N = 2 supersymmetric spin foams in three dimensions

We construct the spin foam model for N = 2 supergravity in three dimensions. Classically, it is a BF theory with gauge algebra \mathfrak{osp}(2|2) . This algebra has representations which are not completely reducible. This complicates the procedure when building a state sum. Fortunately, one can and should excise these representations. We show that the restricted subset of representations form a subcategory closed under tensor product. The resulting state sum is once again a topological invariant. Furthermore, within this framework one can identify positively and negatively charged fermions propagating on the spin foam. These results on \mathfrak{osp}(2|2) representations and intertwiners apply more generally to spin network states for N = 2 loop quantum supergravity (in 3 + 1 dimensions) where it allows us to define a notion of BPS states.