Renormalization of 3d quantum gravity from matrix models

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.

14 pages, 3 figures

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• Semiclassical Universe from First Principles
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• Quantum gravity as sum over spacetimes
• (2+1)-Dimensional Quantum Gravity as the Continuum Limit of Causal Dynamical Triangulations
• CDT---an Entropic Theory of Quantum Gravity
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