Embedding the modified CYBE in Supergravity

Abstract

It has recently been demonstrated that the Classical Yang-Baxter Equation (CYBE) emerges from supergravity via the open-closed string map. Thus, given any solution with an isometry group, there exists a deformed solution based on an $r$-matrix solution to the homogeneous CYBE. In this work, we argue that the CYBE emerges exclusively from the NS sector, while the RR sector acts largely as a spectator that supports the spacetimes. Moreover, shifting the dilaton by a constant, one can incorporate $r$-matrix solutions to the modified CYBE, but only for original geometries that are a direct-product of coset spaces. We illustrate our solution generating technique with deformations of $Ad{S}_3\times S^3\times M_4$, where $M_4=T^4$ (K3) and $S^3\times S^1$, and explicitly construct one and two-parameter (integrable) q-deformations that are solutions to generalised supergravity.

arXiv comment27 pages; v2 references updated, typos corrected; v3 matches published version

References in corpus (35)

• String Theory and Noncommutative Geometry
• Deforming field theories with $U(1)\times U(1)$ global symmetry and their gravity duals
• An integrable deformation of the AdS_5 x S^5 superstring action
• Yang-Baxter $\sigma$-models and dS/AdS T-duality
• Derivation of the action and symmetries of the q-deformed AdS_5 x S^5 superstring
• Scale invariance of the eta-deformed AdS5 x S5 superstring, T-duality and modified type II equations
• Jordanian deformations of the AdS_5xS^5 superstring
• T-Duality, Space-time Spinors and R-R Fields in Curved Backgrounds
• On deformations of AdS_n x S^n supercosets
• Target space supergeometry of $\eta$ and $\lambda$-deformed strings
• Yang-Baxter deformations, AdS/CFT, and twist-noncommutative gauge theory
• Lunin-Maldacena backgrounds from the classical Yang-Baxter equation -- Towards the gravity/CYBE correspondence
• Spacetimes for λ-deformations
• Chaos Rules out Integrability of Strings in AdS_5 x T^{1,1}
• Integrable deformations of T-dual $\sigma$ models
• Towards a two-parameter q-deformation of AdS_3 x S^3 x M^4 superstrings
• Integrability of classical strings dual for noncommutative gauge theories
• Yang-Baxter $\sigma$-models, conformal twists, and noncommutative Yang-Mills theory
• Supersymmetry and non-Abelian T-duality in type II supergravity
• Supergravity backgrounds for deformations of AdS_n x S^n supercoset string models
• A Jordanian deformation of AdS space in type IIB supergravity
• Homogeneous Yang-Baxter deformations as non-abelian duals of the AdS_5 sigma-model
• Almost abelian twists and AdS/CFT
• Remarks on Non-Abelian Duality
• On non-abelian T-duality and deformations of supercoset string sigma-models
• Homogeneous Yang-Baxter deformations as generalized diffeomorphisms
• $T$-folds from Yang-Baxter deformations
• Quantum deformations of the flat space superstring
• On jordanian deformations of AdS_5 and supergravity
• Generalized type IIB supergravity equations and non-Abelian classical r-matrices
• $I$ in generalized supergravity
• Trivial solutions of generalized supergravity vs non-abelian T-duality anomaly
• Non-split and split deformations of AdS_5
• Marginal and non-commutative deformations via non-abelian T-duality
• Unified description for kappa-deformations of orthogonal groups

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• Doubled aspects of generalised dualities and integrable deformations
• Holographic integration of $T\bar{T}$ and $J\bar{T}$ via $O(d,d)$
• Supergravity backgrounds of the eta-deformed AdS2 x S2 x T6 and AdS5 x S5 superstrings
• Tri-vector deformations in $d=11$ supergravity
• Two-parameter integrable deformations of the $Ad{S}_3\times S^3\times T^4$ superstring
• Classical Yang-Baxter equation from beta-supergravity
• Three-parameter integrable deformation of Z_4 permutation supercosets
• Yang-Baxter Deformation as an O(d,d) Transformation
• Yang-Baxter deformations and generalized supergravity -- A short summary
• Resurgence in the Bi-Yang-Baxter Model
• Yang-Baxter Deformations of the $Ad{S}_5\times S^5$ Pure Spinor Superstring
• Spin chains and classical strings in two parameters $q$-deformed AdS${}_3\times$S${}^3$
• Double Yang-Baxter deformation of spinning strings
• Nonlocal charges from marginal deformations of 2D CFTs: Holographic $T\bar{T}$, $T\bar{J}$ and Yang-Baxter deformations