Abstract
A theory of quantum gravity has been recently proposed by means of a novel quantization prescription, which is able to turn the poles of the free propagators that are due to the higher derivatives into fakeons. The classical Lagrangian contains the cosmological term, the Hilbert term, \( \sqrt{-g}{R}_{\mu \nu }{R}^{\mu \nu } \) and \( \sqrt{-g}{R}^2 \). In this paper, we compute the one-loop renormalization of the theory and the absorptive part of the graviton self energy. The results illustrate the mechanism that makes renormalizability compatible with unitarity. The fakeons disentangle the real part of the self energy from the imaginary part. The former obeys a renormalizable power counting, while the latter obeys the nonrenormalizable power counting of the low energy expansion and is consistent with unitarity in the limit of vanishing cosmological constant. The value of the absorptive part is related to the central charge c of the matter fields coupled to gravity.
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References
D. Anselmi, On the quantum field theory of the gravitational interactions, JHEP 06 (2017) 086 [arXiv:1704.07728] [INSPIRE].
D. Anselmi, Fakeons And Lee-Wick Models, JHEP 02 (2018) 141 [arXiv:1801.00915] [INSPIRE].
T.D. Lee and G.C. Wick, Negative Metric and the Unitarity of the S Matrix, Nucl. Phys. B 9 (1969) 209 [INSPIRE].
T.D. Lee and G.C. Wick, Finite Theory of Quantum Electrodynamics, Phys. Rev. D 2 (1970) 1033 [INSPIRE].
R.E. Cutkosky, P.V. Landshoff, D.I. Olive and J.C. Polkinghorne, A non-analytic S matrix, Nucl. Phys. B 12 (1969) 281 [INSPIRE].
B. Grinstein, D. O’Connell and M.B. Wise, Causality as an emergent macroscopic phenomenon: The Lee-Wick O(N) model, Phys. Rev. D 79 (2009) 105019 [arXiv:0805.2156] [INSPIRE].
D. Anselmi and M. Piva, A new formulation of Lee-Wick quantum field theory, JHEP 06 (2017) 066 [arXiv:1703.04584] [INSPIRE].
D. Anselmi and M. Piva, Perturbative unitarity of Lee-Wick quantum field theory, Phys. Rev. D 96 (2017) 045009 [arXiv:1703.05563] [INSPIRE].
S.B. Giddings, The boundary S matrix and the AdS to CFT dictionary, Phys. Rev. Lett. 83 (1999) 2707 [hep-th/9903048] [INSPIRE].
V. Balasubramanian, S.B. Giddings and A.E. Lawrence, What do CFTs tell us about Anti-de Sitter space-times?, JHEP 03 (1999) 001 [hep-th/9902052] [INSPIRE].
J.C. Ward, An Identity in Quantum Electrodynamics, Phys. Rev. 78 (1950) 182 [INSPIRE].
Y. Takahashi, On the generalized Ward identity, Nuovo Cim. 6 (1957) 371 [INSPIRE].
A.A. Slavnov, Ward Identities in Gauge Theories, Theor. Math. Phys. 10 (1972) 99 [INSPIRE].
J.C. Taylor, Ward Identities and Charge Renormalization of the Yang-Mills Field, Nucl. Phys. B 33 (1971) 436 [INSPIRE].
J. Julve and M. Tonin, Quantum Gravity with Higher Derivative Terms, Nuovo Cim. B 46 (1978) 137 [INSPIRE].
E.S. Fradkin and A.A. Tseytlin, Renormalizable asymptotically free quantum theory of gravity, Nucl. Phys. B 201 (1982) 469 [INSPIRE].
I.G. Avramidi and A.O. Barvinsky, Asymptotic freedom in higher derivative quantum gravity, Phys. Lett. 159B (1985) 269 [INSPIRE].
N. Ohta, R. Percacci and A.D. Pereira, Gauges and functional measures in quantum gravity II: Higher derivative gravity, Eur. Phys. J. C 77 (2017) 611 [arXiv:1610.07991] [INSPIRE].
A. Salvio and A. Strumia, Agravity, JHEP 06 (2014) 080 [arXiv:1403.4226] [INSPIRE].
A. Salvio and A. Strumia, Agravity up to infinite energy, Eur. Phys. J. C 78 (2018) 124 [arXiv:1705.03896] [INSPIRE].
I.A. Batalin and G.A. Vilkovisky, Gauge Algebra and Quantization, Phys. Lett. 102B (1981) 27 [INSPIRE].
I.A. Batalin and G.A. Vilkovisky, Quantization of Gauge Theories with Linearly Dependent Generators, Phys. Rev. D 28 (1983) 2567 [Erratum ibid. D 30 (1984) 508] [INSPIRE].
S. Weinberg, The quantum theory of fields, volume 2, Cambridge University Press, Cambridge (1995).
K.S. Stelle, Renormalization of Higher Derivative Quantum Gravity, Phys. Rev. D 16 (1977) 953 [INSPIRE].
J. Zinn-Justin, Renormalization of gauge theories, in Trends in Elementary Particle Physics, Lecture Notes in Physics, Vol. 37, H. Rollnik and K. Dietz eds., Springer-Verlag, Berlin, Germany, (1975).
N. Nakanishi, Indefinite metric quantum field theory, Prog. Theor. Phys. Suppl. 51 (1972) 1 [INSPIRE].
B. Lautrup, Canonical quantum electrodynamics in covariant gauges, Mat. Fys. Medd. Dan. Vid. Selsk. 35 (1967) 11.
D. Anselmi, Background field method and the cohomology of renormalization, Phys. Rev. D 93 (2016) 065034 [arXiv:1511.01244] [INSPIRE].
D. Anselmi, Background field method, Batalin-Vilkovisky formalism and parametric completeness of renormalization, Phys. Rev. D 89 (2014) 045004 [arXiv:1311.2704] [INSPIRE].
S.J. Hathrell, Trace Anomalies and λϕ 4 Theory in Curved Space, Annals Phys. 139 (1982) 136 [INSPIRE].
S.J. Hathrell, Trace Anomalies and QED in Curved Space, Annals Phys. 142 (1982) 34 [INSPIRE].
M.D. Freeman, The Renormalization of Nonabelian Gauge Theories in Curved Space-time, Annals Phys. 153 (1984) 339 [INSPIRE].
D. Anselmi, Ward identities and gauge independence in general chiral gauge theories, Phys. Rev. D 92 (2015) 025027 [arXiv:1501.06692] [INSPIRE].
R.E. Cutkosky, Singularities and discontinuities of Feynman amplitudes, J. Math. Phys. 1 (1960) 429 [INSPIRE].
M.J.G. Veltman, Unitarity and causality in a renormalizable field theory with unstable particles, Physica 29 (1963) 186 [INSPIRE].
D. Anselmi, Aspects of perturbative unitarity, Phys. Rev. D 94 (2016) 025028 [arXiv:1606.06348] [INSPIRE].
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Anselmi, D., Piva, M. The ultraviolet behavior of quantum gravity. J. High Energ. Phys. 2018, 27 (2018). https://doi.org/10.1007/JHEP05(2018)027
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DOI: https://doi.org/10.1007/JHEP05(2018)027