The quantum space-time of c=-2 gravity

الأصل · EN

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 = -2 α₁/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.