Regge gravity on general triangulations

TL;DR

This study explores quantum gravity using Regge calculus on general four-dimensional triangulations, revealing how lattice irregularities influence phase structure and observable dependence on the measure.

Contribution

It introduces analysis of Regge gravity on non-regular triangulations, showing how lattice irregularities affect phase behavior and measure dependence in quantum gravity models.

Findings

Lattice spikes occur at vertices with low coordination numbers.

Observables depend on the measure in non-regular triangulations.

Phase structure varies with triangulation and local coordination numbers.

Abstract

We investigate quantum gravity in four dimensions using the Regge approach on triangulations of the four-torus with general, non-regular incidence matrices. We find that the simplicial lattice tends to develop spikes for vertices with low coordination numbers even for vanishing gravitational coupling. Different to the regular, hypercubic lattices almost exclusively used in previous studies, we find now that the observables depend on the measure. Computations with nonvanishing gravitational coupling still reveal the existence of a region with well-defined expectation values. However, the phase structure depends on the triangulation. Even with additional higher- order terms in the action the critical behavior of the system changes with varying (local) coordination numbers.