Boundary S-matrix of the $O(N)$-symmetric Non-linear Sigma Model

TL;DR

This paper conjectures integrability of the $O(N)$-symmetric non-linear sigma model with boundary conditions and derives the boundary S-matrix for particle reflections in a semi-infinite space.

Contribution

It introduces the boundary S-matrix for the $O(N)$ sigma model under free and fixed boundary conditions, advancing understanding of boundary integrability.

Findings

Boundary S-matrix derived for free boundary conditions

Boundary S-matrix derived for fixed boundary conditions

Supports conjecture of integrability in semi-infinite space

Abstract

We conjecture that the $O(N)$-symmetric non-linear sigma model in the semi-infinite $(1+1)$-dimensional space is ``integrable'' with respect to the ``free'' and the ``fixed'' boundary conditions. We then derive, for both cases, the boundary S-matrix for the reflection of massive particles of this model off the boundary at $x=0$.