Conformal Twists, Yang-Baxter $\sigma$-models & Holographic Noncommutativity

Abstract

Expanding upon earlier results [arXiv:1702.02861], we present a compendium of $\sigma$-models associated with integrable deformations of AdS${}_5$ generated by solutions to homogenous classical Yang-Baxter equation. Each example we study from four viewpoints: conformal (Drinfeld) twists, closed string gravity backgrounds, open string parameters and proposed dual noncommutative (NC) gauge theory. Irrespective of whether the deformed background is a solution to supergravity or generalized supergravity, we show that the open string metric associated with each gravity background is undeformed AdS${}_5$ with constant open string coupling and the NC structure $\Theta$ is directly related to the conformal twist. One novel feature is that $\Theta$ exhibits "holographic noncommutativity": while it may exhibit non-trivial dependence on the holographic direction, its value everywhere in the bulk is uniquely determined by its value at the boundary, thus facilitating introduction of a dual NC gauge theory. We show that the divergence of the NC structure $\Theta$ is directly related to the unimodularity of the twist. We discuss the implementation of an outer automorphism of the conformal algebra as a coordinate transformation in the AdS bulk and discuss its implications for Yang-Baxter $\sigma$-models and self-T-duality based on fermionic T-duality. Finally, we comment on implications of our results for the integrability of associated open strings and planar integrability of dual NC gauge theories.

51 pages, 1 figure, LaTeX; v2 54 pages, presentation improved, references added; v3 appendix added to show that the relation between r-matrix and NC structure extends to modified CYBE; v4 published version

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• Yang-Baxter Deformation as an O(d,d) Transformation
• Non-Abelian T-duality as a Transformation in Double Field Theory
• Homogeneous Yang-Baxter deformations as undeformed yet twisted models
• $O(d,d)$ transformations preserve classical integrability
• Poisson-Lie plurals of Bianchi cosmologies and Generalized Supergravity Equations
• Probing analytical and numerical integrability: The curious case of $(Ad{S}_5\times S^5{)}_{\eta }$
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• Tri-vector deformations on compact isometries
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• Three-parameter deformation of $\mathbb{R}\times S^3$ in the Landau-Lifshitz limit
• Lax pairs for new ${\mathbb{Z}}_N$-symmetric coset $\sigma$-models and their Yang-Baxter deformations
• Marginal deformations and quasi-Hopf algebras
• String Backgrounds of the Yang-Baxter Deformed $Ad{S}_4\times {\mathbb{CP}}^3$ Superstring
• Integrability structures in string theory
• Yang-Baxter Deformations of the $Ad{S}_5\times T^{1,1}$ Superstring and their Backgrounds
• $T\bar{T}$ deformations and the pp wave correspondence
• Investigating (Non)-Integrability and Pulsating String in D3-Brane Background
• Generalized Supergravity Equations for the WZW Model
• Non-isometric U-dualities
• More on (gauged) WZW models over low-dimensional Lie supergroups and their integrable deformations
• T-duality to Scattering Amplitude and Wilson Loop in Non-commutative Super Yang-Mills Theory
• Integrable deformed H${}_{{}_4}$ WZW models and their non-Abelian duals as solutions of generalized supergravity equations
• Nonlocal charges from marginal deformations of 2D CFTs: Holographic $T\bar{T}$, $T\bar{J}$ and Yang-Baxter deformations
• Finite Size Effect from Classical Strings in deformed AdS${}_3\times$ S${}^3$
• From ${\mathrm{AdS}}_5$ to ${\mathrm{AdS}}_3$: TsT deformations, Magnetic fields and Holographic RG Flows
• Brane bound states, deformations and OM
• Holographic Subregion Complexity and Fidelity Susceptibility in Noncommutative Yang--Mills Theory