  Spin foam models of quantum gravity are based on Plebanski's formulation of
general relativity as a constrained BF theory. We give an alternative
formulation of gravity as BF theory plus a certain potential term for the
B-field. When the potential is taken to be infinitely steep one recovers
general relativity. For a generic potential the theory still describes gravity
in that it propagates just two graviton polarizations. The arising class of
theories is of the type amenable to spin foam quantization methods, and, we
argue, may allow one to come to terms with renormalization in the spin foam
context.
