Jumps and twists in affine Toda field theories

TL;DR

This paper explores point-like defects and boundary conditions in affine Toda field theories, deriving conserved quantities and Lax pairs, and analyzing the impact of twisted Yangian boundaries on integrability.

Contribution

It provides explicit expressions for conserved quantities and Lax pairs in affine Toda theories with defects and twisted Yangian boundaries, advancing understanding of their integrable structure.

Findings

Explicit conserved quantities and Lax pairs are derived.

Bulk behavior remains unaffected by boundaries in twisted Yangian cases.

The Hamiltonian formulation effectively analyzes defects and boundary conditions.

Abstract

The concept of point-like "jump" defects is investigated in the context of affine Toda field theories. The Hamiltonian formulation is employed for the analysis of the problem. The issue is also addressed when integrable boundary conditions ruled by the classical twisted Yangian are present. In both periodic and boundary cases explicit expressions of conserved quantities as well as the relevant Lax pairs and sewing conditions are extracted. It is also observed that in the case of the twisted Yangian the bulk behavior is not affected by the presence of the boundaries.