Another derivation of the geometrical KPZ relations

TL;DR

This paper presents a physicist's derivation of the geometrical KPZ relations using heat kernel methods, providing a covariant framework for neighborhoods of fractals in 2D quantum gravity and linking these relations to conformal field theory.

Contribution

It introduces a new covariant derivation of the KPZ relations based on heat kernel techniques, connecting fractal neighborhoods in 2D quantum gravity with conformal field theory.

Findings

Derivation of KPZ relations via heat kernel methods

Covariant definition of fractal neighborhoods in 2D quantum gravity

Connection established between KPZ relations and conformal field theory

Abstract

We give a physicist's derivation of the geometrical (in the spirit of Duplantier-Sheffield) KPZ relations, via heat kernel methods. It gives a covariant way to define neighborhoods of fractals in 2d quantum gravity, and shows that these relations are in the realm of conformal field theory.