Free higher-spin Fronsdal fields generalise Maxwell fields and linearised gravity to higher tensor fields. Whereas for spin-1 and spin-2 there are non-linear completions (e.g. Yang-Mills, gravity), no non-linear, gauge-invariant theory of Fronsdal fields is known. A systematic way to construct them is the Noether procedure in which a gauge invariant action is constructed in a perturbative expansion in powers of the fields.
In three space-time dimensions, there are strong obstructions to construct such an action leading to the conclusion that the interactions of the higher-spin gauge fields are completely fixed by the cubic vertices in the action.
