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.

accepted for publication in Seminaire Lotharingien de Combinatoire; 32 pages (plus 6 scrap pages due to arXiv compiler), 17 figures, 2 tables; reduced review on Hopf algebra basics and several minor clarifying modifications w/r to the previous version

References in corpus (2)

• Just Renormalizable TGFT's on U(1)^d with Gauge Invariance
• Hopf algebras, from basics to applications to renormalization

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