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. The exercise repeats for the type IIB $E_5$ generalised geometry and we discuss the relation to the D3-brane.

中文翻译：

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来自 AKSZ 的 Brane Wess-Zumino 项和作为 $L_\infty$-algebroid 的特殊广义几何

我们将 M 理论 $E_6$ 广义几何的广义李导数重新解释为分级辛超流形上的哈密顿流。汉密尔顿量充当异常场论的张量等级的幂零导数。这种构造是 Courant 代数体的 M 理论模拟，并揭示了张量层次结构背后的 $L_\infty$-代数。AKSZ 构造将相同的哈密顿量与陈-西蒙斯理论的 7 维推广的拉格朗日量相识别，后者简化为 5 膜边界上的 M5 膜 Wess-Zumino 项。对类型 IIB $E_5$ 广义几何重复练习，我们讨论与 D3-膜的关系。