How to understand the Structure of Beta Functions in Six-derivative Quantum Gravity?
arXiv:2205.09893 · doi:10.14311/AP.2022.62.0118
Abstract
We extensively motivate the studies of higher-derivative gravities, and in particular we emphasize which new quantum features theories with six derivatives in their definitions possess. Next, we discuss the mathematical structure of the exact on the full quantum level beta functions obtained previously for three couplings in front of generally covariant terms with four derivatives (Weyl tensor squared, Ricci scalar squared and the Gauss-Bonnet scalar) in minimal six-derivative quantum gravity in spacetime dimensions. The fundamental role here is played by the ratio of the coupling in front of the term with Weyl tensors to the coupling in front of the term with Ricci scalars in the original action. We draw a relation between the polynomial dependence on and the absence/presence of enhanced conformal symmetry and renormalizability in the models where formally in the case of four- and six-derivative theories respectively.
arXiv comment40 pages, contribution to the AAMP XVIII conference "Algebraic and analytic methods in physics'' (CTU, Prague 2021)
References in corpus (38)
- Super-renormalizable Quantum Gravity
- No-ghost theorem for the fourth-order derivative Pais-Uhlenbeck oscillator model
- Making the Case for Conformal Gravity
- Black Holes in Higher-Derivative Gravity
- Super-renormalizable & Finite Gravitational Theories
- Some remarks on high derivative quantum gravity
- Superrenormalizable quantum gravity with complex ghosts
- Einstein Gravity from Conformal Gravity
- Spherically Symmetric Solutions in Higher-Derivative Gravity
- Exactly solvable PT-symmetric Hamiltonian having no Hermitian counterpart
- Unitarity, stability and loops of unstable ghosts
- Super-renormalizable or Finite Lee-Wick Quantum Gravity
- Benign vs malicious ghosts in higher-derivative theories
- Fakeons And Lee-Wick Models
- Perturbative unitarity of Lee-Wick quantum field theory
- Universally Finite Gravitational & Gauge Theories
- Quantum Gravity, Fakeons And Microcausality
- Do we have unitary and (super)renormalizable Quantum Gravity below Planck scale?
- Renormalization group in super-renormalizable quantum gravity
- Consistency of the Regularization of Gauge Theories by High Covariant Derivatives
- Cutkosky rules and perturbative unitarity in Euclidean nonlocal quantum field theories
- Mass Generation, the Cosmological Constant Problem, Conformal Symmetry, and the Higgs Boson
- Finite quantum gauge theories
- On the ghost-induced instability on de Sitter background
- Black hole evaporation in conformal gravity
- Gauge and parametrization dependencies of the one-loop counterterms in the Einstein gravity.
- Exact solutions and spacetime singularities in nonlocal gravity
- Nonlinear stability in nonlocal gravity
- Finite Conformal Quantum Gravity and Nonsingular Spacetimes
- Conformal Symmetry in Field Theory and in Quantum Gravity
- Renormalization Group in Six-derivative Quantum Gravity
- Conformal Invariance and the Metrication of the Fundamental Forces
- Recent Progress in Fighting Ghosts in Quantum Gravity
- Infrared behavior of Weyl Gravity: Functional Renormalization Group approach
- Reflection positivity in nonlocal gravity
- Towards Ghost-Free Gravity and Standard Model
- Asymptotic freedom and higher derivative gauge theories
- Spectral action approach to higher derivative gravity