of High Energy Physics, 2022(2), https://doi.org/10.1007/jhep02%282022%29199

Journal Article Type	Article
Acceptance Date	Feb 13, 2022
Online Publication Date	Feb 25, 2022
Publication Date	2022
Deposit Date	Mar 28, 2022
Publicly Available Date	Mar 28, 2022
Journal	Journal of High Energy Physics
Print ISSN	1126-6708
Publisher	Scuola Internazionale Superiore di Studi Avanzati (SISSA)
Peer Reviewed	Peer Reviewed
Volume	2022
Issue	2
DOI	https://doi.org/10.1007/jhep02%282022%29199

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