Yang-Baxter sigma models based on the CYBE

TL;DR

This paper introduces a new class of Yang-Baxter sigma models based on the classical Yang-Baxter equation, expanding the framework for integrable deformations of sigma models and allowing more flexible target space modifications.

Contribution

It generalizes Yang-Baxter sigma models from the modified to the classical Yang-Baxter equation, enabling broader classification and partial deformations while preserving integrability.

Findings

Classical Yang-Baxter-based models classify more integrable deformations.

Partial target space deformations can be realized without losing integrability.

The approach broadens the scope of integrable sigma model deformations.

Abstract

It is known that Yang-Baxter sigma models provide a systematic way to study integrable deformations of both principal chiral models and symmetric coset sigma models. In the original proposal and its subsequent development, the deformations have been characterized by classical $r$-matrices satisfying the modified classical Yang-Baxter equation (mCYBE). In this article, we propose the Yang-Baxter sigma models based on the classical Yang-Baxter equations (CYBE) rather than the mCYBE. This generalization enables us to utilize various kinds of solutions of the CYBE to classify integrable deformations. In particular, it is straightforward to realize partial deformations of the target space without loss of the integrability of the parent theory.