Journal of High Energy Physics

, 2019:86 | Cite as

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

  • V.E. DidenkoEmail author
  • O.A. Gelfond
  • A.V. Korybut
  • M.A. Vasiliev
Open Access
Regular Article - Theoretical Physics


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.


Higher Spin Gravity Higher Spin Symmetry Gauge-gravity correspondence 


Open Access

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Copyright information

© The Author(s) 2019

Authors and Affiliations

  • V.E. Didenko
    • 1
    Email author
  • O.A. Gelfond
    • 1
    • 2
  • A.V. Korybut
    • 1
  • M.A. Vasiliev
    • 1
  1. 1.TK Tamm Department of Theoretical PhysicsLebedev Physical InstituteMoscowRussia
  2. 2.Federal State Institution “Scientific Research Institute for System Analysis of the Russian Academy of Science”MoscowRussia

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