Computer Simulations of 3d Lorentzian Quantum Gravity

Details Computer Simulations of 3d Lorentzian Quantum Gravity Computer Simulations of 3d Lorentzian Quantum Gravity

2000-11-11

arxiv.org/abs/hep-lat/0011055v2

Nucl.Phys.Proc.Suppl. 94 (2001) 689-692

Physics

High Energy Physics

High Energy Physics - Lattice

4 pages, contribution to Lattice 2000 (Gravity and Matrix Models), typos corrected

Scientific paper

10.1016/S0920-5632(01)00878-7

We investigate the phase diagram of non-perturbative three-dimensional Lorentzian quantum gravity with the help of Monte Carlo simulations. The system has a first-order phase transition at a critical value $k_0^c$ of the bare inverse gravitational coupling constant $k_0$. For $k_0 > k_0^c$ the system reduces to a product of uncorrelated Euclidean 2d gravity models and has no intrinsic interest as a model of 3d gravity. For $k_0 < k_0^c$, extended three-dimensional geometries dominate the functional integral despite the fact that we perform a sum over geometries and no particular background is distinguished at the outset. Furthermore, all systems with $k_0 < k_0^c$ have the same continuum limit. A different choice of $k_0$ corresponds merely to a redefinition of the overall length scale.

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