Batalin-Vilkovisky formality for Chern-Simons theory

We prove that the differential graded Lie algebra of functionals associated to the Chern-Simons theory of a semisimple Lie algebra is homotopy abelian. For a general field theory, we show that the variational complex in the Batalin-Vilkovisky formalism is a differential graded Lie algebra.

Cohomology of the variational complex in the class of exterior forms of finite jet order

We obtain the cohomology of the variational complex on the infinite-order jet space of a smooth fiber bundle in the class of exterior forms of finite jet order. In particular, this provides a solution of the global inverse problem of the calculus of variations of finite order on fiber bundles.

COHOMOLOGY OF THE VARIATIONAL COMPLEX IN FIELD–ANTIFIELD BRST THEORY

We show that cohomology of the variational complex in the field–antifield BRST theory on an arbitrary manifold X equals the de Rham cohomology of X. It follows that there is no topological obstruction to constructing global descent equations in BRST theory.