Built on

Kenneth G. Wilson, “Quantum field theory models in less than four-dimensions,” Phys. Rev. D7
1973
Earlier work this paper cites.
Steven Weinberg, “Critical Phenomena for Field Theorists,” in Erice Subnucl.Phys.1976:1 (1976) p. 1
1976
Earlier work this paper cites.
Steven Weinberg, “ULTRAVIOLET DIVERGENCES IN QUANTUM THEORIES OF GRAVITATION,” General Relativity: An Einstein centenary survey, Eds. Hawking, S.W., Israel, W; Cambridge University Press , 790–831 (1979)
1979
Earlier work this paper cites.
Marc H. Goroff and Augusto Sagnotti, “QUANTUM GRAVITY AT TWO LOOPS,” Phys. Lett. B160
1985
Earlier work this paper cites.
A. O. Barvinsky and G. A. Vilkovisky, “The Generalized Schwinger-Dewitt Technique in Gauge Theories and Quantum Gravity,” Phys. Rept. 119
1985
Earlier work this paper cites.
Marc H. Goroff and Augusto Sagnotti, “The Ultraviolet Behavior of Einstein Gravity,” Nucl. Phys. B266
1986
Earlier work this paper cites.
A. E. M. van de Ven, “Two loop quantum gravity,” Conference on Strings and Symmetries Stony Brook, New York, May 20-25, 1991 , Nucl. Phys. B378
1992
Earlier work this paper cites.
Christof Wetterich, “Exact evolution equation for the effective potential,” Phys.Lett. B301
1993
Earlier work this paper cites.
M. Reuter, “Nonperturbative evolution equation for quantum gravity,” Phys.Rev. D57
1998
Earlier work this paper cites.
Wataru Souma, “Nontrivial ultraviolet fixed point in quantum gravity,” Prog. Theor. Phys. 102
1999
Earlier work this paper cites.
Daniel F. Litim, “Optimized renormalization group flows,” Phys.Rev. D64
2001
Earlier work this paper cites.
M. Reuter and Frank Saueressig, “Renormalization group flow of quantum gravity in the Einstein-Hilbert truncation,” Phys. Rev. D65
2002
Earlier work this paper cites.
Abhay Ashtekar, “The Winding road to quantum gravity,” Curr. Sci. 88
2005
Earlier work this paper cites.
Max Niedermaier and Martin Reuter, “The Asymptotic Safety Scenario in Quantum Gravity,” Living Rev.Rel. 9
2006
Earlier work this paper cites.
Alessandro Codello and Roberto Percacci, “Fixed points of higher derivative gravity,” Phys. Rev. Lett. 97
2006
Earlier work this paper cites.
Yves Decanini and Antoine Folacci, “Off-diagonal coefficients of the Dewitt-Schwinger and Hadamard representations of the Feynman propagator,” Phys. Rev. D73
2006
Earlier work this paper cites.
Damiano Anselmi and Anna Benini, “Improved Schwinger-DeWitt techniques for higher-derivative corrections to operator determinants,” JHEP 10
Original
2007
Earlier work this paper cites.
J. M. Martín-García, R. Portugal, and L. R. U. Manssur, “The Invar tensor package,” Computer Physics Communications 177
Original
2007
Earlier work this paper cites.
Alessandro Codello, Roberto Percacci, and Christoph Rahmede, “Ultraviolet properties of f(R)-gravity,” Int.J.Mod.Phys. A23
Original
2008
Earlier work this paper cites.

Similar

Pedro F. Machado and Frank Saueressig, “On the renormalization group flow of f(R)-gravity,” Phys.Rev. D77
Original
2008
Cited alongside, same era.
J. M. Martín-García, D. Yllanes, and R. Portugal, “The Invar tensor package: Differential invariants of Riemann,” Computer Physics Communications 179
Original
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2009
Cited alongside, same era.
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Then

Andreas Nink and Martin Reuter, “On the physical mechanism underlying Asymptotic Safety,” JHEP 01
Original
2013
Later among the works it cites.
Dario Benedetti, “On the number of relevant operators in asymptotically safe gravity,” Europhys. Lett. 102
Original
2013
Later among the works it cites.
T. Nutma, “xTras: A field-theory inspired xAct package for mathematica,” Computer Physics Communications 185
Original
2014
Later among the works it cites.
Maximilian Demmel, Frank Saueressig, and Omar Zanusso, “RG flows of Quantum Einstein Gravity on maximally symmetric spaces,” JHEP 06
Original
2014
Later among the works it cites.
I. Hamzaan Bridle, Juergen A. Dietz, and Tim R. Morris, “The local potential approximation in the background field formalism,” JHEP 1403

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2016

The Gravitational Two-Loop Counterterm is Asymptotically Safe

Gies, Holger, Knorr, Benjamin, Lippoldt, Stefan et al.

