Affine Toda field theory from tree unitarity

TL;DR

This paper derives affine Toda field theories from tree-level unitarity constraints in 1+1 dimensions, providing a systematic construction method for rank two systems and proposing its extension to higher ranks.

Contribution

It introduces a novel approach to construct affine Toda field theories using tree unitarity, specifically for rank two root systems, and suggests generalization to higher ranks.

Findings

Constructed ATFT for root systems $a_2^{(2)}$ and $c_2^{(1)}$

Provided a general prescription for rank two ATFTs with two scalar fields

Proposed extension of the method to higher rank root systems

Abstract

Elasticity property (i.e. no-particle creation) is used in the tree level scattering of scalar particles in 1+1 dimensions to construct the affine Toda field theory(ATFT) associated with root systems of groups $a_2^{(2)}$ and $c_2^{(1)}$. A general prescription is given for constructing ATFT (associated with rank two root systems) with two self conjugate scalar fields. It is conjectured that the same method could be used to obtain the other ATFT associated with higher rank root systems.