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 of an open graph and prove it is a cellular complex. Using this structure we generalize the topological (Bollob...

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Bibliographic Details
Published in:Annales Henri Poincaré Vol. 11; no. 4; pp. 565 - 584
Main Author: Gurau, Razvan
Format: Journal Article
Language:English
Published: Basel SP Birkhäuser Verlag Basel 01.08.2010
Springer
Subjects:
Classical and Quantum Gravitation
Combinatorics
Combinatorics. Ordered structures
Dynamical Systems and Ergodic Theory
Elementary Particles
Exact sciences and technology
Graph theory
Group theory
Group theory and generalizations
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematics
Other topics in mathematical methods in physics
Physics
Physics and Astronomy
Quantum Field Theory
Quantum Physics
Relativity Theory
Sciences and techniques of general use
Theoretical
Topological groups, lie groups
Ribbon Graph
Active Line
Tutte Polynomial
Half Line
Chord Diagram
Topological structure
Dimension theory
Tutte polynomial
Field theories
Topological group
Topological graph
Color
Group theory
Graph theory
Mathematical physics
ISSN:1424-0637, 1424-0661
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Summary: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 of an open graph 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.
ISSN:1424-0637
1424-0661
DOI:10.1007/s00023-010-0035-6