Group field theory with non-commutative metric variables

Understand

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.