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We have recently introduced a discrete model of Lorentzian quantum gravity, given as a regularized nonperturbative state sum over simplicial Lorentzian space-times, each possessing a unique Wick rotation to the 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 k₀ for which the functional integral is dominated by nondegenerate three-dimensional space-times. We therefore have a situation in which a well-defined ground state of extended geometry is generated dynamically from a nonperturbative state sum of fluctuating geometries. Remarkably, its macroscopic scaling properties resemble those of a semiclassical spherical universe. Measurements so far indicate that k₀ defines an overall scale in this extended phase, without affecting the physics of the continuum limit. These findings provide further evidence that discrete Lorentzian gravity is a promising candidate for a nontrivial theory of quantum gravity.
Ambjørn et al. (Tue,) studied this question.