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arXiv · 1406.2249

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

P. Marcos Crichigno·Takuya Matsumoto·Kentaroh Yoshida
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Abstract

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. It is worth noting that for AdS_5 x T^{1,1}, classical integrability for the full sector has been argued to be lost. Hence our result indicates that the Yang-Baxter sigma model approach is applicable even for non-integrable cosets. This observation suggests that the gravity/CYBE correspondence can be extended beyond integrable cases.

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P. Marcos Crichigno, Takuya Matsumoto, Kentaroh Yoshida. 2014-06-09. Deformations of $T^{1,1}$ as Yang-Baxter sigma models. https://arxiv.org/abs/1406.2249

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