Numerical Analysis of Scaling Behavior in 4D Quantum Simplicial Gravity

概要

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In general two-dimensional quantum gravity has been regarded as the theory of a toy model of four-dimensional quantum gravity. Recent numerical developments started with two-dimensional simplicial gravity and have now reached the point of subjecting to simulate higher dimensional case. Spacetime structures in four dimensions are investigated by using the concept of the geodesic distance in simplicial quantum gravity. On the analogy of the loop length distribution in two dimensions, the scaling relations of the boundary volume distribution in four dimensions are shown in the three phases i. e. weak, critical and strong phase. In each phase the different scaling relations are found. Especially it is shown that the boundary volume distribution gives two different scaling variables in the critical phase. Furthermore recently two-dimensional simplicial gravity has been interesting from the point of view of the string field theory in non-critical dimensions. It is discussed that there is a possibility of the constructive definition of critical strings on the string-worldsheet and four-dimensional quantum gravity as the continuum field theory.
東海大学の論文