For g a dgla over a field of characteristic zero, the dual of the Hochschild homology of the universal enveloping algebra of g *completes* to the Hochschild homology of the Lie algebra cohomology of g.  In this talk we will resolve this completion discrepancy through considerations of formal algebraic geometry.  This will be an instance of our main result, which is a version of Poincare' duality for factorization homology as it interacts with Koszul duality in the sense of formal moduli.  This can be interpreted as a duality among certain topological field theories that exchanges perturbative and non-perturbative.