New results on $\gamma_{\rm str}$ in 2D quantum gravity using Regge calculus

TL;DR

This paper investigates 2D quantum gravity on spherical surfaces using Regge calculus, incorporating an $R^2$ term, to evaluate its impact on the string susceptibility exponent and address methodological issues in its determination.

Contribution

It introduces a new analysis of $ ext{Regge}$ calculus with an $R^2$ term on spherical topologies, highlighting shortcomings and proposing potential solutions for measuring $ ext{γ}_{ ext{str}}$.

Findings

Severe issues in current methods for determining $ ext{γ}_{ ext{str}}$.

Inclusion of $R^2$ term affects the string susceptibility exponent.

Random triangulations help control irregular vertex effects.

Abstract

We study 2D quantum gravity on spherical topologies using the Regge calculus approach. Our goal is to shed new light upon the validity of the Regge approach to quantum gravity, which has recently been questioned in the literature. We incorporate an $R^2$ interaction term and investigate its effect on the value of the string susceptibility exponent $\gamma_{\rm str}$ using two different finite-size scaling Ans\"atze. Our results suggest severe shortcomings of the methods used so far to determine $\GS$ and show a possible cure of the problems. To have better control over the influence of irregular vertices, we choose besides the almost regular triangulation of the sphere as the surface of a cube a random triangulation according to the Voronoi-Delaunay prescription.