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

Abstract

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.

arXiv comment19 pages, Contribution to Proceedings of LMS/EPSRC Durham Symposium Higher Structures in M-Theory, August 2018

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Cited by in corpus (19)

• Kinematic Lie Algebras From Twistor Spaces
• $L_{\infty }$-algebras and the perturbiner expansion
• Loop Amplitudes and Quantum Homotopy Algebras
• Double-Copying Self-Dual Yang-Mills Theory to Self-Dual Gravity on Twistor Space
• Geometrical Aspects of An Abelian (2,0) Action
• The $L_{\infty }$ structure of gauge theories with matter
• Double Copy from Tensor Products of Metric BV${}^{■}$-algebras
• Tree-Level Color-Kinematics Duality from Pure Spinor Actions
• Global Double Field Theory is Higher Kaluza-Klein Theory
• Topological invariant of 4-manifolds based on a 3-group
• Higher Gauge Theory
• Field Theory Equivalences as Spans of $L_{\infty }$-algebras
• Matrix Quantization of Classical Nambu Brackets and Super $p$-Branes
• Generalised wavefunction coefficients and acyclonesto-cosmohedra
• Symmetry breaking mechanisms of the 3BF action for the Standard Model coupled to gravity
• Full S-matrices and Witten diagrams with (relative) L-infinity algebras
• Correspondence between 3BF and Einstein-Cartan formulations of quantum gravity
• Out-of-time-order asymptotic observables are quasi-isomorphic to time-ordered amplitudes
• Ambitwistor Yang-Mills Theory Revisited