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 T1,1, instead of the standard deformations of the 5-sphere S5. For this purpose, we first describe a novel construction of T1,1 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 T1,1 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.
Highlights
Introduction and main resultsTen-dimensional supergravity describes the low energy dynamics of string theory and has a rich mathematical structure
[13], are integrable deformations of the principal chiral model based on an r-matrix satisfying the modified classical Yang-Baxter equation
Our result indicates that the Yang-Baxter sigma models based on the CYBE can be applied beyond non-integrable cosets and the gravity/CYBE correspondence seems to extend to a wider class of supergravity backgrounds than one may have expected
Summary
Introduction and main resultsTen-dimensional supergravity describes the low energy dynamics of string theory and has a rich mathematical structure. [13], are integrable deformations of the principal chiral model based on an r-matrix satisfying the modified classical Yang-Baxter equation (mCYBE in short).2 These were extended to sigma models defined on bosonic symmetric cosets [15], and applied to study an integrable deformation of the AdS5 ×S5 superstring [16] in [17, 18]. Our result indicates that the Yang-Baxter sigma models based on the CYBE can be applied beyond non-integrable cosets and the gravity/CYBE correspondence seems to extend to a wider class of supergravity backgrounds than one may have expected.
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