Background Free Quantum Gravity based on Conformal Gravity and Conformal Field Theory on M^4

TL;DR

This paper develops a background-free quantum gravity framework using conformal field theory on M^4, emphasizing quantum diffeomorphism symmetry and conformal invariance to exclude unphysical fields.

Contribution

It constructs a background-free quantum gravity model based on conformal field theory, introducing a nonperturbative quantization of the conformal factor and analyzing the resulting algebraic structures.

Findings

Physical fields are scalar with conformal dimension 4.

Tensor fields outside the unitarity bound are excluded.

Quantum algebra is computed on M^4 using operator products.

Abstract

We study four dimensional quantum gravity formulated as a certain conformal field theory at the ultraviolet fixed point, whose dynamics is described by the combined system of Riegert-Wess-Zumino and Weyl actions. Background free nature comes out as quantum diffeomorphism symmetry by quantizing the conformal factor of the metric field nonperturbatively. In this paper, Minkowski background M^4 is employed in practice. The generator of quantum diffeomorphism that forms conformal algebra is constructed. Using it, we study the composite scalar operator that becomes a good conformal field. We find that physical fields are described by such scalar fields with conformal dimension 4. Consequently, tensor fields outside the unitarity bound are excluded. Computations of quantum algebra on M^4 are carried out in the coordinate space using operator products of the fields. The nilpotent BRST operator is also constructed.