Yang-Baxter deformations, AdS/CFT, and twist-noncommutative gauge theory

Abstract

We give an AdS/CFT interpretation to homogeneous Yang-Baxter deformations of the AdS_5 x S^5 superstring as noncommutative deformations of the dual gauge theory, going well beyond the canonical noncommutative case. These homogeneous Yang-Baxter deformations can be of so-called abelian or jordanian type. While abelian deformations have a clear interpretation in string theory and many already had well understood gauge theory duals, jordanian deformations appear novel on both counts. We discuss the symmetry structure of the deformed string from the uniformizing perspective of Drinfeld twists and indicate that this structure can be realized on the gauge theory side by considering theories on various noncommutative spaces. We then conjecture that these are the gauge theory duals of our strings, modulo subtleties involving singularities. We support this conjecture by a brane construction for two jordanian examples, corresponding to noncommutative spaces with [x^-,x^i] ~ x^i (i=1,2). We also discuss kappa-Minkowski type deformations of AdS_5 x S^5, one of which may be the gravity dual of gauge theory on spacelike kappa-Minkowski space.

v5, published version up to formatting, 32 pages

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Cited by in corpus (93)

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• Homogeneous Yang-Baxter deformations as non-abelian duals of the AdS_5 sigma-model
• Almost abelian twists and AdS/CFT
• Integrable Deformations of Sigma Models
• Non-abelian T-duality and Yang-Baxter deformations of Green-Schwarz strings
• Poisson-Lie T-duals of the bi-Yang-Baxter models
• Generalized gravity from modified DFT
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• Homogeneous Yang-Baxter deformations as generalized diffeomorphisms
• Generalised fluxes, Yang-Baxter deformations and the O(d,d) structure of non-abelian T-duality
• $T$-folds from Yang-Baxter deformations
• Poisson-Lie U-duality in Exceptional Field Theory
• Conformal Twists, Yang-Baxter $\sigma$-models & Holographic Noncommutativity
• Yang-Baxter Deformations Beyond Coset Spaces (a slick way to do TsT)
• Integrability in dipole-deformed N=4 super Yang-Mills
• On jordanian deformations of AdS_5 and supergravity
• Integrable S matrix, mirror TBA and spectrum for the stringy ${\text{AdS}}_3\times {\text{S}}^3\times {\text{S}}^3\times {\text{S}}^1$ WZW model
• Local $\beta$-deformations and Yang-Baxter sigma model
• Generalized type IIB supergravity equations and non-Abelian classical r-matrices
• $I$ in generalized supergravity
• Combining the bi-Yang-Baxter deformation, the Wess-Zumino term and TsT transformations in one integrable sigma-model
• On the Hamiltonian integrability of the bi-Yang-Baxter sigma-model
• Quantum Spectral Curve for the eta-deformed AdS_5xS^5 superstring
• Superintegrability of Geodesic Motion on the Sausage Model
• General phase spaces: from discrete variables to rotor and continuum limits
• Non-split and split deformations of AdS_5
• Deformations of the Almheiri-Polchinski model
• Marginal deformations of WZW models and the classical Yang-Baxter equation
• Unimodular jordanian deformations of integrable superstrings
• Marginal and non-commutative deformations via non-abelian T-duality
• Non-abelian tri-vector deformations in d=11 supergravity
• Quantum deformations of D=4 Euclidean, Lorentz, Kleinian and quaternionic o^*(4) symmetries in unified o(4;C) setting
• Yang-Baxter Deformation as an O(d,d) Transformation
• Spinning strings in the $\eta$-deformed Neumann-Rosochatius system
• Remarks on simple interpolation between Jordanian twists
• Yang-Baxter invariance of the Nappi-Witten model
• Braided Symmetries in Noncommutative Field Theory
• Supercoset construction of Yang-Baxter deformed AdS${}_5\times$S${}^5$ backgrounds
• Homogeneous Yang-Baxter deformations as undeformed yet twisted models
• Semiclassical spectrum for BMN string in $Sc{h}_5\times S^5$
• Yang-Baxter deformations and generalized supergravity -- A short summary
• Embedding the modified CYBE in Supergravity
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• Quantum Anisotropic Sigma and Lambda Models as Spin Chains
• Towards the gravity/CYBE correspondence beyond integrability -- Yang-Baxter deformations of $T^{1,1}$
• Exploring The Lambda Model Of The Hybrid Superstring
• Yang-Baxter sigma models and Lax pairs arising from $\kappa$-Poincaré $r$-matrices
• Giant magnons and spiky strings in the Schrodinger/dipole-deformed CFT correspondence
• On quantum deformations of $Ad{S}_3\times S^3\times T^4$ and mirror duality
• Yang-Baxter Deformations of the $Ad{S}_5\times S^5$ Pure Spinor Superstring
• Probing analytical and numerical integrability: The curious case of $(Ad{S}_5\times S^5{)}_{\eta }$
• Yang-Baxter deformations of $W_{2,4}\times T^{1,1}$ and the associated T-dual models
• All Jordanian deformations of the $Ad{S}_5\times S^5$ superstring
• Generalized 11D supergravity equations from tri-vector deformations
• Deformed WZW Models and Hodge Theory -- Part I
• Yang-Baxter deformations of the $Ad{S}_4\times {\mathbb{CP}}^3$ superstring sigma model
• Killing spinors from classical r-matrices
• Interpolations between Jordanian Twists Induced by Coboundary Twists
• The twisted story of worldsheet scattering in $\eta$-deformed $Ad{S}_5\times S^5$
• Giant magnon-like solution in Sch_5 x S^5
• String theory on the Schrodinger pp-wave background
• Untwisting the symmetries of $\beta$-deformed Super-Yang--Mills
• Lax pairs for new ${\mathbb{Z}}_N$-symmetric coset $\sigma$-models and their Yang-Baxter deformations
• SUSY and the bi-vector
• Marginal deformations and quasi-Hopf algebras
• Generalized quark-antiquark potentials from a $q$-deformed AdS${}_5\times$S${}^5$ background
• Integrable Hopf twists, marginal deformations and generalised geometry
• Basic quantizations of $D=4$ Euclidean, Lorentz, Kleinian and quaternionic ${\mathfrak{o}}^{\star }(4)$ symmetries
• Yang-Baxter Deformations of the $Ad{S}_5\times T^{1,1}$ Superstring and their Backgrounds
• String Backgrounds of the Yang-Baxter Deformed $Ad{S}_4\times {\mathbb{CP}}^3$ Superstring
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• Tri-vector deformations with external fluxes
• SUSY and tri-vector deformations
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• T-duality to Scattering Amplitude and Wilson Loop in Non-commutative Super Yang-Mills Theory
• Brane bound states, deformations and OM