Observables on multisymplectic manifolds and higher Courant algebroids

Let [Formula: see text] be a closed, non-degenerate differential form of arbitrary degree. Associated to it there are an [Formula: see text]-algebra of observables, and an [Formula: see text]-algebra of sections of the higher Courant algebroid twisted by [Formula: see text]. Our main result is the existence of an [Formula: see text]-embedding of the former into the latter. We display explicit formulae for the embedding, involving the Bernoulli numbers. When [Formula: see text] is an integral symplectic form, the embedding can be realized geometrically via the prequantization construction, and when [Formula: see text] is a 3-form the embedding was found by Rogers in 2010. Further, in the presence of homotopy moment maps, we show that the embedding is compatible with gauge transformations.