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

Alex S. Arvanitakis

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arXiv · 1804.07303

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

Alex S. Arvanitakis

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Abstract

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.

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Alex S. Arvanitakis. 2018-04-19. Brane Wess-Zumino terms from AKSZ and exceptional generalised geometry as an $L_\infty$-algebroid. https://arxiv.org/abs/1804.07303

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