On the Perturbative Quantization of Einstein-Hilbert Gravity Embedded in a Higher Derivative Model

TL;DR

This paper explores the perturbative quantization of Einstein-Hilbert gravity extended with higher derivative terms, aiming for a renormalizable quantum gravity model using advanced renormalization techniques.

Contribution

It introduces a higher derivative extension of Einstein-Hilbert gravity as a regulator, applying the BPHZL renormalization scheme and analyzing the physical state space via the quartet mechanism.

Findings

Achieved a renormalizable perturbative quantum gravity model.

Derived renormalization group and Callan-Symanzik equations for the extended theory.

Established the physical state space using the quartet mechanism.

Abstract

In a perturbative approach Einstein-Hilbert gravity is quantized about a flat background. In order to render the model power counting renormalizable, higher order curvature terms are added to the action. They serve as Pauli-Villars type regulators and require an expansion in the number of fields in addition to the standard expansion in the number of loops. Renormalization is then performed within the BPHZL scheme, which provides the action principle to construct the Slavnov-Taylor identity and invariant differential operators. The final physical state space of the Einstein-Hilbert theory is realized via the quartet mechanism of Kugo and Ojima. Renormalization group and Callan-Symanzik equation are derived for the Green functions and, formally, also for the $S$-matrix.