Yang-Baxter deformations and string dualities

TL;DR

This paper explores integrable deformations of the AdS5×S5 superstring using Yang-Baxter sigma models, identifying new string backgrounds related to classical r-matrices and their connections to supergravity solutions.

Contribution

It introduces a family of multi-parameter deformations of AdS5×S5 backgrounds via classical r-matrices, linking them to known solutions and duality transformations.

Findings

Derived new multi-parameter string backgrounds.

Connected deformed backgrounds to known solutions via dualities.

Proposed R-R sector construction via supercoset approach.

Abstract

We further study integrable deformations of the AdS$_5\times$S$^5$ superstring by following the Yang-Baxter sigma model approach with classical $r$-matrices satisfying the classical Yang-Baxter equation (CYBE). Deformed string backgrounds specified by $r$-matrices are considered as solutions of type IIB supergravity, and therefore the relation between gravitational solutions and $r$-matrices may be called the gravity/CYBE correspondence. In this paper, we present a family of string backgrounds associated with a classical $r$-matrices carrying two parameters and its three-parameter generalization. The two-parameter case leads to the metric and NS-NS two-form of a solution found by Hubeny-Rangamani-Ross [hep-th/0504034] and another solution in [arXiv:1402.6147]. For all of the backgrounds associated with the three-parameter case, the metric and NS-NS two-form are reproduced by performing TsT transformations and S-dualities for the undeformed AdS$_5\times$S$^5$ background. As a result, one can anticipate the R-R sector that should be reproduced via a supercoset construction.