Topological Graph Polynomials in Colored Group Field Theory

Abstract

In this paper we analyze the open Feynman graphs of the Colored Group Field Theory introduced in [arXiv:0907.2582]. We define the boundary graph $\cG_{\partial}$ of an open graph $\cG$ and prove it is a cellular complex. Using this structure we generalize the topological (Bollobas-Riordan) Tutte polynomials associated to (ribbon) graphs to topological polynomials adapted to Colored Group Field Theory graphs in arbitrary dimension.

References in corpus (15)

• A new spinfoam vertex for quantum gravity
• A New Spin Foam Model for 4d Gravity
• The loop-quantum-gravity vertex-amplitude
• Flipped spinfoam vertex and loop gravity
• Vanishing of Beta Function of Non Commutative ${\Phi }_4^4$ Theory to all orders
• Group field theory renormalization - the 3d case: power counting of divergences
• Bosonic Colored Group Field Theory
• A translation-invariant renormalizable non-commutative scalar model
• Two and Three Loops Beta Function of Non Commutative ${\Phi }_4^4$ Theory
• Parametric Representation of Noncommutative Field Theory
• Parametric representation of "critical" noncommutative QFT models
• Towards the graviton from spinfoams: the complete perturbative expansion of the 3d toy model
• Vanishing beta function for Grosse-Wulkenhaar model in a magnetic field
• Wilsonian Renormalization of Noncommutative Scalar Field Theory
• Graph polynomials and their applications II: Interrelations and interpretations

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