Abstract: Combinatorial non-locality occurs in various field theories such as non-commutative field theory, matrix and tensor theories or the group field theory approach to quantum gravity. Though interactions in such theories are not point-like, they are still local in the sense that for any divergent Feynman diagram there is a unique counter term vertex, described in general by a graph. This allows to generalize the renormalization Hopf algebra of Feynman graphs to a Hopf algebra of 2-graphs which gives a concise algorithm for applying Zimmermann’s forest formula to amplitudes in any renormalizable non-local field theory.
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