Exact S-Matrices with Affine Quantum Group Symmetry

TL;DR

This paper constructs exact factorized S-matrices for 1+1D quantum field theories with quantum affine algebra symmetries, revealing a link between algebraic structures and physical scattering properties.

Contribution

It introduces a method to build S-matrices with quantum affine symmetry, accounting for Lorentz spins and gradation, and explicitly constructs examples with $U_q(c_n^{(1)})$ symmetry.

Findings

S-matrices exhibit non-rigid pole structures influenced by quantum dual Coxeter numbers

The approach connects algebraic gradation with physical mass ratios

Explicit S-matrix examples for $U_q(c_n^{(1)})$ symmetry are provided

Abstract

We show how to construct the exact factorized S-matrices of 1+1 dimensional quantum field theories whose symmetry charges generate a quantum affine algebra. Quantum affine Toda theories are examples of such theories. We take into account that the Lorentz spins of the symmetry charges determine the gradation of the quantum affine algebras. This gives the S-matrices a non-rigid pole structure. It depends on a kind of ``quantum'' dual Coxeter number which will therefore also determine the quantum mass ratios in these theories. As an example we explicitly construct S-matrices with $U_q(c_n^{(1)})$ symmetry.