Measure dependence of 2D simplicial quantum gravity

TL;DR

This paper investigates 2D Euclidean quantum gravity with R^2 interactions on spherical lattices, focusing on measuring the string susceptibility exponent using finite-size scaling and examining the effects of different scale-invariant measures.

Contribution

It introduces a method to measure the string susceptibility exponent in 2D quantum gravity with R^2 interactions using finite-size scaling.

Findings

Measured the string susceptibility exponent using finite-size scaling.

Compared effects of different scale-invariant measures on the results.

Analyzed the impact of R^2 interactions on quantum gravity on spherical lattices.

Abstract

We study pure 2D Euclidean quantum gravity with $R^2$ interaction on spherical lattices, employing Regge's formulation. We attempt to measure the string susceptibility exponent $\gamma_{\rm str}$ by using a finite-size scaling Ansatz in the expectation value of $R^2$. To check on effects of the path integral measure we investigate two scale invariant measures, the "computer" measure $dl/l$ and the Misner measure $dl/\sqrt A$.