### Abstract

We continue our study of zero-dimensional field theories in which the fields take values in a strong homotopy Lie algebra. In a first part, we review in detail how higher Chern-Simons theories arise in the AKSZ-formalism. 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 Nambu-Poisson 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 |
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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

- hep-th
- math-ph
- math.MP

## Fingerprint Dive into the research topics of 'L<sub>∞</sub>-Algebra Models and Higher Chern-Simons Theories'. Together they form a unique fingerprint.

## Profiles

## Christian Saemann

- School of Mathematical & Computer Sciences - Professor
- School of Mathematical & Computer Sciences, Mathematics - Professor

Person: Academic (Research & Teaching)

## Cite this

Ritter, P., & Saemann, C. (2016). L

_{∞}-Algebra Models and Higher Chern-Simons Theories.*Reviews in Mathematical Physics*,*28*(9), [1650021]. https://doi.org/10.1142/S0129055X16500215