Centre for Mathematical Physics and Stochastics

Department of Mathematical Sciences, University of Aarhus

Funded by The Danish National Research Foundation

MPS-RR 1998-5

May 1998

We formulate a non-pertubative lattice model of two-dimensional Lorentzian quantum gravity by performing the path integral over geometries with a causal structure. The model can be solved exactly at the discretized level. Its continuum limit coincides with the theory obtained by quantizing 2d continuum gravity in proper-time gauge, but it disagrees with 2d gravity defined via matrix models or Liouville theory. By allowing topology change of the compact spatial slices (i.e. baby universe creation), one obtains agreement with the matrix models and Liouville theory.

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