A membrane-network model for (3+1)D topological phases

Non-chiral topological phases in 2D can be understood using the Levin-Wen string-net model. Here, we construct a membrane-network model in 3D. The model has as input a generalized tensor category, which consists of a collection of modular tensor categories and equipped with a non-associative product structure, such as anyon pair condensation, that respects locality. The construction outputs an exactly soluble Hamiltonian in 3D. We speculate this model describes topological phases in 3D that dynamically generate (1+1)D stringy excitations that host low-energy conformal field theories