Towards the gravity/CYBE correspondence beyond integrability -- Yang-Baxter deformations of $T^{1,1}$

Abstract

Yang-Baxter sigma models, proposed by Klimcik and Delduc-Magro-Vicedo, have been recognized as a powerful framework for studying integrable deformations of two-dimensional non-linear sigma models. In this short article, as an important generalization, we review a non-integrable sigma model in the Yang-Baxter sigma model approach based on [arXiv:1406.2249]. In particular, we discuss a family of deformations of the 5D Sasaki-Einstein manifold $T^{1,1}$, instead of the standard deformations of the $5$-sphere S${}^5$. For this purpose, we first describe a novel construction of $T^{1,1}$ as a supercoset, and provide a physical interpretation of this construction from viewpoint of the dual Klebanov-Witten field theory. Secondly, we consider a $3$-parameter deformation of $T^{1,1}$ by using classical $r$-matrices satisfying the classical Yang--Baxter equation (CYBE). The resulting metric and NS-NS two-form completely agree with the ones previously obtained via TsT (T-dual -- shift -- T-dual) transformations, and contain the Lunin-Maldacena background as a special case. Our result indicates that what we refer to as the gravity/CYBE(Classical Yang-Baxter Equation) correspondence can be extended beyond integrable cosets.

This article is a brief review of the original paper [arXiv:1406.2249] prepared for a proceeding of a talk given by T.M. at "The XXIIIth International Conference on Integrable Systems and Quantum symmetries (ISQS-23)" held in Prague, Czech Republic, from June 23 till June 27, 2015, v2: references added

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• The fate of chaotic strings in a confining geometry
• Yang-Baxter invariance of the Nappi-Witten model
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