Group field theory with non-commutative metric variables

Details Group field theory with non-commutative metric variables Group field theory with non-commutative metric variables

2010-02-25

arxiv.org/abs/1002.4723v3

Phys.Rev.Lett.105:221302,2010

Physics

High Energy Physics

High Energy Physics - Theory

4 pages; v3 published version

Scientific paper

10.1103/PhysRevLett.105.221302

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.

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