Quantum-Gravity Path-Integrals on Simplicial Lattices

TL;DR

This paper explores Euclidean quantum gravity path-integrals using Regge calculus on simplicial lattices, revealing an entropy-dominated phase with small negative curvature through computer simulations.

Contribution

It introduces a lower limit on simplex fatness in Regge calculus and compares regular and irregular triangulations in quantum gravity simulations.

Findings

Identifies an entropy-dominated phase with negative curvature

Demonstrates the effect of fatness restriction on phase structure

Compares regular and irregular triangulations in quantum gravity

Abstract

Euclidean quantum-gravity path-integrals are investigated within Regge calculus by computer simulations. The domain of integration is restricted by introducing a lower limit for the fatness of each simplex. We use the standard hypercubic triangulation of the 4-torus and irregularly triangulated lattices obtained by inserting a small number of vertices using barycentric subdivision. For limited fatness we find an entropy dominated phase with small negative curvature both for the regular and the irregular triangulation.