Hohm, Olaf; Zwiebach, Barton \(L_{\infty}\) algebras and field theory. (English) Zbl 1371.81261 Fortschr. Phys. 65, No. 3-4, 1700014, 33 p. (2017). Summary: We review and develop the general properties of \(L_{\infty}\) algebras focusing on the gauge structure of the associated field theories. Motivated by the \(L_{\infty}\) homotopy Lie algebra of closed string field theory and the work of Roytenberg and Weinstein describing the Courant bracket in this language we investigate the \(L_{\infty}\) structure of general gauge invariant perturbative field theories. We sketch such formulations for non-abelian gauge theories, Einstein gravity, and for double field theory. We find that there is an \(L_{\infty}\) algebra for the gauge structure and a larger one for the full interacting field theory. Theories where the gauge structure is a strict Lie algebra often require the full \(L_{\infty}\) algebra for the interacting theory. The analysis suggests that \(L_{\infty}\) algebras provide a classification of perturbative gauge invariant classical field theories. Cited in 1 ReviewCited in 55 Documents MSC: 81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory 81T13 Yang-Mills and other gauge theories in quantum field theory 70S15 Yang-Mills and other gauge theories in mechanics of particles and systems 18G55 Nonabelian homotopical algebra (MSC2010) PDFBibTeX XMLCite \textit{O. Hohm} and \textit{B. Zwiebach}, Fortschr. Phys. 65, No. 3--4, 1700014, 33 p. (2017; Zbl 1371.81261) Full Text: DOI arXiv