Observables on multisymplectic manifolds and higher Courant algebroids

Abstract

Let ω be a closed, non-degenerate differential form of arbitrary degree. Associated to it there are an L∞-algebra of observables, and an L∞-algebra of sections of the higher Courant algebroid twisted by ω. Our main result is the existence of an L∞-embedding of the former into the latter. We display explicit formulae for the embedding, involving the Bernoulli numbers. When ω is an integral symplectic form, the embedding can be realized geometrically via the prequantization construction, and when ω 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.