Gauge invariant renormalizability of quantum gravity
arXiv:2210.09271 · doi:10.1007/978-981-19-3079-9_9-1
Abstract
The current understanding of renormalization in quantum gravity (QG) is based on the fact that UV divergences of effective actions in the covariant QG models are covariant local expressions. This fundamental statement plays a central role in QG and, therefore, it is important to prove it for the widest possible range of the QG theories. Using the Batalin-Vilkovisky technique and the background field method, we elaborate the proof of gauge invariant renormalizability for a generic model of quantum gravity that is diffeomorphism invariant and does not have additional, potentially anomalous, symmetries.
arXiv commentReferences added. 39 pages, no figures. Invited chapter for the Section "Effective Quantum Gravity" of the "Handbook of Quantum Gravity" (Eds. C. Bambi, L. Modesto and I.L. Shapiro, Springer Singapore, expected in 2023). Review paper is mainly based on arXiv:1902.04687, with permission from Physical Review D
References in corpus (36)
- Super-renormalizable Quantum Gravity
- Consistent couplings between fields with a gauge freedom and deformations of the master equation
- Antibracket, Antifields and Gauge-Theory Quantization
- Geometry of Batalin-Vilkovisky quantization
- Super-renormalizable & Finite Gravitational Theories
- Some remarks on high derivative quantum gravity
- Superrenormalizable quantum gravity with complex ghosts
- Are Nonrenormalizable Gauge Theories Renormalizable?
- Super-renormalizable or Finite Lee-Wick Quantum Gravity
- Nonlocal and quasi-local field theories
- Counting ghosts in the "ghost-free" non-local gravity
- Local BRST cohomology in Einstein--Yang--Mills theory
- Do we have unitary and (super)renormalizable Quantum Gravity below Planck scale?
- Renormalization group in super-renormalizable quantum gravity
- On the gravitational seesaw in higher-derivative gravity
- Renormalization of gauge theories in the background-field approach
- Gauge invariant renormalizability of quantum gravity
- On the ghost-induced instability on de Sitter background
- Field-dependent BRST transformations in Yang-Mills theory
- Stability of Schwarzschild black holes in fourth-order gravity revisited
- Background field method and nonlinear gauges
- Extended antifield-formalism
- Covariant BRST Quantization of Unimodular Gravity I -- Formulation with antisymmetric tensor ghosts --
- A systematic study of finite BRST-BV transformations in field-antifield formalism
- Background gauge renormalization and BRST identities
- On the Gauge-Independence of the S-Matrix
- On a gauge-invariant deformation of a classical gauge-invariant theory
- General Procedure of Gauge Fixings and Ghosts
- Gauge dependence and multiplicative renormalization of Yang-Mills theory with matter fields
- Multiplicative renormalization of Yang-Mills theories in the background-field formalism
- Gauge (in)dependence and background field formalism
- Vacuum stress-tensor in SSB theories
- Closed description of arbitrariness in resolving quantum master equation
- Reflection positivity in nonlocal gravity
- BRST-BV quantization of gauge theories with global symmetries
- On the quantum Batalin-Vilkovisky formalism and the renormalization of non linear symmetries