Feynman diagrams of generalized matrix models and the associated manifolds in dimension four

The problem of constructing a quantum theory of gravity has been tackled with very different strategies, most of which rely on the interplay between ideas from physics and from advanced mathematics. On the mathematical side, a central role 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 four-manifolds with the Feynman diagrams of certain tensor theories.