Polchinski's equation for group field theory

We derive an exact renormalization group equation in the context of (colored) group field theories. This equation describes the variation of the effective action as some of the modes of the fields are integrated out. From a combinatorial point of view, the effective action can be expressed using a boundary triangulation and the corresponding renormalization group equation identifies some of its simplexes, [GRAPHICS] In group field theory, terms in the effective action are parametrized by spin networks, while the group field theory Feynman graphs correspond to spin foams. This provides a formulation of group field theories that only involves boundary graphs. (C) 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim