Quantum geometry of topological gravity

被引:27
作者
Ambjorn, J
Anagnostopoulos, KN
Ichihara, T
Jensen, L
Kawamoto, N
Watabiki, Y
Yotsuji, K
机构
[1] TOKYO INST TECHNOL,DEPT PHYS,TOKYO 152,JAPAN
[2] HOKKAIDO UNIV,DEPT PHYS,SAPPORO,HOKKAIDO 060,JAPAN
关键词
D O I
10.1016/S0370-2693(97)00183-4
中图分类号
P1 [天文学];
学科分类号
0704 ;
摘要
We study a c = -2 conformal field theory coupled to two-dimensional 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(dH)] = dim[N], where the fractal dimension d(H) = 3.58 +/- 0.04. This result lends support to the conjecture d(H) = -2 alpha(1)/alpha(-1), where alpha(-n) is the gravitational dressing exponent of a spin-less primary field of conformal weight (n + 1, n + 1), and it disfavors the alternative prediction d(H) = -2/gamma(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 I 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. (C) 1997 Elsevier Science B.V.
引用
收藏
页码:177 / 184
页数:8
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