Renormalization and dimensional regularization for a scalar field with Gauss-Bonnet-type coupling to curvature

TL;DR

This paper investigates a scalar field with Gauss-Bonnet coupling in curved spacetime, deriving the energy-momentum tensor and counterterms for renormalization using dimensional regularization, applicable in various dimensions.

Contribution

It provides explicit forms of the energy-momentum tensor and counterterms for a scalar field with Gauss-Bonnet coupling, linking n-wave and effective action methods in renormalization.

Findings

Derived the energy-momentum tensor for the coupled scalar field.

Identified the first three counterterms for vacuum averages.

Established equivalence of counterterms in different renormalization schemes.

Abstract

We consider a scalar field with a Gauss-Bonnet-type coupling to the curvature in a curved space-time. For such a quadratic coupling to the curvature, the metric energy-momentum tensor does not contain derivatives of the metric of orders greater than two. We obtain the metric energy-momentum tensor and find the geometric structure of the first three counterterms to the vacuum averages of the energy-momentum tensor for an arbitrary background metric of an N-dimensional space-time. In a homogeneous isotropic space, we obtain the first three counterterms of the n-wave procedure, which allow calculating the renormalized values of the vacuum averages of the energy-momentum tensors in the dimensions N=4,5. Using dimensional regularization, we establish that the geometric structures of the counterterms in the $n$-wave procedure coincide with those in the effective action method.