Barrett-Crane spin foam model from generalized BF-type action for gravity

We study a generalized action for gravity as a constrained BF theory, and its relationship with the Plebanski action. We analyse the discretization of the constraints and the spin foam quantization of the theory, showing that it leads naturally to the Barrett-Crane spin foam model for quantum gravity. We end up with some comments on the possible introduction and role of the Immirzi parameter in this context. Our analysis holds true in both the Euclidean and Lorentzian formulation