Limiting shifted homotopy in higher-spin theory and spin-locality

Abstract

Higher-spin vertices containing up to quintic interactions at the LagTangian level are explicitly calculated in the one-form sector of the non-linear unfolded higher-spin equations using a 𝛽 →-∞-shifted contracting homotopy introduced in the paper. The problem is solved in a background independent way and for any value of the complex parameter 𝜂 in the higher-spin equations. All obtained vertices are shown to be spin-local containing a finite number of derivatives in the spinor space for any given set of spins. The vertices proportional to 𝜂2 and \( {\overline{\eta}}^2 \) are in addition ultra-local, i.e., zero-forms that enter into the vertex in question are free from the dependence on at least one of the spinor variables y or \( \overline{y} \). Also the 𝜂2 and \( {\overline{\eta}}^2 \) vertices are shown to vanish on any purely gravitational background hence not contributing to the higher-spin current interactions on AdS4. This implies in particular that the gravitational constant in front of the stress tensor is positive being proportional to \( \eta \overline{\eta} \). It is shown that the 𝛽-shifted homotopy technique developed in this paper can be reinterpreted as the conventional one but in the 𝛽-dependent deformed star product.

A preprint version of the article is available at ArXiv.

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Didenko, V., Gelfond, O., Korybut, A. et al. Limiting shifted homotopy in higher-spin theory and spin-locality. J. High Energ. Phys. 2019, 86 (2019). https://doi.org/10.1007/JHEP12(2019)086

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Keywords

  • Higher Spin Gravity
  • Higher Spin Symmetry
  • Gauge-gravity correspondence