Twistor methods for AdS5

Abstract

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 fourdimensional 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 bulkto-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.

Supertwistor formulation for massless superparticle in AdS5 × S5 superspace

“…In this case only four bosonic constraints associated with the su(2) ⊕ u(1) gauge symmetry are imposed on the superparticle's wave function that we chose to depend on one c-type supertwistor and one dual c-type supertwistor. This breaks manifest SU(2) symmetry but makes contact with the ambitwistor description of the massless fields on AdS 5 space-time [33], [70]. The constraints imply that the wave function is homogeneous of degree zero in its arguments and can be expanded in the supertwistor odd components.…”

“…[68] and more recent 7 See, however, Ref. [33], where, based on the realization of AdS 5 space as a projective manifold, the Penrose transform for the case of spin 0 and 1/2 fields was considered. 8 Hereinafter the same notation introduced above for the bulk ambitwistors is used for the boundary ones.…”

“…Since SU(2, 2) is not only the covering of the conformal group of 4-dimensional Minkowski space-time but also is the isometry group of 5-dimensional anti-de Sitter space and SU(2, 2|4) is the superisometry of the AdS 5 ×S 5 superspace as well as the N = 4 extended superconformal symmetry of the N = 4 supersymmetric Yang-Mills theory in the D = 4 boundary superspace that provides the crucial symmetry argument in support of the AdS 5 /CF T 4 duality, it is natural to seek for relevant (super)twistors. Because AdS 5 space-time is conformally flat, the incidence relations for Penrose twistors (actually ambitwistors) admit natural extension to accommodate extra bosonic coordinate(s) [32], [33] (see also [34]). It is also quite natural to add odd coordinates for D = 4 N-extended Poincare supersymmetry [35], [36].…”

Lectures on twistor theory

“…For instance, a point in M C corresponds to a CP 3 inside of twistor space. Similar constructions hold for Minkowski spaces of increasingly higher even dimension [67], and these also induce natural twistor spaces on odddimensional anti-de Sitter space [68,69]. The general structure is always that of a projective quadric, thanks to the nature of the pure spinor constraints which arise.…”

Multitwistor mechanics of massless superparticle on AdS5 × S5 superbackground

“…Thus it is natural to wonder whether AdS 5 × S 5 superstring also admits a formulation in terms of supertwistors, what are these supertwistors and what implications such a formulation might have on the study of the AdS 5 /CF T 4 correspondence. In the bosonic limit some of these issues were addressed recently in [12]. 2 In particular, there was given the definition of twistors for AdS 5 space based on its realization as a projective manifold.…”