Analysis of All Dimensionful Parameters Relevant in Gravitational Dressing of Conformal Theories

TL;DR

This paper presents a covariant approach to derive the KPZ relation and analyze how all dimensionful parameters influence N-point functions in gravitationally dressed conformal theories across different genera.

Contribution

It introduces an alternative covariant derivation of the KPZ relation and studies the dependence of N-point functions on all dimensionful parameters for arbitrary genus.

Findings

Derived the KPZ relation using a covariant, background-independent method.

Analyzed the dependence of N-point functions on all dimensionful parameters.

Discussed implications for interpreting gravitationally dressed dimensions.

Abstract

Starting from a covariant and background independent definition of normal ordered vertex operators we give an alternative derivation of the KPZ relation between conformal dimensions and their gravitational dressed partners. With our method we are able to study for arbitrary genus the dependence of N-point functions on all dimensionful parameters. Implications for the interpretation of gravitational dressed dimensions are discussed.