Abstract
We identify a simple physical mechanism which is at the heart of Asymptotic Safety in Quantum Einstein Gravity (QEG) according to all available effective average action-based investigations. Upon linearization the gravitational field equations give rise to an inverse propagator for metric fluctuations comprising two pieces: a covariant Laplacian and a curvature dependent potential term. By analogy with elementary magnetic systems they lead to, respectively, dia- and paramagnetic-type interactions of the metric fluctuations with the background gravitational field. We show that above 3 spacetime dimensions the gravitational antiscreening occurring in QEG is entirely due to a strong dominance of the ultralocal paramagnetic interactions over the diamagnetic ones that favor screening. (Below 3 dimensions both the dia- and paramagnetic effects support antiscreening.) The spacetimes of QEG are interpreted as a polarizable medium with a “paramagnetic” response to external perturbations, and similarities with the vacuum state of Yang-Mills theory are pointed out. As a by-product, we resolve a longstanding puzzle concerning the beta function of Newton’s constant in 2 + ϵ dimensional gravity.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
C. Kiefer, Quantum gravity, third edition, Oxford Science Publications, Oxford U.K. (2012).
H.W. Hamber, Quantum gravitation, Springer, Berlin Germany (2009).
A. Ashtekar, Lectures on non-perturbative canonical gravity, World Scientific, Singapore (1991).
A. Ashtekar and J. Lewandowski, Background independent quantum gravity: a status report, Class. Quant. Grav. 21 (2004) R53 [gr-qc/0404018] [INSPIRE].
C. Rovelli, Quantum gravity, Cambridge University Press, Cambridge U.K. (2004).
T. Thiemann, Modern canonical quantum general relativity, Cambridge University Press, Cambridge U.K. (2007).
J. Ambjørn, J. Jurkiewicz and R. Loll, Emergence of a 4D world from causal quantum gravity, Phys. Rev. Lett. 93 (2004) 131301 [hep-th/0404156] [INSPIRE].
J. Ambjørn, J. Jurkiewicz and R. Loll, Semiclassical universe from first principles, Phys. Lett. B 607 (2005) 205 [hep-th/0411152] [INSPIRE].
J. Ambjørn, J. Jurkiewicz and R. Loll, Spectral dimension of the universe, Phys. Rev. Lett. 95 (2005) 171301 [hep-th/0505113] [INSPIRE].
J. Ambjørn, J. Jurkiewicz and R. Loll, Reconstructing the universe, Phys. Rev. D 72 (2005) 064014 [hep-th/0505154] [INSPIRE].
J. Ambjørn, J. Jurkiewicz and R. Loll, Quantum gravity as sum over spacetimes, Lect. Notes Phys. 807 (2010) 59 [arXiv:0906.3947] [INSPIRE].
J. Ambjørn, S. Jordan, J. Jurkiewicz and R. Loll, A second-order phase transition in CDT, Phys. Rev. Lett. 107 (2011) 211303 [arXiv:1108.3932] [INSPIRE].
D. Benedetti and J. Henson, Spectral geometry as a probe of quantum spacetime, Phys. Rev. D 80 (2009) 124036 [arXiv:0911.0401] [INSPIRE].
T. Regge and R.M. Williams, Discrete structures in gravity, J. Math. Phys. 41 (2000) 3964 [gr-qc/0012035] [INSPIRE].
H.W. Hamber, Quantum gravity on the lattice, Gen. Rel. Grav. 41 (2009) 817 [arXiv:0901.0964] [INSPIRE].
H.W. Hamber, Phases of four-dimensional simplicial quantum gravity, Phys. Rev. D 45 (1992) 507.
H.W. Hamber, On the gravitational scaling dimensions, Phys. Rev. D 61 (2000) 124008 [hep-th/9912246] [INSPIRE].
H.W. Hamber, Discrete and continuum quantum gravity, arXiv:0704.2895 [INSPIRE].
S. Weinberg, Ultraviolet divergences in quantum theories of gravitation, in General relativity, an Einstein centenary survey, S.W. Hawking and W. Israel eds., Cambridge University Press, Cambridge U.K. (1979), pg. 790 [INSPIRE].
S. Weinberg, Gravitation and cosmology, Wiley, New York U.S.A. (1972).
M. Reuter, Nonperturbative evolution equation for quantum gravity, Phys. Rev. D 57 (1998) 971 [hep-th/9605030] [INSPIRE].
E. Manrique and M. Reuter, Bare action and regularized functional integral of asymptotically safe quantum gravity, Phys. Rev. D 79 (2009) 025008 [arXiv:0811.3888] [INSPIRE].
W. Souma, Nontrivial ultraviolet fixed point in quantum gravity, Prog. Theor. Phys. 102 (1999) 181 [hep-th/9907027] [INSPIRE].
M. Reuter and F. Saueressig, Renormalization group flow of quantum gravity in the Einstein-Hilbert truncation, Phys. Rev. D 65 (2002) 065016 [hep-th/0110054] [INSPIRE].
