Twistor methods for AdS$_5$

TL;DR

This paper applies twistor theory to five-dimensional anti-de Sitter space, establishing a correspondence with boundary conformal structures and deriving bulk field representations and propagators via twistor methods.

Contribution

It introduces a twistor-based framework for AdS$_5$, including explicit bulk-to-boundary propagators and twistor action functionals for free fields, connecting bulk and boundary data.

Findings

Constructed explicit bulk-to-boundary propagators for scalars and spinors.

Derived twistor action functionals that reproduce two-point functions.

Established the geometric correspondence between AdS$_5$ twistor space and boundary conformal structures.

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.