Using Noether's procedure we present a complete solution for the trilinear interactions of arbitrary spins s 1 , s 2 , s 3 in a flat background, and discuss the possibility to enlarge this construction to higher order interactions in the gauge field. Some classification theorems of the cubic (self)interaction with different numbers of derivatives and depending on relations between the spins are presented. Finally the expansion of a general spin s gauge transformation into powers of the field and the related closure of the gauge algebra in the general case are discussed.
We formulate off-shell N = 1 superconformal higher spin multiplets in four spacetime dimensions and briefly discuss their coupling to conformal supergravity. As an example, we explicitly work out the coupling of the superconformal gravitino multiplet to conformal supergravity. The corresponding action is super-Weyl invariant for arbitrary supergravity backgrounds. However, it is gauge invariant only if the supersymmetric Bach tensor vanishes. This is similar to linearised conformal supergravity in curved background.
We present an off-shell generating function for all cubic interactions of Higher Spin gauge fields constructed in [1]. It is a generalization of the on-shell generating function proposed in [2], is written in a very compact way, and turns out to have a remarkable structure.
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