Making the gravitational path integral more Lorentzian or Life beyond Liouville gravity

In two space-time dimensions, there is a theory of Lorentzian quantum gravi ty which can be defined by a rigorous, non-perturbative path integral and i s inequivalent to the well-known theory of (Euclidean) quantum Liouville gr avity. It has a number of appealing features: i) its quantum geometry is no n-fractal, ii) it remains consistent when coupled to matter, even beyond th e c=1 barrier, iii) it is closer to canonical quantization approaches than previous path-integral formulations, and iv) its construction generalizes t o higher dimensions.