# A Toy Model of Discretized Gravity in Two Dimensions and its Extentions

## TL;DR

This paper introduces a novel discretized toy model of two-dimensional Euclidean quantum gravity, demonstrating a continuum limit and calculating physical quantities, with extensions to higher dimensions explored.

## Contribution

It presents a new discretization approach for 2D quantum gravity distinct from dynamical triangulation, establishing a continuum limit and extending the model to higher dimensions.

## Key findings

- Existence of a continuum limit for the model
- Calculation of the expectation value of the space-time volume
- Extensions of the model to higher dimensions

## Abstract

We propose a toy model of quantum gravity in two dimensions with Euclidean signature. The model is given by a kind of discretization which is different from the dynamical triangulation. We show that there exists a continuum limit and we can calculate some physical quantities such as the expectation value of the area, that is, the volume of the two dimensional euclidean space-time. We also consider the extensions of the model to higher dimensions.