BRST Analysis of Physical Fields and States for 4D Quantum Gravity on R x S^3

TL;DR

This paper investigates the structure of physical fields and states in a background-free quantum gravity model based on conformal gravity, using BRST analysis on an R x S^3 background, revealing key properties like state-operator correspondence.

Contribution

It constructs a nilpotent BRST operator for 4D quantum gravity on R x S^3 and analyzes physical states as real primary scalars with conformal weight, clarifying their properties.

Findings

Identification of physical fields as real primary scalars

Construction of a nilpotent BRST operator for background-free quantum gravity

Clarification of state-operator correspondence and norm structure

Abstract

We consider the background-free quantum gravity based on conformal gravity with the Riegert-Wess-Zumino action, which is formulated in terms of a conformal field theory. Employing the $R \times S^3$ background in practice, we construct the nilpotent BRST operator imposing diffeomorphism invariance. Physical fields and states are analyzed, which are given only by real primary scalars with a definite conformal weight. With attention to the presence of background charges, various significant properties, such as the state-operator correspondence and the norm structure, are clarified with some examples.