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

Understand

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.