Crossing the c=1 barrier in 2D Lorentzian quantum gravity - art. no. 044010

In an extension of earlier work we investigate the behavior of two-dimensio nal (2D) Lorentzian quantum gravity under coupling to a conformal field the ory with c > 1. This is done by analyzing numerically a system of eight Isi ng models (corresponding to c = 4) coupled to dynamically triangulated Lore ntzian geometries. It is known that a single Ising model couples weakly to Lorentzian quantum gravity, in the sense that the Hausdorff dimension of th e ensemble of two-geometries is two (as in pure Lorentzian quantum gravity) and the matter behavior is governed by the Onsager exponents. By increasin g the amount of matter to eight Ising models, we find that the geometry of the combined system has undergone a phase transition. The new phase is char acterized by an anomalous scaling of spatial length relative to proper time at large distances, and as a consequence the Hausdorff dimension is now th ree. In spite of this qualitative change in the geometric sector, and a ver y strong interaction between matter and geometry, the critical exponents of the Ising model retain their Onsager values. This provides evidence for th e 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 .