Brane Wess-Zumino terms from AKSZ and exceptional generalised geometry as an $L_\infty$-algebroid

Understand

We reinterpret the generalised Lie derivative of M-theory $E_6$ generalised geometry as hamiltonian flow on a graded symplectic supermanifold.

• The hamiltonian acts as the nilpotent derivative of the tensor hierarchy of exceptional field theory.
• This construction is an M-theory analogue of the Courant algebroid and reveals the $L_\infty$-algebra underlying the tensor hierarchy.
• The AKSZ construction identifies that same hamiltonian with the lagrangian of a 7-dimensional generalisation of Chern-Simons theory that reduces to the M5-brane Wess-Zumino term on 5-brane boundaries.