Twistor methods for AdS${}_5$

Abstract

We consider the application of twistor theory to five-dimensional anti-de Sitter space. The twistor space of AdS${}_5$ is the same as the ambitwistor space of the four-dimensional conformal boundary; the geometry of this correspondence is reviewed for both the bulk and boundary. A Penrose transform allows us to describe free bulk fields, with or without mass, in terms of data on twistor space. Explicit representatives for the bulk-to-boundary propagators of scalars and spinors are constructed, along with twistor action functionals for the free theories. Evaluating these twistor actions on bulk-to-boundary propagators is shown to produce the correct two-point functions.

24 pages, 4 figures. v2: typos fixed, published version

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• The String Dual to Free $\mathcal{N}=4$ Super Yang-Mills
• The Worldsheet Dual of Free Super Yang-Mills in 4D
• Symmetries and Covering Maps for the Minimal Tension String on $\mathbf{Ad}{\mathbf{S}}_3\times {\mathbf{S}}^3\times {\mathbf{T}}^4$
• Supertwistor formulation for massless superparticle in $Ad{S}_5\times S^5$ superspace
• The holographic dual of the Penrose transform
• Twistor Coverings and Feynman Diagrams
• Ambitwistors, oscillators and massless fields on $Ad{S}_5$
• Embedding formalism for $\mathcal{N}$-extended AdS superspace in four dimensions
• Twistor description of spinning particles in AdS
• Multitwistor mechanics of massless superparticle on $Ad{S}_5\times S^5$ superbackground
• On polarized scattering equations for superamplitudes of 11D supergravity and ambitwistor superstring
• Twistor action for general relativity
• Oscillator approach to quantization of $Ad{S}_5\times S^5$ superparticle in twistor formulation
• Massless spinning particle and null-string on $Ad{S}_d$: projective-space approach
• String theory in twistor space and minimal tension holography