Quantum Gravity as a Broken Symmetry Phase of a BF Theory

We explain how General Relativity with a cosmological constant arises as a broken symmetry phase of a BF theory. In particular we show how to treat de Sitter and anti-de Sitter cases simultaneously. This is then used to formulate a quantisation of General Relativity through a spin foam perturbation theory. We then briefly discuss how to calculate the effective action in this quantization procedure.