Feynman Diagrams of Generalized Matrix Models and the Associated Manifolds in Dimension 4

The problem of constructing a quantum theory of gravity has been tackled with very different strategies, most of which relying on the interplay between ideas from physics and from advanced mathematics. On the mathematical side, a central rôle is played by combinatorial topology, often used to recover the space-time manifold from the other structures involved. An extremely attractive possibility is that of encoding all possible space-times as specific Feynman diagrams of a suitable field theory. In this work we analyze how exactly one can associate combinatorial 4-manifolds to the Feynman diagrams of certain tensor theories. PACS: 04.60.Nc, 02.40.Sf MSC (2000): 57Q05 (primary), 57M99 (secondary).