  We introduce a dual formulation of group field theories, making them a type
of non-commutative field theories. In this formulation, the variables of the
field are Lie algebra variables with a clear interpretation in terms of
simplicial geometry. For Ooguri-type models, the Feynman amplitudes are
simplicial path integrals for BF theories. This formulation suggests ways to
impose the simplicity constraints involved in BF formulations of 4d gravity
directly at the level of the group field theory action. We illustrate this by
giving a new GFT definition of the Barrett-Crane model.
