Poisson sigma models sit at the intersection of deformation theory, geometry, and quantum field theory; specifically, the perturbative expansion of the two-dimensional Poisson sigma model with boundary is known to recover Kontsevich’s deformation quantization formula. In this talk, we introduce a higher-dimensional holomorphic–topological generalization of Poisson sigma models and explain their connections to the deformation quantization (or obstruction) of holomorphic–topological factorization algebras. This construction can be viewed as a field-theoretic incarnation of the higher Deligne conjecture. We also explain how these models relate to the construction of Hopf-type algebras via Koszul duality, and explore examples related to the quantization of Lie bialgebras, W-algebras, and Yangians.