Geodesic
Gauge-noninvariant higher-spin currents in four-dimensional Minkowski space
Teoretičeskaâ i matematičeskaâ fizika, Tome 181 (2014) no. 3, pp. 449-463

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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.
Keywords: higher-spin theory, conservation law. 
@article{TMF_2014_181_3_a2,
     author = {M. A. Vasiliev and P. A. Smirnov},
     title = {Gauge-noninvariant higher-spin currents in four-dimensional {Minkowski} space},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {449--463},
     publisher = {mathdoc},
     volume = {181},
     number = {3},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2014_181_3_a2/}
}
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M. A. Vasiliev; P. A. Smirnov. Gauge-noninvariant higher-spin currents in four-dimensional Minkowski space. Teoretičeskaâ i matematičeskaâ fizika, Tome 181 (2014) no. 3, pp. 449-463. http://geodesic.mathdoc.fr/item/TMF_2014_181_3_a2/