Classically integrable field theories with defects

TL;DR

This paper explores a Lagrangian framework for analyzing boundary conditions in integrable field theories, focusing on scalar fields with various potential types at domain junctions.

Contribution

It introduces a Lagrangian approach to boundary conditions in integrable fields, exemplified by scalar fields with different potential types at domain interfaces.

Findings

Scalar fields can be free, Liouville, or sinh-Gordon types at boundaries.

The approach provides a systematic way to study boundary conditions in integrable models.

Abstract

Some ideas and remarks are presented concerning a possible Lagrangian approach to the study of internal boundary conditions relating integrable fields at the junction of two domains. The main example given in the article concerns single real scalar fields in each domain and it is found that these may be free, of Liouville type, or of sinh-Gordon type.