Abstract
A Kaluza–Klein-like approach for a 4d spin foam model is considered. By applying this approach to a model based on group field theory in 4d (TOCY model), and using the Peter–Weyl expansion of the gravitational field, reconstruction of new non-gravitational fields and interactions in the action are found. The perturbative expansion of the partition function produces graphs colored with SU(2) algebraic data, from which one can reconstruct a 3d simplicial complex representing space-time and its geometry (like in the Ponzano–Regge formulation of pure 3d quantum gravity), as well as the Feynman graph for typical matter fields. Thus a mechanism for generation of matter and construction of new dimensions are found from pure gravity.
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