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

Understand

We consider a family of deformations of T^{1,1} in the Yang-Baxter sigma model approach.

• We first discuss a supercoset description of T^{1,1}, which makes manifest the full symmetry of the space and leads to the standard Sasaki-Einstein metric.
• Next, we consider three-parameter deformations of T^{1,1} by using classical r-matrices satisfying the classical Yang-Baxter equation (CYBE).
• The resulting metric and NS-NS two-form agree exactly with the ones obtained via TsT transformations, and contain the Lunin-Maldacena background as a special case.