Higher Spin Conformal Currents in Minkowski Space

TL;DR

This work provides explicit, gauge-invariant higher-spin conformal currents in $4d$ Minkowski space by exploiting the unfolded, zero-curvature formulation for massless fields of all spins. Currents are bilinear in HS field strengths and are organized via a generalized stress tensor $T_{\alpha_1\ldots\alpha_n}(x)$, constructed as $T_{\alpha_1\ldots\alpha_n}(x) = \frac{\partial}{\partial y^{\alpha_1}} \cdots \frac{\partial}{\partial y^{\alpha_n}} (C^k(y|x) C^l(i y|x))|_{y=0}$, and conserved through the unfolded equations, yielding charges $Q(\eta) = \int_{\Sigma^3} \Omega^3(\eta)$. The framework reveals a rich $sp(8)$-symmetric structure encompassing the conformal algebra $su(2,2)$ and allows explicit examples for spins $0$, $1/2$, $1$, and $2$, including the Bel-Robinson-type currents for the Weyl tensor. While the construction produces an infinite set of HS currents, it is not exhaustive of all symmetry generators, and the authors discuss potential extensions via HS pseudotensors and links to higher-dimensional formulations. The results advance explicit handling of HS conformal charges and highlight the interplay between unfolded dynamics and conformal HS symmetries in Minkowski space.

Abstract

Using unfolded formulation of free equations for massless fields of all spins we obtain explicit form of higher-spin conformal conserved charges bilinear in 4d massless fields of arbitrary spins.