L-infinity algebras of local observables from higher prequantum bundles

Understand

To any manifold equipped with a higher degree closed form, one can associate an L-infinity algebra of local observables that generalizes the Poisson algebra of a symplectic manifold.

• Here, by means of an explicit homotopy equivalence, we interpret this L-infinity algebra in terms of infinitesimal autoequivalences of higher prequantum bundles.
• By truncating the connection data on the prequantum bundle, we produce analogues of the (higher) Lie algebras of sections of the Atiyah Lie algebroid and of the Courant Lie 2-algebroid.
• We also exhibit the L-infinity cocycle that realizes the L-infinity algebra of local observables as a Kirillov-Kostant-Souriau-type L-infinity extension of the Hamiltonian vector fields.