#####
Séminaire Lotharingien de Combinatoire, B70d (2014), 28 pp.

# Matti Raasakka and Adrian Tanasa

# Combinatorial Hopf Algebra for the Ben Geloun-Rivasseau Tensor Field Theory

**Abstract.**
The Ben Geloun-Rivasseau quantum field theoretical model is the first tensor model shown to be
perturbatively renormalizable.
We define here an appropriate Hopf algebra describing the
combinatorics of this new tensorial renormalization.
The structure we propose is significantly different from the previously defined Connes-Kreimer
combinatorial Hopf algebras due to the involved combinatorial and topological properties of the tensorial Feynman graphs. In particular, the 2- and 4-point function insertions must be defined to be
non-trivial only if the superficial divergence degree of the associated Feynman integral
is conserved.

Received: June 5, 2013.
Revised: November 20, 2013.
Accepted: November 25, 2013.

The following versions are available: