BRST Invariant Higher Derivative Operators in 4D Quantum Gravity based on CFT

TL;DR

This paper develops BRST invariant higher derivative operators in 4D quantum gravity using conformal field theory, focusing on constructing physical operators related to Ricci scalar powers and analyzing their correlation functions.

Contribution

It introduces a method to construct BRST invariant operators for powers of Ricci scalar in background free 4D quantum gravity based on conformal field theory.

Findings

Constructed physical operators for Ricci scalar powers.

Defined correlation functions and discussed their physical interpretation.

Extended the understanding of gauge-invariant operators in 4D quantum gravity.

Abstract

We continue the study of physical fields for the background free 4D quantum gravity based on the Riegert-Wess-Zumino action, developed in Phys. Rev. D {\bf 85} (2012) 024028. The background free model is formulated in terms of a certain conformal field theory on M^4 in which conformal symmetry arises as gauge symmetry, namely diffeomorphism invariance. In this paper, we construct the physical field operator corresponding to any integer power of Ricci scalar curvature in the context of the BRST quantization. We also discuss how to define the correlation function and its physical meanings.