Conformal Field Theory on R x S^3 from Quantized Gravity

TL;DR

This paper explores a renormalizable quantum gravity model on R x S^3, demonstrating how conformal symmetry emerges from quantized gravitational fields and analyzing the structure of physical states and unitarity within this framework.

Contribution

It shows that residual diffeomorphism invariance corresponds to conformal symmetry and constructs physical states with specific scaling dimensions in a quantized gravity setting.

Findings

Conformal symmetry is realized as residual gauge invariance in the model.

Negative-metric modes do not appear as independent physical states.

The model maintains unitarity despite mixing of metric modes.

Abstract

Conformal algebra on R x S^3 derived from quantized gravitational fields is examined. The model we study is a renormalizable quantum theory of gravity in four dimensions described by a combined system of the Weyl action for the traceless tensor mode and the induced Wess-Zumino action managing non-perturbative dynamics of the conformal factor in the metric field. It is shown that the residual diffeomorphism invariance in the radiation^+ gauge is equal to the conformal symmetry, and the conformal transformation preserving the gauge-fixing condition that forms a closed algebra quantum mechanically is given by a combination of naive conformal transformation and a certain field-dependent gauge transformation. The unitarity issue of gravity is discussed in the context of conformal field theory. We construct physical states by solving the conformal invariance condition and calculate their scaling dimensions. It is shown that the conformal symmetry mixes the positive-metric and the negative-metric modes and thus the negative-metric mode does not appear independently as a gauge invariant state at all.