We hereby introduce and extensively study a class of non-polynomial higher derivative theories gravity that realize ultraviolet (UV) completion Einstein general relativity. These are unitary (ghost free) at most only one-loop divergences survive. The outcome is super-renormalizable in even dimension finite odd dimension. Moreover, we explicitly prove D=4 there exists an extension the theory completely all beta functions vanish one-loop. results can be easily extended extra dimensions it...

It is well known that standard gauge theories are renormalizable in D=4 while Einstein gravity D=2. This where the research field of two derivatives currently standing. We hereby present a class weakly non-local higher derivative gravitational and universally consistent at quantum level any spacetime dimension. These unitary (ghost-free) perturbatively renormalizable. Moreover, we can always find simple extension these super-renormalizable or finite even odd dimensions. Finally, propose...

We explicitly prove that the Weyl conformal symmetry solves black hole singularity problem, otherwise unavoidable in a generally covariant local or non-local gravitational theory. Moreover, we yield explicit examples of and theories enjoying diffeomorphism (in short co-covariant theories). Following seminal paper by Narlikar Kembhavi, provide an construction singularity-free spherically symmetric axi-symmetric exact solutions for spacetimes conformally equivalent to Schwarzschild Kerr...

The $R+R^2$, shortly named "$R^2$" ("Starobinsky") inflationary model, represents a fully consistent example of one-parameter scenario. This model has "graceful exit" from inflation and provides mechanism for subsequent creation final thermalization the standard matter. Moreover, it produces very good fit observed spectrum primordial perturbations. In present paper we show explicitly that $R^2$ spacetime is an exact solution range weakly non-local (quasi-polynomial) gravitational theories,...

One of the main advantages super-renormalizable higher derivative quantum gravity models is possibility to derive exact beta functions, by making perturbative one-loop calculations. We perform such a calculation for Newton constant using Barvinsky-Vilkovisky trace technology. The result well-defined in large class sense that renormalization group functions do not depend on gauge-fixing condition. Finally, we discuss apply results nonlocal gravitational theories which are free massive...

We explicitly compute the tree-level on-shell four-graviton amplitudes in four, five and six dimensions for local weakly nonlocal gravitational theories that are quadratic both, Ricci scalar curvature with form factors of d'Alembertian operator inserted between. More specifically we interested renormalizable, super-renormalizable or finite theories. The scattering these turn out to be same as ones Einstein gravity regardless explicit factors. As a special case Weyl conformal identically...

We give here a list of exact classical solutions large class weakly nonlocal theories gravity, which are unitary and super-renormalizable (or finite) at quantum level. It is explicitly shown that flat Ricci-flat spacetimes as well maximally symmetric manifolds the equation motion. Therefore, well-known physical like Schwarzschild, Kerr, (Anti-) de Sitter serve for standard matter content. In dimension higher than four we can also have Anti-de in presence positive cosmological constant....

We explicitly compute the one-loop exact beta function for a nonlocal extension of standard gauge theory, in particular Yang-Mills and QED. The made weakly kinetic term local potential field, is unitary (ghost-free) perturbatively super-renormalizable. Moreover, action we can always choose (consisting one "killer operator") to make zero running coupling constant. outcome "a UV finite theory any interaction". Our calculations are done D=4, but results be generalized even or odd spacetime...

We analyze the unitarity properties of higher derivative quantum field theories which are free ghosts and ultraviolet singularities. point out that in spite absence most these not unitary. This result confirms difficulties finding a consistent theory gravity.

We explicitly prove that a class of finite quantum gravitational theories (in odd as well in even dimension) is actually range anomaly-free conformally invariant the spontaneously broken phase conformal Weyl symmetry. At classical level we show how invariance likely able to tame spacetime singularities plague not only Einstein gravity, but also local and weakly non-local higher derivative theories. This latter statement rigorously proved by singularity theorem applies large Following seminal...

We hereby study the properties of a large class weakly nonlocal gravitational theories around (anti--) de Sitter spacetime background. In particular, we explicitly prove that kinetic operator for graviton field has same structure as one in Einstein-Hilbert theory any maximally symmetric spacetime. Therefore, perturbative spectrum is standard general relativity, while propagator on mere generalization from Einstein's gravity derived and extensively studied several previous papers. At quantum...

