Lunin-Maldacena backgrounds from the classical Yang-Baxter equation — towards the gravity/CYBE correspondence

By Takuya Matsumoto, Kentaroh Yoshida. 2014

142 citations recorded by the source corpus.

A bstractWe consider γ-deformations of the AdS5×S5 superstring as Yang-Baxter sigma models with classical r-matrices satisfying the classical Yang-Baxter equation (CYBE). An essential point is that the classical r-matrices are composed of Cartan generators only and then generate abelian twists. We present examples of the r-matrices that lead to real γ-deformations of the AdS5×S5 superstring. Finally we discuss a possible classification of integrable deformations and the corresponding gravity solution in terms of solutions of CYBE. This classification may be called the gravity/CYBE correspondence.

Subfields: Geometry and Topology, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/5a58c381fe3a65831b80e460b8aa44e6575e03d2

How researchers see this paper

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In Geometry and Topology

1. S. J. Tongeren
2. David Osten
3. B. Vicedo
4. Aritra Banerjee
5. K. Panigrahi
6. A. Tseytlin
7. B. Hoare

In Nuclear and High Energy Physics

1. David Osten
2. S. J. Tongeren
3. B. Vicedo
4. Aritra Banerjee
5. K. Panigrahi
6. C. Klimčík

In Statistical and Nonlinear Physics

1. David Osten
2. S. J. Tongeren
3. B. Vicedo
4. Aritra Banerjee
5. K. Panigrahi
6. C. Klimčík
7. B. Hoare
8. A. Tseytlin

Citations in the corpus

• Abelian Yang–Baxter deformations and TsT transformations (2016, background): “[44, 40, 41], but a general proof is still missing.”
• Deformed integrable σ-models, classical R-matrices and classical exchange algebra on Drinfel’d doubles (2015, background): “Such a phenomenon was first observed in the context of strings propagating on the TsT-transformed AdS5 × S 5 background [32, 33], which was later shown to belong to the class of Yang-Baxter type deformations [34].”
• On the rotating and oscillating strings in (AdS3 × S3)ϰ (2014, methodology): “Also in [9, 10] non-standard q-deformed model based on the classical r-matrix satisfying classical YangBaxter equations was explored.”
• Yang-Baxter deformations, AdS/CFT, and twist-noncommutative gauge theory (2015, background): “The abelian solutions mostly have nice interpretations in terms of string theory and AdS/CFT, including for example the Lunin-Maldacena background mentioned above [26], and the gravity dual of canonical noncommutative SYM [27], which is hence integrable.”