Renormalizability of Massive Gravity in Three Dimensions

Higher order renormalization in 4D quantum gravity is carried out using dimensional regularization with great care concerning the conformal-mode dependence. In this regularization, resummation can be automatically carried out without making an assumption like that of David, Distler and Kawai. In this paper we consider a model of 4D quantum gravity coupled to QED. Resummation inevitably implies a four-derivative quantum gravity. The renormalizability is directly checked up to ...

The quantum gravity is formulated based on principle of local gauge invariance. The model discussed in this paper has local gravitational gauge symmetry and gravitational field appears as gauge field. The problems on quantization and renormalization of the theory are also discussed in this paper. In leading order approximation, the gravitational gauge field theory gives out classical Newton's theory of gravity. In first order approximation and for vacuum, the gravitational ga...

A particular higher-derivative extension of the Einstein-Hilbert action in three spacetime dimensions is shown to be equivalent at the linearized level to the (unitary) Pauli-Fierz action for a massive spin-2 field. A more general model, which also includes `topologically-massive' gravity as a special case, propagates the two spin 2 helicity states with different masses. We discuss the extension to massive ${\cal N}$-extended supergravity, and we present a `cosmological' exte...

We introduce new techniques that can preserve unitarity of the system including ghost particles. Negative norms of the particles can be involved in zero-norm states by constraints of the physical space. These are useful to apply the higher-derivative propagator for quantum gravity to suppress divergences of vacuum energy and graviton mass correction. The quantum effects are mainly depending on the ghost mass scale. As the scale can be chosen in any order, the observed cosmolo...

We explore how the stability of metric perturbations in higher derivative theories of gravity depends on the energy scale of initial seeds of such perturbations and on a typical energy scale of the gravitational vacuum background. It is shown that, at least in the cases of specific cosmological backgrounds, that the unphysical massive ghost which is present in the spectrum of such theories is not growing up as a physical excitation and remains in the vacuum state, until the i...

Gauge theory of gravity is formulated based on principle of local gauge invariance. Because the model has strict local gravitational gauge symmetry, gauge theory of gravity is a perturbatively renormalizable quantum model. However, in the original model, all gauge gravitons are massless. We want to ask that whether there exists massive gravitons in Nature? In this paper, we will propose a gauge model with massive gravitons. The mass term of gravitational gauge field is introd...

We present a short and intuitive argument explaining why gravity is non-renormalizable. The argument is based on black-hole domination of the high energy spectrum of gravity and not on the standard perturbative irrelevance of the gravitational coupling. This is a pedagogical note, containing textbook material that is widely appreciated by experts and is by no means original.

We extensively study the ultraviolet quantum properties of a nonlocal action for gravity nonminimally coupled to matter. The theory unifies matter and gravity in an action principle such that all the classical solutions of Einstein's theory coupled to matter are also solutions of the nonlocal theory. At the quantum level, we show that the theory is power-counting super-renormalizable in even dimensions and finite in odd dimensions. A simple extension of the model compatible w...

A renormalizable theory of gravity is obtained if the dimension-less 4-derivative kinetic term of the graviton, which classically suffers from negative unbounded energy, admits a sensible quantisation. We find that a 4-derivative degree of freedom involves a canonical coordinate with unusual time-inversion parity, and that a correspondingly unusual representation must be employed for the relative quantum operator. The resulting theory has positive energy eigenvalues, normalis...

In a recent paper in EPJC March 2016, Faria has shown that quantum massive conformal gravity is renormalizable but has ghost states. We comment this paper on the aspect of renormalizability.