Topological Graph Polynomials in Colored Group Field Theory

In this paper, we analyze the open Feynman graphs of the Colored Group Field Theory introduced in Gurau (Colored group field theory, arXiv:0907.2582 hep-th]). We define the boundary graph ${\mathcal{G}_{\partial}}In this paper, we analyze the open Feynman graphs of the Colored Group Field Theory introduced in Gurau (Colored group field theory, arXiv:0907.2582 hep-th]). We define the boundary graph G_?{\mathcal{G}_{\partial}} of an open graph G{\mathcal{G}} and prove it is a cellular complex. Using this structure we generalize the topological (Bollobás–Riordan) Tutte polynomials associated to (ribbon) graphs to topological polynomials adapted to Colored Group Field Theory graphs in arbitrary dimension.