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

Abstract

We construct a combined non-perturbative path integral over geometries and topolo- gies 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 well- defined double-scaling limit, a property which has eluded similar models of Euclidean quantum gravity in the past.