Twistor formulation of massless $6D$ infinite spin fields

TL;DR

This paper develops a twistor-based framework for describing massless infinite spin fields in six dimensions, providing explicit equations of motion and a transform to space-time fields, advancing the understanding of higher-spin representations.

Contribution

It introduces a twistor formulation for 6D massless infinite spin fields, including equations of motion and a space-time transform, which was not previously established.

Findings

Massless infinite spin representations realized on two-twistor fields

Explicit equations of motion for two-twistor spin-tensors

Constructed a field twistor transform linking twistor and space-time formulations

Abstract

We construct massless infinite spin irreducible representations of the six-dimensional Poincar\'{e} group in the space of fields depending on twistor variables. It is shown that the massless infinite spin representation is realized on the two-twistor fields. We present a full set of equations of motion for two-twistor fields represented by the totally symmetric $\mathrm{SU}(2)$ rank $2s$ two-twistor spin-tensor and show that they carry massless infinite spin representations. A field twistor transform is constructed and infinite spin fields are found in the space-time formulation with an additional spinor coordinate.