O. Lauscher and M. Reuter, Ultraviolet fixed point and generalized flow equation of quantum gravity, Phys. Rev. D 65 (2002) 025013 [hep-th/0108040] [INSPIRE].
O. Lauscher and M. Reuter, Flow equation of quantum Einstein gravity in a higher derivative truncation, Phys. Rev. D 66 (2002) 025026 [hep-th/0205062] [INSPIRE].
O. Lauscher and M. Reuter, Is quantum Einstein gravity nonperturbatively renormalizable?, Class. Quant. Grav. 19 (2002) 483 [hep-th/0110021] [INSPIRE].
M. Reuter and F. Saueressig, Quantum Einstein gravity, New J. Phys. 14 (2012) 055022 [arXiv:1202.2274] [INSPIRE].
M. Niedermaier and M. Reuter, The asymptotic safety scenario in quantum gravity, Living Rev. Rel. 9 (2006) 5 [INSPIRE].
M. Reuter and F. Saueressig, Functional renormalization group equations, Asymptotic Safety and quantum Einstein gravity, in Geometric and topological methods for quantum field theory, H. Ocampo, S. Paycha and A. Vargas eds., Cambridge University Press, Cambridge U.K. (2010) [arXiv:0708.1317] [INSPIRE].
R. Percacci, Asymptotic Safety, in Approaches to quantum gravity: towards a new understanding of space, time and matter, D. Oriti ed., Cambridge University Press, Cambridge U.K. (2009) [arXiv:0709.3851] [INSPIRE].
A. Codello, R. Percacci and C. Rahmede, Investigating the ultraviolet properties of gravity with a Wilsonian renormalization group equation, Annals Phys. 324 (2009) 414 [arXiv:0805.2909] [INSPIRE].
E. Manrique and M. Reuter, Bimetric truncations for quantum Einstein gravity and asymptotic safety, Annals Phys. 325 (2010) 785 [arXiv:0907.2617] [INSPIRE].
E. Manrique, M. Reuter and F. Saueressig, Matter induced bimetric actions for gravity, Annals Phys. 326 (2011) 440 [arXiv:1003.5129] [INSPIRE].
E. Manrique, M. Reuter and F. Saueressig, Bimetric renormalization group flows in quantum Einstein gravity, Annals Phys. 326 (2011) 463 [arXiv:1006.0099] [INSPIRE].
B.S. DeWitt, The global approach to quantum field theory, Clarendon Press, Oxford U.K. (2003).
H.B. Lawson and M.-L. Michelsohn, Spin geometry, Princeton University Press, Princeton U.S.A. (1989).
N. Nielsen, Asymptotic freedom as a spin effect, Am. J. Phys. 49 (1981) 1171 [INSPIRE].
A.M. Polyakov, Gauge fields and strings, Harwood, Chur Switzerland (1987).
K. Johnson, , in Asymptotic realms in physics, A. Guth, K. Huang and R.L. Jaffe eds., MIT Press, Cambridge U.S.A. (1983).
K. Huang, Quarks, leptons and gauge fields, World Scientific, Singapore (1992).
K. Gottfried and V.F. Weisskopf, Concepts of particle physics: volume II, Oxford University Press, Oxford U.K. (1986).
W. Dittrich and M. Reuter, Effective QCD Lagrangian with zeta function regularization, Phys. Lett. B 128 (1983) 321 [INSPIRE].
M. Reuter, Renormalization of the topological charge in Yang-Mills theory, Mod. Phys. Lett. A 12 (1997) 2777 [hep-th/9604124] [INSPIRE].
G.A. Vilkovisky, Heat kernel: rencontre entre physiciens et mathematiciens, CERN preprint TH-6392-92, CERN, Geneva Switzerland (1992) [INSPIRE].
H.D. Politzer, Reliable perturbative results for strong interactions?, Phys. Rev. Lett. 30 (1973) 1346 [INSPIRE].
D. Gross and F. Wilczek, Ultraviolet behavior of nonabelian gauge theories, Phys. Rev. Lett. 30 (1973) 1343 [INSPIRE].
C. Wetterich, Exact evolution equation for the effective potential, Phys. Lett. B 301 (1993) 90 [INSPIRE].
M. Reuter and C. Wetterich, Effective average action for gauge theories and exact evolution equations, Nucl. Phys. B 417 (1994) 181 [INSPIRE].
M. Reuter and C. Wetterich, Exact evolution equation for scalar electrodynamics, Nucl. Phys. B 427 (1994) 291 [INSPIRE].
M. Reuter and C. Wetterich, Gluon condensation in nonperturbative flow equations, Phys. Rev. D 56 (1997) 7893 [hep-th/9708051] [INSPIRE].
M. Reuter and C. Wetterich, Average action for the Higgs model with Abelian gauge symmetry, Nucl. Phys. B 391 (1993) 147 [INSPIRE].
