Geometrical Construction of Heterogeneous Loop Amplitudes in 2D Gravity

TL;DR

This paper demonstrates that heterogeneous loop amplitudes in 2D gravity can be derived purely through geometrical considerations, confirmed by matrix model calculations, suggesting a universal geometric approach.

Contribution

It introduces a geometric method to derive heterogeneous loop amplitudes in 2D gravity, validated by matrix model analysis, advancing understanding of boundary configurations.

Findings

Disk amplitude matches geometrical and matrix model results

Geometrical considerations can reproduce heterogeneous loop amplitudes

Potential universality of geometric derivation for all heterogeneous amplitudes

Abstract

We study a disk amplitude which has a complicated heterogeneous matter configuration on the boundary in a system of the (3,4) conformal matter coupled to two-dimensional gravity. It is analyzed using the two-matrix chain model in the large N limit. We show that the disk amplitude calculated by Schwinger-Dyson equations can completely be reproduced through purely geometrical consideration. From this result, we speculate that all heterogeneous loop amplitudes can be derived from the geometrical consideration and the consistency among relevant amplitudes.