Universally Finite Gravitational & Gauge Theories

It is well known that standard gauge theories are renormalizable in D=4 while Einstein gravity is renormalizable in D=2. This is where the research in the field of two derivatives theories is currently standing. We hereby present a class of weakly non-local higher derivative gravitational and gauge theories universally consistent at quantum level in any spacetime dimension. These theories are unitary (ghost-free) and perturbatively renormalizable. Moreover, we can always find a simple extension of these theories that is super-renormalizable or finite at quantum level in even and odd spacetime dimensions. Finally, we propose a super-renormalizable or finite theory for gravity coupled to matter laying the groundwork for a "finite standard model of particle physics" and/or a grand unified theory of all fundamental interactions.Comment: 19 page

Super-renormalizable & Finite Gravitational Theories

We hereby introduce and extensively study a class of non-polynomial higher derivative theories of gravity that realize a ultraviolet (UV) completion of Einstein general relativity. These theories are unitary (ghost free) and at most only one-loop divergences survive. The outcome is a class of theories super-renormalizable in even dimension and finite in odd dimension. Moreover, we explicitly prove in D=4 that there exists an extension of the theory that is completely finite and all the beta functions vanish even at one-loop. These results can be easily extended in extra dimensions and it is likely that the higher dimensional theory can be made finite too. Therefore we have the possibility for "finite quantum gravity" in any dimension.Comment: 17 page

Ultraviolet Finiteness or Asymptotic Safety in Higher Derivative Gravitational Theories

We present and discuss well known conditions for ultraviolet finiteness and asymptotic safety. The requirements for complete absence of ultraviolet divergences in quantum field theories and existence of a non-trivial fixed point for renormalization group flow in the ultraviolet regime are compared based on the example of a six-derivative quantum gravitational theory in $d=4$ spacetime dimensions. In this model, it is possible for the first time to have fully UV-finite quantum theory without adding matter or special symmetry, but by inclusion of additional terms cubic in curvatures. We comment on similarities and some apparent differences between the two approaches, but we show that they are both compatible to each other. Finally, we motivate the claim that actually asymptotic safety needs UV-finite models for providing explicit form of the ultraviolet limit of Wilsonian effective actions describing special situations at fixed points.Comment: 30 pages, contribution to the the Special Issue: Alternative Gravities and Fundamental Cosmolog

Conformal Symmetry in Field Theory and in Quantum Gravity

Conformal symmetry always played an important role in field theory (both quantum and classical) and in gravity. We present construction of quantum conformal gravity and discuss its features regarding scattering amplitudes and quantum effective action. First, the long and complicated story of UV-divergences is recalled. With the development of UV-finite higher derivative (or non-local) gravitational theory, all problems with infinities and spacetime singularities are solved. Moreover, the non-local quantum conformal theory reveals itself to be ghost-free, so the unitarity of the theory is safe. After the construction of UV-finite theory, we focused on making it manifestly conformally invariant using the dilaton trick. We also argue that in this class of theories conformal anomaly vanishes by fine-tuning the couplings. As applications of this theory, the constraints of the conformal symmetry on the form of the effective action and on the scattering amplitudes are shown. We also remark about the preservation of the unitarity bound for scattering. Finally, the old model of conformal supergravity by Fradkin and Tseytlin is briefly presented.Comment: 44 pages, review, journal version, Best Paper Award in Special Issue "Gravity, Black Holes and Cosmology XXI

Models for RG running for Gravitational couplings and applications

The plan for this thesis is as follows. In the first part we discuss the relation between two different RG flows: functional and holographic one. The bigger emphasis is put on the novel holographic RG flow and we devote full third chapter for studying holographic RG flow geometries. We are not only interested in flows for gravitational couplings, we also consider standard RG flows from field theories with matter. The second part of this work is divided into two chapters. In the fourth chapter we study classicalization for nonlinear sigma model understood as a toy example before attacking more diffcult problems of full quantum gravity. We also point there possible relations between classicalization and asymptotic safety as between two similar in some conditions mechanisms for UV completion. In the fofth chapter we consider universal 1-loop effective action in system of gravitating scalar field. We use new methods to derive its IR limit and we compute few low-energetic observables in such effective field theory of gravitational interactions. Finally in the sixth chapter we shortly collect main obtained results and conclude. The material presented in this work is partially based on two scientific articles [42] and [63], I published during my PhD studies

Exact solutions and spacetime singularities in nonlocal gravity

We give here a list of exact classical solutions of a large class of weakly nonlocal theories of gravity, which are unitary and super-renormalizable (or finite) at quantum level. It is explicitly shown that flat and Ricci-flat spacetimes as well as maximally symmetric manifolds are exact solutions of the equation of motion. Therefore, well-known physical spacetimes like Schwarzschild, Kerr, (Anti-) de Sitter serve as solutions for standard matter content. In dimension higher than four we can also have Anti-de Sitter solutions in the presence of positive cosmological constant. We pedagogically show how to obtain these exact solutions. Furthermore, for another version of the theory, written in the Weyl basis, Friedmann-Robertson-Walker (FRW) spacetimes are also exact solutions, when the matter content is given by conformal matter (radiation). We also comment on the presence of singularities and possible resolution of them in finite and conformally invariant theories. "Delocalization" is proposed as a way to solve the black hole singularity problem. In order to solve the problem of cosmological singularities it seems crucial to have a conformally invariant or asymptotically free quantum gravitational theory.Comment: 33 page