  We propose a new method of unifying gravity and the Standard Model by
introducing a spin-foam model. We realize a unification between an SU(2)
Yang-Mills interaction and 3D general relativity by considering a Spin(4)
Plebanski action. The theory is quantized a la spin-foam by implementing the
analogue of the simplicial constraints for the broken phase of the Spin(4)
SO(4) symmetry. A natural 4D extension of the theory is shown. We also present
a way to recover 2-point correlation functions between the connections as a
first way to implement scattering amplitudes between particle states, aiming to
connect Loop Quantum Gravity to new physical predictions.
