Network Gravity: A New Framework for Emergent Geometry

Abstract

We introduce the construction of a new framework for probing discrete emergent geometry and boundary-boundary observables based on a fundamentally a-dimensional underlying network structure. Using a gravitationally motivated action with Forman weighted combinatorial curvatures and simplicial volumes relying on a decomposition of an abstract simplicial complex into realized embeddings of proper skeletons, we demonstrate model phenomenology such as a minimal volume-scale cutoff, a positive-definite cosmological constant as a regulator for non-degenerate geometries, and naturally emergent simplicial structures from Metropolis network evolution simulations with no restrictions on attachment rules or regular building blocks. Properties which echo results from both the spinfoam formalism and causal dynamical triangulations in quantum gravity will also be illustrated. We conclude with prospects for future investigations into the model, discussing ongoing simulations, modifications to the structure of the theory, and broader applications of the framework.