Operator Product Expansion in Two-Dimensional Quantum Gravity

TL;DR

This paper investigates the operator product expansion in two-dimensional quantum gravity by analyzing correlation functions with fixed geodesic distances, suggesting OPE validity in quantum gravity with careful interpretation.

Contribution

It introduces a framework for studying correlation functions with fixed geodesic distances and demonstrates the potential validity of the operator product expansion in quantum gravity.

Findings

OPE may hold in two-dimensional quantum gravity

Correlation functions with fixed geodesic distances are useful

Careful interpretation is needed for physical meaning

Abstract

We consider correlation functions of operators and the operator product expansion in two-dimensional quantum gravity. First we introduce correlation functions with geodesic distances between operators kept fixed. Next by making two of the operators closer, we examine if there exists an analog of the operator product expansion in ordinary field theories. Our results suggest that the operator product expansion holds in quantum gravity as well, though special care should be taken regarding the physical meaning of fixing geodesic distances on a fluctuating geometry.