Abstract
In this overview, the framelike formulation of the dynamics of massless gauge fields of arbitrary spin propagating in Minkowski and (anti-)de Sitter spaces of an arbitrary dimension is discussed. In the framework of the framelike description, the notions of the higher spin field, gauge symmetries and gauge-invariant field strengths are introduced. The general procedure of construction of explicit gauge-invariant action functionals for free higher spin fields is discussed, and some substantial examples of action for fields of particular spins are given. The proposed framelike formulation is an efficient tool for the construction of interaction of higher spin fields on the background of anti-de Sitter geometry. As an example, the nonlinear AdS 5 N = 1 SUSY higher spin field theory describing the interaction of massless higher spin fields between themselves and with gravity in the cubic approximation of action functional is constructed.
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