Renormalization of 3d quantum gravity from matrix models

TL;DR

This paper demonstrates how a 3D Lorentzian quantum gravity model, mapped to a two-matrix model, exhibits additive renormalizations of key constants, providing insights into its non-perturbative structure.

Contribution

It introduces a mapping of 3D Lorentzian quantum gravity to a two-matrix model, revealing renormalization behavior of gravitational constants.

Findings

Cosmological constant undergoes additive renormalization.

Gravitational coupling constant is renormalized consistently with canonical quantization.

Model provides a non-perturbative framework for 3D quantum gravity.

Abstract

Lorentzian simplicial quantum gravity is a non-perturbatively defined theory of quantum gravity which predicts a positive cosmological constant. Since the approach is based on a sum over space-time histories, it is perturbatively non-renormalizable even in three dimensions. By mapping the three-dimensional theory to a two-matrix model with ABAB interaction we show that both the cosmological and the (perturbatively) non-renormalizable gravitational coupling constant undergo additive renormalizations consistent with canonical quantization.