L∞-Algebras, the BV Formalism, and Classical Fields

Branislav Jurčo, Tommaso Macrelli, Lorenzo Raspollini, Christian Saemann, Martin Wolf

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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 languageEnglish
Publication statusAccepted/In press - 7 Mar 2019
EventLondon Mathematical Society/EPSRC Durham Symposium on Higher Structures in M-Theory - Durham, United Kingdom
Duration: 12 Aug 201818 Aug 2018

Seminar

SeminarLondon Mathematical Society/EPSRC Durham Symposium on Higher Structures in M-Theory
CountryUnited Kingdom
CityDurham
Period12/08/1818/08/18

Keywords

  • hep-th

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    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.