4-dimensional BF gravity on the lattice Original Research Article

We propose the lattice version of BF gravity action whose partition function leads to the product of a particular form of 15-j symbol which corresponds to a 4-simplex. The action is explicitly constructed by the lattice B field defined on triangles and link variables defined on dual links and is shown to be invariant under lattice local Lorentz transformation and Kalb–Ramond gauge transformation. We explicitly show that the partition function is Pachner move invariant and thus topological. The action includes the vanishing holonomy constraint which can be interpreted as a gauge fixing condition. This formulation of lattice BF theory can be generalized into arbitrary dimensions. Article Outline 1. Introduction