Affine Toda field theories related to Coxeter groups of non-crystallographic type

TL;DR

This paper develops affine Toda field theories based on non-crystallographic Coxeter groups H_2, H_3, and H_4, analyzing their mass spectra, couplings, and quantum corrections through a reduction from crystallographic groups.

Contribution

It introduces a novel construction of affine Toda theories linked to non-crystallographic Coxeter groups, expanding the theoretical framework.

Findings

Classical mass spectra and three-point couplings are determined.

One-loop quantum corrections to mass renormalization are calculated.

Particle masses exhibit ratios related to the golden ratio.

Abstract

We propose affine Toda field theories related to the non-crystallographic Coxeter groups H_2, H_3 and H_4. The classical mass spectrum, the classical three-point couplings and the one-loop corrections to the mass renormalisation are determined. The construction is carried out by means of a reduction procedure from crystallographic to non-crystallographic Coxeter groups. The embedding structure explains for various affine Toda field theories that their particles can be organised in pairs, such that their relative masses differ by the golden ratio.