We study the formation and evaporation of a spherically symmetric black hole in conformal gravity. From collapse thin shell radiation, we find singularity-free non-rotating hole. This has same Hawking temperature as Schwarzschild with mass, it completely evaporates either finite or an infinite time, depending on ensemble. consider analysis both canonical micro-canonical statistical ensembles. Last, discuss corresponding Penrose diagram this physical process.

The "exact" or "functional" renormalization group equation describes the flow of effective average action $$\Gamma _k$$ . ordinary _0$$ can be obtained by integrating from an ultraviolet scale $$k=\Lambda $$ down to $$k=0$$ We give several examples such calculations at one-loop, both in renormalizable and field theories. reproduce four-point scattering amplitude case a real scalar theory with quartic potential pion chiral Lagrangian. In gauge theories, we vacuum polarization QED Yang–Mills...

Abstract We explore quantum field theories with fractional d'Alembertian □ γ . Both a scalar theory derivative-dependent potential and gauge are super-renormalizable for power 1 < ≤ 2, one-loop > 2 finite if one introduces killer operators. Unitarity is achieved by splitting the kinetic term into product of massive operators, eventually sending masses to zero so desired. Fractional gravity also discussed found be 4 4. To make it unitary, we combine procedure generalization Anselmi-Piva...

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

Extending previous work on the formation and evaporation of black holes in conformal gravity, present paper we study gravitational collapse a spherically symmetric electrically charged thin shell radiation. The process creates singularity-free hole. Assuming that charge $Q$ is constant, final product an extremal remnant with $M=Q$, which reached infinite amount time. We also discuss issue singularity thermodynamics Weyl's gravity.

Abstract We study the quantum gravitational system coupled to a charged scalar, Dirac fermions, and electromagnetic fields. use “exact” or “functional” renormalization group equation derive effective action $$\Gamma _0$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>Γ</mml:mi> <mml:mn>0</mml:mn> </mml:msub> </mml:math> by integrating flow from ultraviolet scale down $$k=0$$ <mml:mrow> <mml:mi>k</mml:mi> <mml:mo>=</mml:mo> </mml:mrow> . The resulting consists of...

We consider the phenomenon of classicalization in nonlinear sigma models with both positive and negative target space curvature any number derivatives. find that theories only two derivatives exhibit a weak form classicalization, quantitative results depend on sign curvature. Nonlinear higher show strong which is independent argue may actually be equivalent to asymptotic safety, whereas seems genuinely different phenomenon. also discuss possible ambiguities definition classical limit.

Conformal symmetry always played an important role in field theory (both quantum and classical) gravity. We present construction of conformal gravity discuss its features regarding scattering amplitudes effective action. First, the long complicated story UV-divergences is recalled. With development UV-finite higher derivative (or non-local) gravitational theory, all problems with infinities spacetime singularities might be completely solved. Moreover, non-local reveals itself to ghost-free,...

The exact one-loop beta functions for the four-derivative terms (Weyl tensor squared, Ricci scalar squared and Gauss-Bonnet) are derived minimal six-derivative quantum gravity (QG) theory in four spacetime dimensions. calculation is performed by means of Barvinsky Vilkovisky generalized Schwinger-DeWitt technique. With this result we gain, first time, full set relevant a super-renormalizable model QG. complete renormalization group (RG) equations, including also those Newton cosmological...

We compute the scale-dependence of Planck mass and vacuum expectation value Higgs field using two very different renormalization group methods: a "holographic" procedure based on Einstein's equations in five dimensions with matter confined to 3-brane, "functional" four Wilsonian momentum cutoff. Both calculations lead similar results, suggesting that coupled theory approaches non-trivial fixed point ultraviolet.

We compute the area term contribution to black holes' entanglement entropy (using conical technique) for a class of local or weakly non-local super-renormalizable gravitational theories coupled matter. For first time, we explicitly prove that all beta functions in proposed theory, except cosmological constant, are identically zero cut-off regularization scheme and not only dimensional scheme. In particular, show there is no divergence quadratic hence function Newton constant. As consequence...