### Abstract

We summarise some of our recent works on L∞-algebras and quasi-groups with regard to higher principal bundles and their applications in twistor theory and gauge theory. In particular, after a lightning review of L∞-algebras, we discuss their Maurer-Cartan theory and explain that any classical field theory admitting an action can be reformulated in this context with the help of the Batalin-Vilkovisky formalism. As examples, we explore higher Chern-Simons theory and Yang-Mills theory. We also explain how these ideas can be combined with those of twistor theory to formulate maximally superconformal gauge theories in four and six dimensions by means of L∞-quasi-isomorphisms, and we propose a twistor space action.

Original language | English |
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Publication status | Accepted/In press - 7 Mar 2019 |

Event | London Mathematical Society/EPSRC Durham Symposium on Higher Structures in M-Theory - Durham, United Kingdom Duration: 12 Aug 2018 → 18 Aug 2018 |

### Seminar

Seminar | London Mathematical Society/EPSRC Durham Symposium on Higher Structures in M-Theory |
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Country | United Kingdom |

City | Durham |

Period | 12/08/18 → 18/08/18 |

### Keywords

- hep-th

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## Cite this

Jurčo, B., Macrelli, T., Raspollini, L., Saemann, C., & Wolf, M. (Accepted/In press).

*L∞-Algebras, the BV Formalism, and Classical Fields*. Paper presented at London Mathematical Society/EPSRC Durham Symposium on Higher Structures in M-Theory, Durham, United Kingdom.