L∞-algebras, the BV formalism, and classical fields: LMS/EPSRC Durham Symposium on Higher Structures in M-Theory

0518730 - MÚ 2020 RIV DE eng J - Journal Article
Jurčo, Branislav - Macrelli, T. - Raspollini, L. - Sämann, Ch. - Wolf, M.
L∞-algebras, the BV formalism, and classical fields: LMS/EPSRC Durham Symposium on Higher Structures in M-Theory.
Fortschritte der Physik - Progress of Physics. Roč. 67, č. 8-9 (2019), č. článku 1910025. ISSN 0015-8208. E-ISSN 1521-3978
R&D Projects: GA ČR(CZ) GA18-07776S
Institutional support: RVO:67985840
Keywords : Batalin–Vilkovisky formalism * higher Gauge theories * twistor geometry
OECD category: Pure mathematics
Impact factor: 3.921, year: 2019
Method of publishing: Limited access
http://dx.doi.org/10.1002/prop.201910025

We summarise some of our recent works on (Formula presented.) -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 (Formula presented.) -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 (Formula presented.) -quasi-isomorphisms, and we propose a twistor space action.
Permanent Link: http://hdl.handle.net/11104/0303792