Unfolded Equations for Current Interactions of 4d Massless Fields as a Free System in Mixed Dimensions

TL;DR

The paper develops an unfolded, linear framework in which current interactions of 4d massless fields of all spins arise from a gluing of rank-one (massless) and rank-two (current) systems in a higher-dimensional, matrix-extended space ${\cal M}_M$, with the rank-two sector dual to a rank-one field in ${\cal M}_{8}$ corresponding to 6d conformal fields. Through this construction, currents built from bilinears of 4d fields source the dynamical equations, yielding Yukawa couplings for spins 0 and 1/2, Maxwell and Einstein equations with external currents, and HS current corrections to Fronsdal and Fang–Fronsdal equations for higher spins, all within AdS$_4$ and its flat limit. The approach leverages the unfolded dynamics, $\,\sigma_-$ cohomology, and the Howe dual algebra structure to classify current parameters and ensure consistency across zero- and one-form sectors. The results illuminate a novel interpretation of HS interactions as linear realizations tied to higher-dimensional conformal data, offering a path toward deeper understanding of dimensional dualities in AdS/CFT and the nature of space-time in HS theories.

Abstract

Interactions of massless fields of all spins in four dimensions with currents of any spin is shown to result from a solution of the linear problem that describes a gluing between rank-one (massless) system and rank-two (current) system in the unfolded dynamics approach. Since the rank-two system is dual to a free rank-one higher-dimensional system, that effectively describes conformal fields in six space-time dimensions, the constructed system can be interpreted as describing a mixture between linear conformal fields in four and six dimensions. Interpretation of the obtained results in spirit of AdS/CFT correspondence is discussed.