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.
Highlights
Bulk-to-boundary propagators for spinor fields with scaling dimension ∆ are given in twistor space by modifying those used for the scalar
In this paper we have investigated the twistor space of AdS5
It is worth noting that the bulk-to-boundary representatives and free twistor actions presented here can be adapted to AdS3 using the language of ‘minitwistors’ [40,41,42]
Summary
The geometry of anti-de Sitter space (or hyperbolic space) is an old and well-studied topic. For the purposes of describing twistor theory in the context of five-dimensional AdS, a particular description of hyperbolic geometry in terms of an open subset of projective space will prove useful. While this description is standard, it is not often utilized in the physics literature so we being with a brief review of AdS5 geometry from a projective point of view. The twistor space of AdS5 and various aspects of its geometry are discussed
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