Restrictions for n-point vertices in higher-spin theories

Abstract

We give a simple classification of the independent n-point interaction vertices for bosonic higher-spin gauge fields in d-dimensional Minkowski spacetimes. We first give a characterisation of such vertices for large dimensions, d ≥ 2n − 1, where one does not have to consider Schouten identities due to over-antisymmetrisation of spacetime 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 a large number of Schouten identities leads to strong restrictions on independent vertices. We also comment on the generalisation of our results to the intermediate region n ≤ d ≤ 2n − 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.

A preprint version of the article is available at ArXiv.

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Fredenhagen, S., Krüger, O. & Mkrtchyan, K. Restrictions for n-point vertices in higher-spin theories. J. High Energ. Phys. 2020, 118 (2020). https://doi.org/10.1007/JHEP06(2020)118

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Keywords

  • Higher Spin Gravity
  • Scattering Amplitudes
  • Higher Spin Symmetry
  • Space- Time Symmetries