Fractal Structure in Two-Dimensional Quantum Regge Calculus

Abstract

We study the fractal structure of the surface in two-dimensional quantum Regge calculus by performing Monte Carlo simulation with up to 200,000 triangles. The result can be compared with the universal scaling function obtained analytically in the continuum limit of dynamical triangulation, which provides us with a definite criterion whether Regge calculus serves as a proper regularization of quantum gravity. When the scale-invariant measure is taken as the measure of the link-length integration, we observe the correct scaling behavior in the data for the type of loop attached to a baby universe. The data seem to converge to the universal scaling function as the number of triangles is increased. The data for the type of loop attached to the mother universe, on the other hand, shows no scaling behavior up to the present size.

13 pages + 8 figures, LaTeX, UT-683, KEK-TH-401 (double-spacing command removed. sorry.)

References in corpus (2)

• Transfer Matrix Formalism for Two-Dimensional Quantum Gravity and Fractal Structures of Space-time
• Baby universes in 2d quantum gravity

Cited by in corpus (6)

• Tensor network approach to 2d Lorentzian quantum Regge calculus
• Measuring the string susceptibility in 2D simplicial quantum gravity using the Regge approach
• Multicanonical simulation of 3D dynamical triangulation model and a new phase structure
• Feynman Rules for Simplicial Gravity
• Simplicial Quantum Gravity on a Randomly Triangulated Sphere
• How to Measure the Fractal Geometry of the Relativistic Fermion Propagator