On the phase diagram of 2d Lorentzian Quantum Gravity

The phase diagram of 2d Lorentzian quantum gravity (LQG) coupled to conformal matter is studied. A phase transition is observed at $c=c_{\rm crit}$ ($1/2<c_{\rm crit}<4$) which can be thought of as the analogue of the $c=1$ barrier of Euclidean quantum gravity (EQG). The non--trivial properties of the quantum geometry are discussed.