Off-shell construction of some trilinear higher spin gauge field interactions

Several trilinear interactions of higher spin fields involving two equal (s=s1=s2) and one higher even (s3⩾2s) spin are presented. Interactions are constructed on the Lagrangian level using Noether's procedure together with the corresponding next to free level fields of the gauge transformations. In certain cases when the number of derivatives in the transformation is 2s−1 the interactions lead to the currents constructed from the generalization of the gravitational Bell-Robinson tensors. In other cases when the number of derivatives in the transformation is more than 2s−1 we obtain the finite tower of interactions with smaller even spins less than s3 in full agreement with our previous results for the interaction of the higher even spins field with a conformal scalar [R. Manvelyan, K. Mkrtchyan, Conformal invariant interaction of a scalar field with the higher spin field in AdSD, arXiv:0903.0058 [hep-th]; R. Manvelyan, W. Rühl, Conformal coupling of higher spin gauge fields to a scalar field in AdS4 and generalized Weyl invariance, Phys. Lett. B 593 (2004) 253 arXiv:hep-th/0403241].