Abstract
We continue our study of zerodimensional field theories in which the fields take values in a strong homotopy Lie algebra. In a first part, we review in detail how higher ChernSimons theories arise in the AKSZformalism. These theories form a universal starting point for the construction of $L_\infty$algebra models. We then show how to describe superconformal field theories and how to perform dimensional reductions in this context. In a second part, we demonstrate that NambuPoisson and multisymplectic manifolds are closely related via their Heisenberg algebras. As a byproduct of our discussion, we find central Lie $p$algebra extensions of $\mathfrak{so}(p+2)$. Finally, we study a number of $L_\infty$algebra models which are physically interesting and which exhibit quantized multisymplectic manifolds as vacuum solutions.
Original language  English 

Article number  1650021 
Number of pages  46 
Journal  Reviews in Mathematical Physics 
Volume  28 
Issue number  9 
DOIs  
Publication status  Published  7 Oct 2016 
Keywords
 hepth
 mathph
 math.MP
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Christian Saemann
 School of Mathematical & Computer Sciences  Professor
 School of Mathematical & Computer Sciences, Mathematics  Professor
Person: Academic (Research & Teaching)