Quantum Gravity and Renormalization: The Tensor Track
Vincent Rivasseau
TL;DR
The paper proposes tensor field theory (TFT) as a renormalization-group–driven program to quantize gravity using large random tensors and their $1/N$ expansion, connecting pre-geometric dynamics to emergent spacetime. By defining renormalizable tensor models and exploring their RG flows, universality, and phase structure, the work argues for geometrogenesis as the mechanism by which Einstein-Hilbert-like physics could arise in a continuum limit. It situates TFT within a landscape of related approaches (GFT, NCQFT, matrix models) while outlining its unique emphasis on renormalization, phase transitions, and hierarchies of RG, and it discusses potential links to string theory and LQG. The significance lies in providing a concrete, analytically tractable framework to study emergent geometry and RG-driven transitions that could bridge pre-geometric tensor dynamics with familiar gravitational physics.
Abstract
We propose a new program to quantize and renormalize gravity based on recent progress on the analysis of large random tensors. We compare it briefly with other existing approaches.