Dynamics of Higher Spin Fields and Tensorial Space

TL;DR

This work shows that massless conformal higher-spin fields in $D=3,4,6,10$ emerge as the quantum spectrum of a twistor-like particle propagating in tensorial spaces with $n=2(D-2)$. The fields organize into $OSp(1|2n)$-invariant multiplets and satisfy geometric, self-dual curvature equations that generalize Bargmann–Wigner, Labastida, and Damour–Deser structures; compensator and unfolded-formulations connect local and non-local higher-spin equations. Key new results include detailed spectra and geometric equations in $D=6$ and $D=10$, along with a clear unfolded/dynamical bridge between scalar/spinor tensorial-space equations and spacetime higher-spin curvatures. The findings provide a unified tensorial-space foundation for conformal higher-spin fields and point toward AdS generalizations and the challenges of integrating interactions within this framework.

Abstract

The structure and the dynamics of massless higher spin fields in various dimensions are reviewed with an emphasis on conformally invariant higher spin fields. We show that in D=3,4,6 and 10 dimensional space-time the conformal higher spin fields constitute the quantum spectrum of a twistor-like particle propagating in tensorial spaces of corresponding dimensions. We give a detailed analysis of the field equations of the model and establish their relation with known formulations of free higher spin field theory.