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Journal Article

Non-perturbative 3d Lorentzian Quantum Gravity


Loll,  Renate
Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Ambjörn, J., Jurkiewicz, J., & Loll, R. (2001). Non-perturbative 3d Lorentzian Quantum Gravity. Physical Review D, 64: 044011.

Cite as: http://hdl.handle.net/11858/00-001M-0000-0013-565B-0
We have recently introduced a discrete model of Lorentzian quantum gravity, given as a regularized non-perturbative state sum over simplicial Lorentzian space-times, each possessing a unique Wick rotation to Euclidean signature. We investigate here the phase structure of the Wick-rotated path integral in three dimensions with the aid of computer simulations. After fine-tuning the cosmological constant to its critical value, we find a whole range of the gravitational coupling constant $k_0$ for which the functional integral is dominated by non-degenerate three-dimensional space-times. We therefore have a situation in which a well-defined ground state of extended geometry is generated dynamically from a non-perturbative state sum of fluctuating geometries. Remarkably, its macroscopic scaling properties resemble those of a semi-classical spherical universe. Measurements so far indicate that $k_0$ defines an overall scale in this extended phase, without affecting the physics of the continuum limit. These findings provide further evidence that discrete {it Lorentzian} gravity is a promising candidate for a non-trivial theory of quantum gravity