On classical Yang-Baxter based deformations of the AdS_5 x S^5 superstring

TL;DR

This paper investigates the properties of classical Yang-Baxter deformations of the AdS_5 x S^5 superstring, clarifying their reality, integrability, and relation to TsT transformations, and exploring preserved symmetries and new deformation backgrounds.

Contribution

It provides a comprehensive analysis of real R matrices for Yang-Baxter deformations, clarifies their connection to TsT transformations, and introduces a generalized deformation with open questions.

Findings

Identified conditions for R matrices to be real and integrable.

Clarified when deformations correspond to TsT transformations.

Discovered a generalized deformation with potential string background implications.

Abstract

Interesting deformations of AdS_5 x S^5 such as the gravity dual of noncommutative SYM and Sch\"odinger spacetimes have recently been shown to be integrable. We clarify questions regarding the reality and integrability properties of the associated construction based on R matrices that solve the classical Yang-Baxter equation, and present an overview of manifestly real R matrices associated to the various deformations. We also discuss when these R matrices should correspond to TsT transformations, which not all do, and briefly analyze the symmetries preserved by these deformations, for example finding Schr\"odinger superalgebras that were previously obtained as subalgebras of psu(2,2|4). Our results contain a (singular) generalization of an apparently non-TsT deformation of AdS_5 x S^5, whose status as a string background is an interesting open question.