Integrable defects and B\"acklund transformations in Yang-Baxter models

TL;DR

This paper introduces two novel methods for incorporating integrable defects into Yang-Baxter sigma-models, demonstrating their construction and explicit examples, thereby advancing the understanding of defect integration in integrable field theories.

Contribution

It presents two distinct approaches—modified monodromy matrices and frozen Bäcklund transformations—for constructing integrable defects in Yang-Baxter models, including explicit examples for the $SU(2)$ case.

Findings

Constructed integrable defects in ultralocal $S^2$ Yang-Baxter model.

Developed defect matrices for inhomogeneous Yang-Baxter models.

Provided explicit expressions for $SU(2)$ non-split Yang-Baxter defect matrices.

Abstract

We explore two distinct methods to introduce integrable defects in a family of integrable sigma-models known as Yang-Baxter models. The first method invokes a modified monodromy matrix encoding an integrable defect separating two integrable systems. As an example we construct integrable defects in the ultralocal version of the $S^2$ Yang-Baxter model or 2d Fateev sausage model. The second method is based on the so-called "frozen" B\"acklund transformations. Lifting the construction to the Drinfel'd double, we show how defect matrices can be constructed for inhomogeneous Yang-Baxter models. We provide explicit expressions for the $SU(2)$ non-split Yang-Baxter model for this class of integrable defects.