On the prequantisation map for 2-plectic manifolds

Abstract

For a manifold M with an integral closed 3-form ω, we construct a P U (H)bundle and a Lie groupoid over its total space, together with a curving in the sense of gerbes. If the form is non-degenerate, we furthermore give a natural Lie 2-algebra quasi-isomorphism from the observables of (M, ω) to the weak symmetries of the above geometric structure, generalising the prequantisation map of Kostant and Souriau.