Sigma models in the presence of dynamical point-like defects

TL;DR

This paper introduces point-like dynamical defects into integrable models like Landau-Lifshitz and Principal Chiral models, identifying integrals of motion, Lax pairs, and sewing conditions to preserve integrability.

Contribution

It provides a novel framework for incorporating dynamical defects into classical integrable field theories using quadratic algebra methods.

Findings

Identified local integrals of motion in defect models

Derived Lax pairs and sewing conditions at defect points

Showed involution of integrals considering sewing conditions

Abstract

Point-like Liouville integrable dynamical defects are introduced in the context of the Landau-Lifshitz and Principal Chiral (Faddeev-Reshetikhin) models. Based primarily on the underlying quadratic algebra we identify the first local integrals of motion, the associated Lax pairs as well as the relevant sewing conditions around the defect point. The involution of the integrals of motion is shown taking into account the sewing conditions.