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We consider a family of deformations of T^{1,1} in the Yang-Baxter sigmamodel approach. We first discuss a supercoset description of T^{1,1}, whichmakes manifest the full symmetry of the space and leads to the standardSasaki-Einstein metric. Next, we consider three-parameter deformations ofT^{1,1} by using classical r-matrices satisfying the classical Yang-Baxterequation (CYBE). The resulting metric and NS-NS two-form agree exactly with theones obtained via TsT transformations, and contain the Lunin-Maldacenabackground as a special case. It is worth noting that for AdS_5 x T^{1,1},classical integrability for the full sector has been argued to be lost. Henceour result indicates that the Yang-Baxter sigma model approach is applicableeven for non-integrable cosets. This observation suggests that the gravity/CYBEcorrespondence can be extended beyond integrable cases.

Deformations of $T^{1,1}$ as Yang-Baxter sigma models