M. Reuter and C. Wetterich, Running gauge coupling in three-dimensions and the electroweak phase transition, Nucl. Phys. B 408 (1993) 91 [INSPIRE].
H. Gies and J. Jaeckel, Renormalization flow of QED, Phys. Rev. Lett. 93 (2004) 110405 [hep-ph/0405183] [INSPIRE].
H. Gies, Renormalizability of gauge theories in extra dimensions, Phys. Rev. D 68 (2003) 085015 [hep-th/0305208] [INSPIRE].
W. Heisenberg and H. Euler, Consequences of Dirac’s theory of positrons, Z. Phys. 98 (1936) 714 [physics/0605038] [INSPIRE].
D.F. Litim, Optimized renormalization group flows, Phys. Rev. D 64 (2001) 105007 [hep-th/0103195] [INSPIRE].
D. Becker and M. Reuter, Running boundary actions, Asymptotic Safety and black hole thermodynamics, JHEP 07 (2012) 172 [arXiv:1205.3583] [INSPIRE].
R. Gastmans, R. Kallosh and C. Truffin, Quantum gravity near two-dimensions, Nucl. Phys. B 133 (1978) 417 [INSPIRE].
S. Christensen and M. Duff, Quantum gravity in two + ϵ dimensions, Phys. Lett. B 79 (1978) 213 [INSPIRE].
L.S. Brown, Stress tensor trace anomaly in a gravitational metric: scalar fields, Phys. Rev. D 15 (1977) 1469 [INSPIRE].
H.-S. Tsao, Conformal anomalies in a general background metric, Phys. Lett. B 68 (1977) 79 [INSPIRE].
H. Kawai and M. Ninomiya, Renormalization group and quantum gravity, Nucl. Phys. B 336 (1990) 115 [INSPIRE].
I. Jack and D. Jones, The ϵ-expansion of two-dimensional quantum gravity, Nucl. Phys. B 358 (1991) 695 [INSPIRE].
A. Codello and O. Zanusso, Fluid membranes and 2D quantum gravity, Phys. Rev. D 83 (2011) 125021 [arXiv:1103.1089] [INSPIRE].
G. Gibbons and S. Hawking, Action integrals and partition functions in quantum gravity, Phys. Rev. D 15 (1977) 2752 [INSPIRE].
C. Wetterich, The average action for scalar fields near phase transitions, Z. Phys. C 57 (1993) 451 [INSPIRE].
M. Reuter and H. Weyer, Renormalization group improved gravitational actions: a Brans-Dicke approach, Phys. Rev. D 69 (2004) 104022 [hep-th/0311196] [INSPIRE].
M. Reuter and H. Weyer, Running Newton constant, improved gravitational actions, and galaxy rotation curves, Phys. Rev. D 70 (2004) 124028 [hep-th/0410117] [INSPIRE].
W. Dittrich and M. Reuter, Effective Lagrangians in quantum electrodynamics, Springer, Berlin Germany (1985).
A. Bonanno and M. Reuter, Renormalization group improved black hole space-times, Phys. Rev. D 62 (2000) 043008 [hep-th/0002196] [INSPIRE].
A. Bonanno and M. Reuter, Spacetime structure of an evaporating black hole in quantum gravity, Phys. Rev. D 73 (2006) 083005 [hep-th/0602159] [INSPIRE].
A. Bonanno and M. Reuter, Quantum gravity effects near the null black hole singularity, Phys. Rev. D 60 (1999) 084011 [gr-qc/9811026] [INSPIRE].
M. Reuter and E. Tuiran, Quantum gravity effects in the Kerr spacetime, Phys. Rev. D 83 (2011) 044041 [arXiv:1009.3528] [INSPIRE].
M. Reuter and E. Tuiran, Quantum gravity effects in rotating black holes, in Proceedings of the eleventh Marcel Grossmann meeting, H. Kleinert, R. Jantzen and R. Ruffini eds., World Scientific, Singapore (2007) [hep-th/0612037] [INSPIRE].
J.F. Donoghue, Leading quantum correction to the Newtonian potential, Phys. Rev. Lett. 72 (1994) 2996 [gr-qc/9310024] [INSPIRE].
J.F. Donoghue, General relativity as an effective field theory: the leading quantum corrections, Phys. Rev. D 50 (1994) 3874 [gr-qc/9405057] [INSPIRE].
A. Bonanno, An effective action for asymptotically safe gravity, Phys. Rev. D 85 (2012) 081503 [arXiv:1203.1962] [INSPIRE].
E. Manrique, S. Rechenberger and F. Saueressig, Asymptotically safe Lorentzian gravity, Phys. Rev. Lett. 106 (2011) 251302 [arXiv:1102.5012] [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1208.0031
Rights and permissions
About this article
Cite this article
Nink, A., Reuter, M. On the physical mechanism underlying asymptotic safety. J. High Energ. Phys. 2013, 62 (2013). https://doi.org/10.1007/JHEP01(2013)062
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP01(2013)062