Understand

Weinberg's asymptotic safety scenario provides an elegant mechanism to construct a quantum theory of gravity within the framework of quantum field theory based on a non-Gau{\ss}ian fixed point of the renormalization group flow.

In this work we report novel evidence for the validity of this scenario, using functional renormalization group techniques to determine the renormalization group flow of the Einstein-Hilbert action supplemented by the two-loop counterterm found by Goroff and Sagnotti.
The resulting system of beta functions comprises three scale-dependent coupling constants and exhibits a non-Gau{\ss}ian fixed point which constitutes the natural extension of the one found at the level of the Einstein-Hilbert action.
The fixed point exhibits two ultraviolet attractive and one repulsive direction supporting a low-dimensional UV-critical hypersurface.

Built on

Kenneth G. Wilson, “Quantum field theory models in less than four-dimensions,” Phys. Rev. D7
1973
Earlier work this paper cites.
Steven Weinberg, “Critical Phenomena for Field Theorists,” in Erice Subnucl.Phys.1976:1 (1976) p. 1
1976
Earlier work this paper cites.
Steven Weinberg, “ULTRAVIOLET DIVERGENCES IN QUANTUM THEORIES OF GRAVITATION,” General Relativity: An Einstein centenary survey, Eds. Hawking, S.W., Israel, W; Cambridge University Press , 790–831 (1979)
1979
Earlier work this paper cites.
Marc H. Goroff and Augusto Sagnotti, “QUANTUM GRAVITY AT TWO LOOPS,” Phys. Lett. B160
1985
Earlier work this paper cites.
A. O. Barvinsky and G. A. Vilkovisky, “The Generalized Schwinger-Dewitt Technique in Gauge Theories and Quantum Gravity,” Phys. Rept. 119
1985
Earlier work this paper cites.
Marc H. Goroff and Augusto Sagnotti, “The Ultraviolet Behavior of Einstein Gravity,” Nucl. Phys. B266
1986
Earlier work this paper cites.
A. E. M. van de Ven, “Two loop quantum gravity,” Conference on Strings and Symmetries Stony Brook, New York, May 20-25, 1991 , Nucl. Phys. B378
1992
Earlier work this paper cites.
Christof Wetterich, “Exact evolution equation for the effective potential,” Phys.Lett. B301
1993
Earlier work this paper cites.
M. Reuter, “Nonperturbative evolution equation for quantum gravity,” Phys.Rev. D57
1998
Earlier work this paper cites.
Wataru Souma, “Nontrivial ultraviolet fixed point in quantum gravity,” Prog. Theor. Phys. 102
1999
Earlier work this paper cites.
Daniel F. Litim, “Optimized renormalization group flows,” Phys.Rev. D64
2001
Earlier work this paper cites.
M. Reuter and Frank Saueressig, “Renormalization group flow of quantum gravity in the Einstein-Hilbert truncation,” Phys. Rev. D65
2002
Earlier work this paper cites.
Abhay Ashtekar, “The Winding road to quantum gravity,” Curr. Sci. 88
2005
Earlier work this paper cites.
Max Niedermaier and Martin Reuter, “The Asymptotic Safety Scenario in Quantum Gravity,” Living Rev.Rel. 9
2006
Earlier work this paper cites.
Alessandro Codello and Roberto Percacci, “Fixed points of higher derivative gravity,” Phys. Rev. Lett. 97
2006
Earlier work this paper cites.
Yves Decanini and Antoine Folacci, “Off-diagonal coefficients of the Dewitt-Schwinger and Hadamard representations of the Feynman propagator,” Phys. Rev. D73
2006
Earlier work this paper cites.
Damiano Anselmi and Anna Benini, “Improved Schwinger-DeWitt techniques for higher-derivative corrections to operator determinants,” JHEP 10
Original
2007
Earlier work this paper cites.
J. M. Martín-García, R. Portugal, and L. R. U. Manssur, “The Invar tensor package,” Computer Physics Communications 177
Original
2007
Earlier work this paper cites.
Alessandro Codello, Roberto Percacci, and Christoph Rahmede, “Ultraviolet properties of f(R)-gravity,” Int.J.Mod.Phys. A23
Original
2008
Earlier work this paper cites.