Factorization algebras and abelian CS/WZW-type correspondences

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