The quantum space-time of c = −2 gravity

Abstract

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 α 1/ α −1, where α n is the gravitational dressing exponent of a spinless primary field of conformal weight ( n + 1, n + 1), and it disfavours the alternative prediction d H = 2/| γ|. On the other hand, 〈 l n 〉 ∼ r 2 n for n > 1 with good accuracy, i.e. the boundary length l has an anomalous dimension relative to the area of the surface.