L∞ algebras and field theory

By O. Hohm, B. Zwiebach. 2017

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We review and develop the general properties of L∞ algebras focusing on the gauge structure of the associated field theories. Motivated by the L∞ 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∞ 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∞ 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∞ algebra for the interacting theory. The analysis suggests that L∞ algebras provide a classification of perturbative gauge invariant classical field theories.

Subfields: Algebra and Number Theory, Geometry and Topology, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/f13376cff339922397145edc613dbcdc8f8d5aff