Restrictions for \(n\)-point vertices in higher-spin theories

DOI10.1007/JHEP06(2020)118zbMATH Open1437.83092arXiv1912.13476OpenAlexW3106283798MaRDI QIDQ783932

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Publication date: 4 August 2020

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Abstract: We give a simple classification of the independent $n$-point interaction vertices for bosonic higher-spin gauge fields in $d$-dimensional Minkowski space-times. We first give a characterisation of such vertices for large dimensions, $dgeq2n-1$, where one does not have to consider Schouten identities due to over-antisymmetrisation of space-time indices. When the dimension is lowered, such identities have to be considered, but their appearance only leads to equivalences of large-$d$ vertices and does not lead to new types of vertices. We consider the case of low dimensions, $d<n$, in detail, where the large number of Schouten identities leads to strong restrictions on independent vertices. We also comment on the generalisation of our results to the intermediate case $nleqdleq2n-2$. In all cases, the independent vertices are expressed in terms of elementary manifestly gauge-invariant quantities, suggesting that no deformations of the gauge transformations are induced.

Full work available at URL: https://arxiv.org/abs/1912.13476

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