# $L_\infty$-Algebras, the BV Formalism, and Classical Fields

## TL;DR

This paper explores the use of $L_$-algebras and the BV formalism to reformulate classical field theories, including higher gauge theories and superconformal theories, with applications in twistor and gauge theories.

## Contribution

It demonstrates how $L_$-algebras and quasi-groups can reformulate classical field theories within the BV formalism, connecting higher gauge theories with twistor theory.

## Key findings

- Reformulation of classical field theories using $L_$-algebras and BV formalism
- Application to higher Chern-Simons and Yang-Mills theories
- Formulation of superconformal gauge theories via twistor space

## Abstract

We summarise some of our recent works on $L_\infty$-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 $L_\infty$-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 $L_\infty$-quasi-isomorphisms, and we propose a twistor space action.