Factorization algebras and abelian CS/WZW-type correspondences

We develop a method of quantization for free field the-ories on manifolds with boundary where the bulk theory is topo-logical in the direction normal to the boundary and a local bound-ary condition is imposed. Our approach is within the Batalin-Vilkovisky formalism. At the level of observables, the construction produces a stratified factorization algebra that in the bulk recovers the factorization algebra introduced by Costello and Gwilliam. The factorization algebra on the boundary stratum enjoys a perturba-tive bulk-boundary correspondence with this bulk factorization al-gebra. A central example is the factorization algebra version of the abelian Chern-Simons/Wess-Zumino-Witten correspondence, but we examine higher dimensional generalizations that are related to holomorphic truncations of string theory and M-theory and involve intermediate Jacobians.