Vertex Operators in 4D Quantum Gravity Formulated as CFT

TL;DR

This paper investigates vertex operators in 4D quantum gravity formulated as a conformal field theory, demonstrating their invariance, singularity structure, and algebraic properties under conformal symmetry.

Contribution

It constructs conformally invariant gravitational vertex operators in 4D quantum gravity and analyzes their algebraic and singularity properties.

Findings

Vertex operators are invariant under conformal transformations.

Short distance singularities have physically correct signs.

Conformal algebra persists with cosmological constant perturbation.

Abstract

We study vertex operators in 4D conformal field theory derived from quantized gravity, whose dynamics is governed by the Wess-Zumino action by Riegert and the Weyl action. Conformal symmetry is equal to diffeomorphism symmetry in the ultraviolet limit, which mixes positive-metric and negative-metric modes of the gravitational field and thus these modes cannot be treated separately in physical operators. In this paper, we construct gravitational vertex operators such as the Ricci scalar, defined as space-time volume integrals of them are invariant under conformal transformations. Short distance singularities of these operator products are computed and it is shown that their coefficients have physically correct sign. Furthermore, we show that conformal algebra holds even in the system perturbed by the cosmological constant vertex operator as in the case of the Liouville theory shown by Curtright and Thorn.