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Asymptotic safety (sometimes also referred to as nonperturbative renormalizability) is a concept in quantum field theory which aims at finding a consistent and predictive quantum theory of the gravitational field. Its key ingredient is a nontrivial fixed point of the theory's renormalization group flow which controls the behavior of the coupling constants in the ultraviolet (UV) regime and renders physical quantities safe from divergences. Although originally proposed by Steven Weinberg to find a theory of quantum gravity, the idea of a nontrivial fixed point providing a possible UV completion can be applied also to other field theories, in particular to perturbatively nonrenormalizable ones. In this respect, it is similar to quantum triviality. The essence of asymptotic safety is the observation that nontrivial renormalization group fixed points can be used to generalize the procedure of perturbative renormalization. In an asymptotically safe theory the couplings do not need to be small or tend to zero in the high energy limit but rather tend to finite values: they approach a nontrivial UV fixed point. The running of the coupling constants, i.e. their scale dependence described by the renormalization group (RG), is thus special in its UV limit in the sense that all their dimensionless combinations remain finite. This suffices to avoid unphysical divergences, e.g. in scattering amplitudes. The requirement of a UV fixed point restricts the form of the bare action and the values of the bare coupling constants, which become predictions of the asymptotic safety program rather than inputs. As for gravity, the standard procedure of perturbative renormalization fails since Newton's constant, the relevant expansion parameter, has negative mass dimension rendering general relativity perturbatively nonrenormalizable. This has driven the search for nonperturbative frameworks describing quantum gravity, including asymptotic safety which — in contrast to other approaches—is characterized by its use of quantum field theory methods, without depending on perturbative techniques, however. At the present time, there is accumulating evidence for a fixed point suitable for asymptotic safety, while a rigorous proof of its existence is still lacking.
References
- 't Hooft, Gerard; Veltman, Martinus J. G. (1974). "One-loop divergences in the theory of gravitation". Annales de l'Institut Henri Poincaré. A 20 (1): 69–94. Bibcode: 1974AIHPA..20...69T. http://adsabs.harvard.edu/abs/1974AIHPA..20...69T
- Goroff, Marc H.; Sagnotti, Augusto (1986). "The ultraviolet behavior of Einstein gravity". Nuclear Physics. B 266 (3–4): 709–736. doi:10.1016/0550-3213(86)90193-8. Bibcode: 1986NuPhB.266..709G. https://dx.doi.org/10.1016%2F0550-3213%2886%2990193-8
- Weinberg, Steven (1978). "Critical Phenomena for Field Theorists". in Zichichi, Antonino. Understanding the Fundamental Constituents of Matter. The Subnuclear Series. 14. pp. 1–52. doi:10.1007/978-1-4684-0931-4_1. ISBN 978-1-4684-0931-4. https://dx.doi.org/10.1007%2F978-1-4684-0931-4_1
- Weinberg, Steven (1979). "Ultraviolet divergences in quantum theories of gravitation". General Relativity: An Einstein centenary survey. Cambridge University Press. pp. 790–831.
- Hamber, H. W. (2009). Quantum Gravitation - The Feynman Path Integral Approach. Springer Publishing. ISBN 978-3-540-85292-6.
- Wilson, Kenneth G.; Kogut, John B. (1974). "The renormalization group and the ε expansion". Physics Reports 12 (2): 75–199. doi:10.1016/0370-1573(74)90023-4. Bibcode: 1974PhR....12...75W. https://dx.doi.org/10.1016%2F0370-1573%2874%2990023-4
- Parisi, Giorgio (1976). On Non-Renormalizable Interactions. 281–305. doi:10.1007/978-1-4615-8918-1_12. ISBN 978-1-4615-8920-4. https://dx.doi.org/10.1007%2F978-1-4615-8918-1_12
- Brezin, Eduard; Zinn-Justin, Jean (1976). "Renormalization of the nonlinear sigma model in 2 + epsilon dimensions". Physical Review Letters 36 (13): 691–693. doi:10.1103/PhysRevLett.36.691. Bibcode: 1976PhRvL..36..691B. https://dx.doi.org/10.1103%2FPhysRevLett.36.691
- Gawędzki, Krzysztof; Kupiainen, Antti (1985). "Renormalizing the nonrenormalizable". Physical Review Letters 55 (4): 363–365. doi:10.1103/PhysRevLett.55.363. PMID 10032331. Bibcode: 1985PhRvL..55..363G. https://dx.doi.org/10.1103%2FPhysRevLett.55.363
- Wetterich, Christof (1993). "Exact evolution equation for the effective potential". Phys. Lett.. B 301 (1): 90–94. doi:10.1016/0370-2693(93)90726-X. Bibcode: 1993PhLB..301...90W. https://dx.doi.org/10.1016%2F0370-2693%2893%2990726-X
- Morris, Tim R. (1994-06-10). "The exact renormalization group and approximate solutions". International Journal of Modern Physics A 09 (14): 2411–2449. doi:10.1142/S0217751X94000972. ISSN 0217-751X. Bibcode: 1994IJMPA...9.2411M. https://dx.doi.org/10.1142%2FS0217751X94000972
- Reuter, Martin; Wetterich, Christof (1994). "Effective average action for gauge theories and exact evolution equations". Nuclear Physics B 417 (1–2): 181–214. doi:10.1016/0550-3213(94)90543-6. Bibcode: 1994NuPhB.417..181R. https://dx.doi.org/10.1016%2F0550-3213%2894%2990543-6
- See e.g. the review article by Berges, Tetradis and Wetterich (2002) in Further reading.
- Reuter, Martin (1998). "Nonperturbative evolution equation for quantum gravity". Phys. Rev.. D 57 (2): 971–985. doi:10.1103/PhysRevD.57.971. Bibcode: 1998PhRvD..57..971R. https://dx.doi.org/10.1103%2FPhysRevD.57.971
- Dou, Djamel; Percacci, Roberto (1998). "The running gravitational couplings". Classical and Quantum Gravity 15 (11): 3449–3468. doi:10.1088/0264-9381/15/11/011. Bibcode: 1998CQGra..15.3449D. https://dx.doi.org/10.1088%2F0264-9381%2F15%2F11%2F011
- For reviews on asymptotic safety and QEG with comprehensive lists of references see Further reading.
