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The Ben Geloun-Rivasseau quantum field theoretical model is the first tensormodel shown to be perturbatively renormalizable. We define here an appropriateHopf algebra describing the combinatorics of this new tensorialrenormalization. The structure we propose is significantly different from thepreviously defined Connes-Kreimer combinatorial Hopf algebras due to theinvolved combinatorial and topological properties of the tensorial Feynmangraphs. In particular, the 2- and 4-point function insertions must be definedto be non-trivial only if the superficial divergence degree of the associatedFeynman integral is conserved.

Combinatorial Hopf algebra for the Ben Geloun-Rivasseau tensor field theory