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

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

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...

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Hauptverfasser: Jurco, Branislav, Macrelli, Tommaso, Raspollini, Lorenzo, Saemann, Christian, Wolf, Martin
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Macrelli, Tommaso
Raspollini, Lorenzo
Saemann, Christian
Wolf, Martin
description 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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title L_\infty$-Algebras, the BV Formalism, and Classical Fields
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