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Colored group field theory. (English) Zbl 1214.81170
Summary: Random matrix models generalize to Group Field Theories (GFT) whose Feynman graphs are dual to higher dimensional topological spaces. The perturbative development of the usual GFT’s is rather involved combinatorially and plagued by topological singularities (which we discuss in great detail in this paper), thus very difficult to control and unsatisfactory.
Both these problems simplify greatly for the “colored” GFT (CGFT) model we introduce in this paper. Not only this model is combinatorially simpler but also it is free from the worst topological singularities. We establish that the Feynman graphs of our model are combinatorial cellular complexes dual to manifolds or pseudomanifolds, and study their cellular homology. We also relate the amplitude of CGFT graphs to their fundamental group.

81T18 Feynman diagrams
22A26 Topological semilattices, lattices and applications
81T15 Perturbative methods of renormalization applied to problems in quantum field theory
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