Network Gravity

TL;DR

This paper presents a new network-based framework for exploring discrete emergent geometry, utilizing combinatorial curvatures and simplicial volumes, revealing properties akin to quantum gravity models through analytical and simulation methods.

Contribution

It introduces a novel network approach to emergent geometry, combining combinatorial curvature and simplicial volume concepts, bridging ideas from quantum gravity formalisms.

Findings

Emergent simplicial structures from network evolution.

Existence of a volume-scale cutoff.

Positive cosmological constant-like term as a regulator.

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 properties such as a minimal volume-scale cutoff, the necessity of a positive-definite cosmological constant-like term 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. We see emergent properties which echo results from both the spinfoam formalism and causal dynamical triangulations in quantum gravity, and provide analytical and numerical results to support the analogy. We conclude with a summary of open questions and intent for future work in developing the program.