Defect fusing rules in affine Toda field theory

TL;DR

This paper introduces defect fusing rules in affine Toda field theories and applies them to derive a new transmission matrix for the a^(1)_3 theory, satisfying key consistency relations.

Contribution

It presents the first formulation of defect fusing rules in both classical and quantum affine Toda theories and constructs a novel transmission matrix for a^(1)_3.

Findings

Derived a new transmission matrix for a^(1)_3 theory

Established defect fusing rules in classical and quantum contexts

Ensured the transmission matrix obeys triangle and crossing-unitarity relations

Abstract

The concept of fusing rules for defects in a^(1)_r affine Toda field theories is introduced in the classical and quantum contexts. This idea is employed in finding a new transmission matrix for the a^(1)_3 theory which obeys the triangle relations and the crossing-unitarity relations.