Abstract
We find the conserved currents of any spin t > 0 constructed from massless gauge fields of any integer spin s ≥ 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.
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Vasiliev, M.A., Smirnov, P.A. Gauge-noninvariant higher-spin currents in four-dimensional Minkowski space. Theor Math Phys 181, 1509–1521 (2014). https://doi.org/10.1007/s11232-014-0231-5
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DOI: https://doi.org/10.1007/s11232-014-0231-5