Common Structures in 2,3 and 4D Simplicial Quantum Gravity

Abstract

Two kinds of statistical properties of dynamical-triangulated manifolds (DT mfds) have been investigated. First, the surfaces appearing on the boundaries of 3D DT mfds were investigated. The string-susceptibility exponent of the boundary surfaces (${\tilde{\gamma }}_{st}$) of 3D DT mfds with $S^3$ topology near to the critical point was obtained by means of a MINBU (minimum neck baby universes) analysis; actually, we obtained ${\tilde{\gamma }}_{st}\approx -0.5$. Second, 3 and 4D DT mfds were also investigated by determining the string-susceptibility exponent near to the critical point from measuring the MINBU distributions. As a result, we found a similar behavior of the MINBU distributions in 3 and 4D DT mfds, and obtained ${\gamma }_{st}^{(3)}\approx {\gamma }_{st}^{(4)}\approx 0$. The existence of common structures in simplicial quantum gravity is also discussed.

Comments: 3 pages, latex, 3 ps figures, uses espcrc2.sty. Talk presented at LATTICE97(gravity)