The quantum space-time of c=-2 gravity

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 d(H) = 3.58 +/- 0.04. This result supports the conjecture d(H) = -2 alpha(1)/alpha(-1), where alpha(n) is the gravitational dressing exponent of a spinless primary held of conformal weight (n + 1, n + 1), and it disfavours the alternative prediction d(H) = 2/\gamma\. On the other hand, (l(n)) similar to r(2n) for n > 1 with good accuracy, i.e. the boundary length l has an anomalous dimension relative to the area of the surface. (C) 1998 Elsevier Science B.V.