MINBU Distribution of Two Dimensional Quantum Gravity: Simulation Result and Semiclassical Analysis

TL;DR

This paper investigates the distribution of minimal neck baby universes in two-dimensional quantum gravity through Monte Carlo simulations and semiclassical analysis, revealing a crossover phenomenon influenced by the $R^2$-term and central charge.

Contribution

It provides new simulation data and a semiclassical framework for understanding MINBU distributions in 2D quantum gravity with $R^2$-terms, highlighting the crossover behavior.

Findings

Identification of crossover at certain baby universe sizes

Dependence of distribution on central charge and $R^2$-coupling

Role of $R^2$-Liouville solution in semiclassical analysis

Abstract

We analyse MINBU distribution of 2 dimensional quantum gravity. New data of R$^2$-gravity by the Monte Carlo simulation and its theoretical analysis by the semiclassical approach are presented. The cross-over phenomenon takes place at some size of the baby universe where the randomness competes with the smoothing force of $R^2$-term. The dependence on the central charge $c_m$\ and on the $R^2$-coupling are explained for the ordinary 2d quantum gravity and for $R^2$-gravity. The $R^2$-Liouville solution plays the central role in the semiclassical analysis. A total derivative term (surface term) and the infrared regularization play important roles . The surface topology is that of a sphere.