$L_{\infty}$ Algebras and Field Theory

Understand

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.