Conserved charges and $L_\infty$ algebras

Abstract

We give a formula for conserved charges in an arbitrary Lagrangian field theory expressed in the framework of $L_\infty$ algebras. The formula is expressed in terms of the theory's $L_\infty$ data alone, without reference to the derivative structure of the Lagrangian. Therefore conserved charges can be computed in nonlocal models, such as string field theory, where conventional methods break down. We also show that the formula correctly expresses the surface charge of general relativity in terms of the Brown-York stress tensor. Related computations in Yang-Mills theory suggest that spatial boundaries are dealt with in a natural fashion.