  In two space-time dimensions, there is a theory of Lorentzian quantum gravity
which can be defined by a rigorous, non-perturbative path integral and is
inequivalent to the well-known theory of (Euclidean) quantum Liouville gravity.
It has a number of appealing features: i) its quantum geometry is non-fractal,
ii) it remains consistent when coupled to matter, even beyond the c=1 barrier,
iii) it is closer to canonical quantization approaches than previous
path-integral formulations, and iv) its construction generalizes to higher
dimensions.
