  In an extension of earlier work we investigate the behaviour of
two-dimensional Lorentzian quantum gravity under coupling to a conformal field
theory with c>1. This is done by analyzing numerically a system of eight Ising
models (corresponding to c=4) coupled to dynamically triangulated Lorentzian
geometries. It is known that a single Ising model couples weakly to Lorentzian
quantum gravity, in the sense that the Hausdorff dimension of the ensemble of
two-geometries is two (as in pure Lorentzian quantum gravity) and the matter
behaviour is governed by the Onsager exponents. By increasing the amount of
matter to 8 Ising models, we find that the geometry of the combined system has
undergone a phase transition. The new phase is characterized by an anomalous
scaling of spatial length relative to proper time at large distances, and as a
consequence the Hausdorff dimension is now three. In spite of this qualitative
change in the geometric sector, and a very strong interaction between matter
and geometry, the critical exponents of the Ising model retain their Onsager
values. This provides evidence for the conjecture that the KPZ values of the
critical exponents in 2d Euclidean quantum gravity are entirely due to the
presence of baby universes. Lastly, we summarize the lessons learned so far
from 2d Lorentzian quantum gravity.
