Living Reviews in Relativity

"The Asymptotic Safety Scenario in Quantum Gravity"
Max Niedermaier and Martin Reuter  

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1 Introduction and Survey
1.1 Survey of the scenario
1.2 Evidence for asymptotic safety
1.3 Some working definitions
1.4 Relation to other approaches
1.5 Discussion of possible objections
2 Renormalizing the Non-Renormalizable
2.1 Perturbation theory and continuum limit
2.2 Functional flow equations and UV renormalization
2.3 Towards Quantum Gravidynamics
2.4 Dimensional reduction of residual interactions in UV
3 Asymptotic Safety from Dimensional Reduction
3.1 2 + 2 truncation of Einstein gravity + matter
3.2 Collinear gravitons, Dirac quantization, and conformal factor
3.3 Tamed non-renormalizability
3.4 Non-Gaussian fixed point and asymptotic safety
4 Asymptotic Safety from the Effective Average Action
4.1 The effective average action for gravity and its FRGE
4.2 Geometries at different resolution scales
4.3 Truncated flow equations
4.4 Einstein–Hilbert and R2 truncations
5 Conclusions
6 Acknowledgements
A Reminder on Kadanoff–Wilson Renormalization
B The Background Effective Action
B.1 Standard effective action and its perturbative construction
B.2 Survey of background field formalisms
B.3 Renormalization of Riemannian sigma-models
C The Effective Average Action
C.1 Definition and basic properties
C.2 Flow equation
C.3 Decoupling properties
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