# Geometrical Interpretation of the KPZ Exponents

## TL;DR

This paper offers a geometric perspective on KPZ exponents in 2D quantum gravity, interpreting them as scaling exponents of correlation functions based on invariant geodesic distances.

## Contribution

It introduces a novel geometric interpretation of KPZ exponents as correlation function scaling exponents related to geodesic distances.

## Key findings

- KPZ exponents can be understood through correlation functions of invariant geodesic distances.
- Provides a new geometric framework for analyzing KPZ exponents in 2D quantum gravity.
- Supports the interpretation with theoretical evidence.

## Abstract

We provide evidence that the KPZ exponents in two-dimensional quantum gravity can be interpreted as scaling exponents of correlation functions which are functions of the invariant geodesic distance between the fields.