Ambitwistors, oscillators and massless fields on $AdS_5$

TL;DR

This paper explores the relationship between ambitwistor space, oscillator constructions, and massless fields in $AdS_5$, providing a framework to reconstruct these fields and discussing potential applications in theoretical physics.

Contribution

It introduces a novel approach linking ambitwistor space with massless fields on $AdS_5$ using oscillator methods and Penrose transform techniques.

Findings

Established correspondence between massless representations and ambitwistor functions

Demonstrated reconstruction of $AdS_5$ massless fields from ambitwistor data

Discussed applications in gauge field theory and holography

Abstract

Positive energy unitary irreducible representations of $SU(2,2)$ can be constructed with the aid of bosonic oscillators in (anti)fundamental representation of $SU(2)_L\times SU(2)_R$ that are closely related to Penrose twistors. Starting with the correspondence between the doubleton representations, homogeneous functions on projective twistor space and on-shell $SL(2,\mathbb C)$ generalized Weyl curvature 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.