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.
|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||London Mathematical Society/EPSRC Durham Symposium on Higher Structures in M-Theory|
|Period||12/08/18 → 18/08/18|
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.