Quantum Gravity, Dynamical Triangulation and Higer Derivative Regularization

TL;DR

This paper investigates a four-dimensional discrete quantum gravity model incorporating higher derivative terms, analyzing its phase structure and continuum limit prospects through numerical simulations of simplicial manifolds.

Contribution

It introduces an $R^2$-term into the Euclidean quantum gravity model and studies its effects on phase transitions and universality classes.

Findings

Model with $R^2$-term shares phase transition characteristics with pure Einstein-Hilbert model.

The phase transition may be second order or higher, depending on parameters.

Average curvature at transition is positive, complicating scaling analysis.

Abstract

We consider a discrete model of euclidean quantum gravity in four dimensions based on a summation over random simplicial manifolds. The action used is the Einstein-Hilbert action plus an $R^2$-term. The phase diagram as a function of the bare coupling constants is studied in the search for a sensible continuum limit. For small values of the coupling constant of the $R^2$ term the model seems to belong to the same universality class as the model with pure Einstein-Hilbert action and exhibits the same phase transition. The order of the transition may be second or higher. The average curvature is positive at the phase transition, which makes it difficult to understand the possible scaling relations of the model.