Nonperturbative 3D Lorentzian quantum gravity - art. no. 044011

We have recently introduced a discrete model of Lorentzian quantum gravity, given as a regularized nonperturbative state sum over simplicial Lorentzia n space-times, each possessing a unique Wick rotation to the Euclidean sign ature. We investigate here the phase structure of the Wick-rotated path int egral in three dimensions with the aid of computer simulations. After fine tuning the cosmological constant to its critical value, we find a whole ran ge of the gravitational coupling constant k(0) for which the functional int egral is dominated by nondegenerate three-dimensional space-times. We there fore have a situation in which a well-defined ground state of extended geom etry is generated dynamically from a nonperturbative state sum of fluctuati ng geometries. Remarkably, its macroscopic scaling properties resemble thos e of a semiclassical 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 th at discrete Lorentzian gravity is a promising candidate for a nontrivial th eory of quantum gravity.