Sum over topologies and double-scaling limit in 2D Lorentzian quantum gravity

We construct a combined non-perturbative path integral over geometries and topologies for two-dimensional Lorentzian quantum gravity. The Lorentzian structure is used in an essential way to exclude geometries with unacceptably large causality violations. The remaining sum can be performed analytically and possesses a unique and welldefined double-scaling limit, a property which has eluded similar models of Euclidean quantum gravity in the past. 1 Summing over topologies? A central question that arises in the construction of a theory of quantum gravity is that of the fundamental, microscopic degrees of freedom whose dynamics the theory should describe. The idea that the information contained in the metric field tensor gμν may not constitute an adequate description of the geometric properties of spacetime at the very shortest scales goes back all the way to Riemann himself [1]. More email: [email protected] email: [email protected]