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arXiv · 1903.02887

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

Branislav Jurco·Tommaso Macrelli·Lorenzo Raspollini·Christian Saemann·Martin Wolf
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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.

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Branislav Jurco, Tommaso Macrelli, Lorenzo Raspollini, Christian Saemann, Martin Wolf. 2019-03-07. $L_\infty$-Algebras, the BV Formalism, and Classical Fields. https://doi.org/10.1002/prop.201910025

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