Einstein-Hilbert gravity, higher derivatives and a scalar matter field

TL;DR

This paper investigates the renormalization of Einstein-Hilbert gravity with higher derivatives coupled to a massless scalar field, demonstrating the removal of negative norm states at one-loop and establishing finiteness properties.

Contribution

It extends previous pure gravity studies by including matter fields and analyzes the renormalization and finiteness in this combined framework.

Findings

Negative norm states from higher derivatives vanish at one-loop.

Finiteness properties are established in the Landau gauge.

Provides Slavnov-Taylor identity and symmetric PDEs for the theory.

Abstract

The present paper extends two previous one's on pure gravity dealing with Einstein-Hilbert and higher derivatives by including a massless scalar field as representative of matter. We study the renormalization to all orders of perturbation theory, provide the Slavnov-Taylor identity, symmetric partial differential equations and derive finiteness properties in the Landau gauge. It is shown that beginning with one-loop negative norm states originating from higher derivatives disappear.