Quantum geometry of topological gravity
Abstract
We study a c = 2 conformal field theory coupled to twodimensional quantum gravity by means of dynamical triangulations. We define the geodesic distance r on the triangulated surface with N triangles, and show that dim[r^{d}^{H}] = dim[N], where the fractal dimension d_{H} = 3.58 +/ 0.04. This result lends support to the conjecture d_{H} =2α_{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 disfavors the alternative prediction d_{H} = 2/γ_{str}. On the other hand, we find dim[l] = dim[r^{2}] with good accuracy, where l is the length of one of the boundaries of a circle with (geodesic) radius r, i.e. the length l has an anomalous dimension relative to the area of the surface. It is further shown that the spectral dimension d_{s} = 1.980 +/ 0.014 for the ensemble of (triangulated) manifolds used. The results are derived using finite size scaling and a very efficient recursive sampling technique known previously to work well for c = 2.
 Publication:

Physics Letters B
 Pub Date:
 February 1997
 DOI:
 10.1016/S03702693(97)001834
 arXiv:
 arXiv:heplat/9611032
 Bibcode:
 1997PhLB..397..177A
 Keywords:

 High Energy Physics  Lattice;
 High Energy Physics  Theory
 EPrint:
 12 pages, LaTeX, 4 figures using psfig.sty and epsf.sty