Ambitwistors, oscillators and massless fields on AdS5

Abstract

Positive energy unitary irreducible representations of SU (2, 2) can be constructed with the aid of bosonic oscillators in (anti)fundamental representation of SU (2) L × SU (2) R that are closely related to Penrose twistors. Starting with the correspondence between the doubleton representations, homogeneous functions on projective twistor space and on-shell generalized Weyl curvature SL(2, C) spinors and their low-spin counterparts, we study in the similar way the correspondence between the massless representations, homogeneous functions on ambitwistor space and, via the Penrose transform, with the gauge fields on Minkowski boundary of AdS 5 . The possibilities of reconstructing massless fields on AdS 5 and some applications are also discussed.

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.…”

“…Turning to the discussion of the correspondence between the fermionic fields of N = 4 conformal supergravity and odd components in the decomposition (3.18) we find that eight gravitini ψ αα (2) A (x) and ψ α(2)αA (x) are obtained via the Penrose transform of ψ (1,0) A (Z,W ) and ψ (0,1)A [70].…”

Cubic interaction vertices for continuous-spin fields and arbitrary spin massive fields

“…In the frameworks of world-line particle and twistor-like approaches, higher-spin fields are considered, e.g., in refs. [60] and [61][62][63][64]. Interesting approach for analysing interacting conformal higher-spin fields in curved background is discussed in ref.…”

Twistor description of spinning particles in AdS

“…In particular, for AdS 5 it should be possible to extend the N = 0 quantum results of [27] to N = 1. It should also be possible to make contact with the work of Adamo et al on a twistor formulation of free field equations in AdS 5 [48], as well as other related work [49] and perhaps other approaches to particle mechanics in AdS backgrounds [50].…”