# Comment on “Quantum massive conformal gravity” by F. F. Faria

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## Abstract

In a recent paper in EPJC doi: 10.1140/epjc/s10052-016-4037-5, Faria has shown that quantum massive conformal gravity is renormalizable but has ghost states. We comment this paper on the aspect of renormalizability.

### Keywords

Ghost Conformal Transformation Conformal Symmetry Counter Term Euler DensityOn the other hand, Stelle has proposed the conformally non-invariant Lagrangian of \(\sqrt{-g}( R+a \tilde{C}^2+b R^2)\) to improve the perturbative properties of Einstein gravity [4]. The first two terms could be derived from (1) by making use of the conformal transformation (2). Also, one includes \(R^2\) term as a counter term of \(g_{\mu \nu }\). If \(ab\not =0\), the renormalizability was achieved but the unitarity was violated, which shows that the renormalizability is not compatible with the unitarity. Although the Weyl-squared term (\(\tilde{C}^2\)) improves the ultraviolet divergence, it induces ghost excitations which spoil the unitarity simultaneously. Here, the price one has to pay for making the theory renormalizable is the loss of unitarity.

Up to now, there is no obvious way to attain the renormalizability without violating the unitarity in quantizing the gravity.

### References

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## Copyright information

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