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Limiting Shifted Homotopy in Higher-Spin Theory and Spin-Locality | | V.E. Didenko
; O.A. Gelfond
; A.V. Korybut
; M.A. Vasiliev
; | | Date: |
11 Sep 2019 | | Abstract: | Higher-spin vertices containing up to quintic interactions at the Lagrangian
level are explicitly calculated in the one-form sector of the non-linear
unfolded higher-spin equations using a $eta o-infty$--shifted contracting
homotopy introduced in the paper. The problem is solved in a background
independent way and for any value of the complex parameter $eta$ in the HS
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 $eta^2$ and $ar eta^2$ 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 $ar y$.
Also the $eta^2$ and $ar eta^2$ vertices are shown to vanish on any purely
gravitational background hence not contributing to the higher-spin current
interactions on $AdS_4$. This implies in particular that the gravitational
constant in front of the stress tensor is positive being proportional to
$etaar eta$. It is shown that the $eta$-shifted homotopy technique
developed in this paper can be reinterpreted as the conventional one but in the
$eta$-dependent deformed star product. | | Source: | arXiv, 1909.4876 | | Services: | Forum | Review | PDF | Favorites | |
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