Spinor description of $D=5$ massless low-spin gauge fields

TL;DR

This paper develops a spinor-based framework for describing massless low-spin gauge fields in five dimensions, including their equations, solutions, and supersymmetric extensions, using Lorentz harmonic variables and superparticle models.

Contribution

It introduces a novel spinor description for $D=5$ massless gauge fields, extending to higher spins and incorporating harmonic superspace techniques.

Findings

Derived first-order Dirac-like equations for massless fields

Constructed solutions using Lorentz harmonic integrals over $S^3$

Proposed a superparticle model capturing the spectrum of massless supermultiplets

Abstract

Spinor description for the curvatures of $D=5$ Yang-Mills, Rarita-Schwinger and gravitational fields is elaborated. Restrictions imposed on the curvature spinors by the dynamical equations and Bianchi identities are analyzed. In the absence of sources symmetric curvature spinors with $2s$ indices obey first-order equations that in the linearized limit reduce to Dirac-type equations for massless free fields. These equations allow for a higher-spin generalization similarly to $4d$ case. Their solution in the form of the integral over Lorentz-harmonic variables parametrizing coset manifold $SO(1,4)/(SO(1,1)\times ISO(3))$ isomorphic to the three-sphere is considered. Superparticle model that contains such Lorentz harmonics as dynamical variables, as well as harmonics parametrizing the two-sphere $SU(2)/U(1)$ is proposed. The states in its spectrum are given by the functions on $S^3$ that upon integrating over the Lorentz harmonics reproduce on-shell symmetric curvature spinors for various massless supermultiplets of $D=5$ space-time supersymmetry.