On Yang-Baxter models, twist operators, and boundary conditions

TL;DR

This paper explores the role of twist operators in Yang-Baxter deformations of integrable sigma models, establishing their connection to Drinfeld twists and boundary conditions, especially for abelian cases, and discusses challenges for non-abelian deformations.

Contribution

It introduces twist operators as classical analogues of Drinfeld twists in Yang-Baxter models and reinterprets TsT transformations through boundary conditions.

Findings

Twist operators act as classical Drinfeld twists for abelian deformations.

TsT transformations are equivalent to boundary condition modifications.

Challenges are identified in extending boundary condition interpretations to non-abelian cases.

Abstract

We discuss homogeneous Yang-Baxter deformations of integrable sigma models in terms of twist operators. We show that the twist operators behave as the classical analogue of a Drinfeld twist, for all abelian and almost abelian deformations. We also use twist operators to rederive the well-known interpretation of TsT transformations -- equivalent to abelian deformations -- in terms of twisted boundary conditions. We discuss complications in extending this boundary condition picture to non-abelian deformations.