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arXiv · 1410.0575

Integrable deformations of the AdS$_5\times$S$^5$ superstring and the classical Yang-Baxter equation -- Towards the gravity/CYBE correspondence --

Takuya Matsumoto·Kentaroh Yoshida
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Abstract

Based on the formulation of Yang-Baxter sigma models developed by Klimcik and Delduc-Magro-Vicedo, we explain that various deformations of type IIB superstring on AdS$_5\times$S$^5$ can be characterized by classical $r$-matrices satisfying the classical Yang-Baxter equation (CYBE). The relation may be referred to as `the gravity/CYBE correspondence.' We present non-trivial examples of the correspondence including Lunin-Maldacena backgrounds for $\beta$-deformations of the ${\cal N} = 4$ super Yang-Mills theory and the gravity duals for non-commutative gauge theories. We also discuss non-integrable backgrounds such as AdS$_5\times T^{1,1}$ as a generalization.

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Takuya Matsumoto, Kentaroh Yoshida. 2014-10-02. Integrable deformations of the AdS$_5\times$S$^5$ superstring and the classical Yang-Baxter equation -- Towards the gravity/CYBE correspondence --. https://doi.org/10.1088/1742-6596/563/1/012020

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