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Keywords = super-renormalizable gravity

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30 pages, 405 KB  
Article
Ultraviolet Finiteness or Asymptotic Safety in Higher Derivative Gravitational Theories
by Lesław Rachwał
Universe 2022, 8(4), 229; https://doi.org/10.3390/universe8040229 - 8 Apr 2022
Cited by 3 | Viewed by 3667
Abstract
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Alternative Gravities and Fundamental Cosmology)
44 pages, 416 KB  
Review
Conformal Symmetry in Field Theory and in Quantum Gravity
by Lesław Rachwał
Universe 2018, 4(11), 125; https://doi.org/10.3390/universe4110125 - 15 Nov 2018
Cited by 27 | Viewed by 4638
Abstract
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 [...] Read more.
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 might be completely solved. Moreover, the non-local quantum conformal theory reveals itself to be ghost-free, so the unitarity of the theory should be 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 can be taken to vanish 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. Full article
(This article belongs to the Special Issue Gravity, Black Holes and Cosmology XXI)
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