L∞ algebras and field theory
Author(s)Hohm, Olaf; Zwiebach, Barton
MetadataShow full item record
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.
DepartmentMassachusetts Institute of Technology. Department of Physics; Massachusetts Institute of Technology. Laboratory for Nuclear Science
Fortschritte der Physik
Hohm, Olaf, and Barton Zwiebach. “L∞ Algebras and Field Theory.” Fortschritte Der Physik 65, no. 3–4 (March 2017): 1700014.