The quantum space-time of c = −2 gravity Original Research Article

We study the fractal structure of space-time of two-dimensional quantum gravity coupled to c = −2 conformal matter by means of computer simulations. We find that the intrinsic Hausdorff dimension dH = 3.58 ± 0.04. This result supports the conjecture dH = −2α1/α−1, where αn is the gravitational dressing exponent of a spinless primary field of conformal weight (n + 1, n + 1), and it disfavours the alternative prediction dH = 2/|γ|. On the other hand, 〈ln〉 ∼ r2n for n > 1 with good accuracy, i.e. the boundary length l has an anomalous dimension relative to the area of the surface.