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Non-perturbative 3d Lorentzian quantum gravity

By J. Ambjørn, J. Jurkiewicz and R. Loll


We have recently introduced a discrete model of Lorentzian quantum gravity,\ud given as a regularized non-perturbative state sum over simplicial Lorentzian spacetimes,\ud each possessing a uniqueWick rotation to Euclidean signature. We investigate\ud here the phase structure of the Wick-rotated path integral in three dimensions with\ud the aid of computer simulations. After fine-tuning the cosmological constant to\ud its critical value, we find a whole range of the gravitational coupling constant k0\ud for which the functional integral is dominated by non-degenerate three-dimensional\ud space-times. We therefore have a situation in which a well-defined ground state\ud of extended geometry is generated dynamically from a non-perturbative state sum\ud of fluctuating geometries. Remarkably, its macroscopic scaling properties resemble\ud those of a semi-classical spherical universe. Measurements so far indicate that k0\ud defines an overall scale in this extended phase, without affecting the physics of the\ud continuum limit. These findings provide further evidence that discrete Lorentzian\ud gravity is a promising candidate for a non-trivial theory of quantum gravity

Topics: Natuur- en Sterrenkunde
Publisher: American Physical Society
Year: 2001
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