The quantum space-time of c=-2 gravity
High Energy Physics - Lattice
2009-10-30 v1 General Relativity and Quantum Cosmology
High Energy Physics - Theory
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 \alpha_1/\alpha_{-1}, where \alpha_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/|\gamma|. On the other hand <l^n> ~ 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.
Cite
@article{arxiv.hep-lat/9706009,
title = {The quantum space-time of c=-2 gravity},
author = {J. Ambjorn and K. N. Anagnostopoulos and T. Ichihara and L. Jensen and N. Kawamoto and Y. Watabiki and K. Yotsuji},
journal= {arXiv preprint arXiv:hep-lat/9706009},
year = {2009}
}
Comments
46 pages, 16 figures, 32 eps files, using psfig.sty and epsf.sty