Monte Carlo Simulation of 2-D Quantum Gravity as Open Dynamically Triangulate Random Surfaces

TL;DR

This paper presents a Monte Carlo simulation method for 2-D quantum gravity using dynamically triangulated random surfaces with boundaries, successfully reproducing theoretical predictions in pure gravity scenarios.

Contribution

Introduces a Monte Carlo algorithm for simulating 2-D quantum gravity with boundaries, allowing boundary length fluctuations while keeping the total number of triangles fixed.

Findings

Algorithm reproduces theoretical expectations for pure gravity

Works with matter fields presence

Validates the Monte Carlo approach for boundary fluctuations

Abstract

We describe a Monte Carlo procedure for the simulation of dynamically triangulate random surfaces with a boundary (topology of a disk). The algorithm keeps the total number of triangles fixed, while the length of the boundary is allowed to fluctuate. The algorithm works in the presence of matter fields. We here present results for the pure gravity case. The algorithm reproduces the theoretical expectations.