QUANTUM GRAVITY VIA MANIFOLD POSITIVITY

Abstract. The macroscopic dimensions of space-time should not be input but rather output of a general model for physics. Here, dimensionality arises from a recently discovered mathematical bifurcation: “positive versus indefi-nite manifold pairings. ” It is used to build actions on a “formal chain ” of com-binatorial space-times of arbitrary dimension. The context for such actions is 2-field theory where Feynman integrals are not over classical, but previously quantized configurations. A topologically enforced singularity of the action can terminate the dimension at four and, in fact, the final fourth dimension is Lorentzian due to light-like vectors in the four dimensional manifold pairing. Our starting point is the action of “causal dynamical triangulations ” but in a dimension-agnostic setting. Curiously, some hint of extra compact dimensions emerges from our action. 1