Gauge-noninvariant higher-spin currents in four-dimensional Minkowski space

We find the conserved currents of any spin $t>0$ constructed from massless gauge fields of any integer spin $s\ge t$ in four-dimensional Minkowski space. In particular, we construct the stress–energy tensor for a field of any higher spin. Analogously to the spin-two stress (pseudo)tensor, the currents we consider are not gauge invariant, but we show that they generate gauge-invariant charges. In addition to the expected even-parity higher-spin currents, we find unexpected odd-parity currents that generate fewer symmetries than the even currents. We argue that these odd currents most likely do not admit a consistent AdS deformation.