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Yang-Baxter sigma models based on the CYBE. (English) Zbl 1348.81379
Summary: 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.

81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
81T60 Supersymmetric field theories in quantum mechanics
16T25 Yang-Baxter equations
81R12 Groups and algebras in quantum theory and relations with integrable systems
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