Weyl-Invariant Higher Curvature Gravity Theories in n Dimensions

TL;DR

This paper analyzes the particle spectrum and unitarity of Weyl-invariant quadratic curvature gravity theories in n dimensions, revealing conditions for unitarity and symmetry breaking in various vacua.

Contribution

It identifies the unique Weyl-invariant quadratic gravity theory that maintains unitarity in higher dimensions, extending previous models and analyzing symmetry breaking mechanisms.

Findings

Graviton remains massless in most cases, ensuring unitarity.

Weyl gauge field acquires mass through symmetry breaking.

The Weyl-invariant extension of Einstein-Gauss-Bonnet is the only viable quadratic theory.

Abstract

We study the particle spectrum and the unitarity of the generic n-dimensional Weyl-invariant quadratic curvature gravity theories around their (anti-)de Sitter [(A)dS] and flat vacua. Weyl symmetry is spontaneously broken in (A)dS and radiatively broken at the loop level in flat space. Save the three dimensional theory (which is the Weyl-invariant extension of the new massive gravity), the graviton remains massless and the unitarity requires that the only viable Weyl-invariant quadratic theory is the Weyl-invariant extension of the Einstein-Gauss-Bonnet theory. The Weyl gauge field on the other hand becomes massive. Symmetry breaking scale fixes all the dimensionful parameters in the theory.