New boundary monodromy matrices for classical sigma models

TL;DR

This paper introduces new integrable boundary conditions for classical sigma models that include free parameters, expanding the symmetry possibilities beyond previously known fixed-parameter boundary conditions.

Contribution

The authors derive novel boundary conditions with free parameters for classical sigma models, along with the corresponding boundary monodromy matrices, broadening the scope of integrable boundary conditions.

Findings

New boundary conditions with free parameters are found.

Boundary monodromy matrices are explicitly constructed.

Symmetry groups are extended to include G×H or H×G.

Abstract

The 2d principal models without boundaries have $G\times G$ symmetry. The already known integrable boundaries have either $H\times H$ or $G_{D}$ symmetries, where $H$ is such a subgroup of $G$ for which $G/H$ is a symmetric space while $G_{D}$ is the diagonal subgroup of $G\times G$. These boundary conditions have a common feature: they do not contain free parameters. We have found new integrable boundary conditions for which the remaining symmetry groups are either $G\times H$ or $H\times G$ and they contain one free parameter. The related boundary monodromy matrices are also described.