Combinatorial Quantum Gravity: Emergence of Geometric Space from Random Graphs. (September 2019)

• Record Type: Journal Article
• Authors: Kelly, C; Trugenberger, C A
• Is Part Of: Journal of physics. Volume 1275(2019)
• Publication Date: 2019-09
• Subjects: Physics -- Congresses; 530.5
• DOI: 10.1088/1742-6596/1275/1/012016
• Languages: English
• ISSNs: 1742-6588

Abstract

Abstract: We review and extend the recently proposed model of combinatorial quantum gravity. Contrary to previous discrete approaches, this model is defined on (regular) random graphs and is driven by a purely combinatorial version of Ricci curvature, the Ollivier curvature, defined on generic metric spaces equipped with a Markov chain. It dispenses thus of notions such as simplicial complexes and Regge calculus and is ideally suited to extend quantum gravity to combinatorial structures which have a priori nothing to do with geometry. Indeed, our results show that geometry and general relativity emerge from random structures in a second-order phase transition due to the condensation of cycles on random graphs, a critical point that defines quantum gravity non-perturbatively according to asymptotic safety. In combinatorial quantum gravity the entropy area law emerges naturally as a consequence of infinite-dimensional critical behaviour on networks rather than on lattices. We propose thus that the entropy area law is a signature of the random graph nature of space-(time) on the smallest scales.