Abstract
We extensively study the ultraviolet quantum properties of a nonlocal action for gravity nonminimally coupled to matter. The theory unifies matter and gravity in an action principle such that all the classical solutions of Einstein’s theory coupled to matter are also solutions of the nonlocal theory. At the quantum level, we show that the theory is power-counting super-renormalizable in even dimensions and finite in odd dimensions. A simple extension of the model compatible with the above properties is finite also in even dimensions.
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References
N.V. Krasnikov, Nonlocal gauge theories, Theor. Math. Phys. 73 (1987) 1184 [INSPIRE].
Y.V. Kuzmin, The convergent nonlocal gravitation (in Russian), Sov. J. Nucl. Phys. 50 (1989) 1011 [INSPIRE].
L. Modesto, Super-renormalizable quantum gravity, Phys. Rev. D 86 (2012) 044005 [arXiv:1107.2403] [INSPIRE].
T. Biswas, E. Gerwick, T. Koivisto and A. Mazumdar, Towards singularity and ghost free theories of gravity, Phys. Rev. Lett. 108 (2012) 031101 [arXiv:1110.5249] [INSPIRE].
P. Donà et al., Scattering amplitudes in super-renormalizable gravity, JHEP 08 (2015) 038 [arXiv:1506.04589] [INSPIRE].
A. Bas i Beneito, G. Calcagni and L. Rachwał, Classical and quantum nonlocal gravity, arXiv:2211.05606 [INSPIRE].
L. Buoninfante, B.L. Giacchini and T. de Paula Netto, Black holes in non-local gravity, arXiv:2211.03497 [INSPIRE].
G. Calcagni, Non-local gravity, in Modified Gravity and Cosmology, E.N. Saridakis et al. eds., Springer (2021) [https://doi.org/10.1007/978-3-030-83715-0_9] [arXiv:2105.12582] [INSPIRE].
A.S. Koshelev, K.S. Kumar and A.A. Starobinsky, Cosmology in nonlocal gravity, arXiv:2305.18716 [INSPIRE].
L. Modesto, Nonlocal spacetime-matter, arXiv:2103.04936 [INSPIRE].
L. Modesto, The Higgs mechanism in nonlocal field theory, JHEP 06 (2021) 049 [arXiv:2103.05536] [INSPIRE].
L. Modesto and G. Calcagni, Tree-level scattering amplitudes in nonlocal field theories, JHEP 10 (2021) 169 [arXiv:2107.04558] [INSPIRE].
L. Modesto and G. Calcagni, Early universe in quantum gravity, arXiv:2206.06384 [INSPIRE].
G. Calcagni and L. Modesto, Testing quantum gravity with primordial gravitational waves, arXiv:2206.07066 [INSPIRE].
M. Kaku, Quantum field theory: A Modern introduction, Oxford University Press (1993) [INSPIRE].
M.E. Peskin and D.V. Schroeder, An Introduction to Quantum Field Theory, Perseus (1995).
I.L. Buchbinder and I. Shapiro, Introduction to Quantum Field Theory with Applications to Quantum Gravity, Oxford University Press (2023) [INSPIRE].
F.W.J. Olver et al. eds., NIST Handbook of Mathematical Functions, Cambridge University Press, U.K. (2010).
F. Briscese and L. Modesto, Cutkosky rules and perturbative unitarity in Euclidean nonlocal quantum field theories, Phys. Rev. D 99 (2019) 104043 [arXiv:1803.08827] [INSPIRE].
J. Liu, L. Modesto and G. Calcagni, Quantum field theory with ghost pairs, JHEP 02 (2023) 140 [arXiv:2208.13536] [INSPIRE].
M. Eran, Higher-derivative Gauge And Gravitational Theories, Ph.D. thesis, Calif. U. Los Angeles, U.S.A. (1998) [INSPIRE].
N. Ohta and L. Rachwał, Effective action from the functional renormalization group, Eur. Phys. J. C 80 (2020) 877 [arXiv:2002.10839] [INSPIRE].
K.S. Stelle, Renormalization of higher-derivative quantum gravity, Phys. Rev. D 16 (1977) 953 [INSPIRE].
M. Asorey, J.L. López and I.L. Shapiro, Some remarks on high derivative quantum gravity, Int. J. Mod. Phys. A 12 (1997) 5711 [hep-th/9610006] [INSPIRE].
E. Elizalde, A.G. Zheksenaev, S.D. Odintsov and I.L. Shapiro, A four-dimensional theory for quantum gravity with conformal and nonconformal explicit solutions, Class. Quant. Grav. 12 (1995) 1385 [hep-th/9412061] [INSPIRE].
P.M. Lavrov and I.L. Shapiro, Gauge invariant renormalizability of quantum gravity, Phys. Rev. D 100 (2019) 026018 [arXiv:1902.04687] [INSPIRE].
G. ’t Hooft and M.J.G. Veltman, One loop divergencies in the theory of gravitation, Ann. Inst. H. Poincare Phys. Theor. A 20 (1974) 69 [INSPIRE].
S. Deser and P. van Nieuwenhuizen, One-loop divergences of quantized Einstein-Maxwell fields, Phys. Rev. D 10 (1974) 401 [INSPIRE].
M.H. Goroff and A. Sagnotti, The ultraviolet behavior of Einstein gravity, Nucl. Phys. B 266 (1986) 709 [INSPIRE].
A.E.M. van de Ven, Two loop quantum gravity, Nucl. Phys. B 378 (1992) 309 [INSPIRE].
E.T. Tomboulis, Superrenormalizable gauge and gravitational theories, hep-th/9702146 [INSPIRE].
A.A. Starobinsky, A new type of isotropic cosmological models without singularity, Phys. Lett. B 91 (1980) 99 [INSPIRE].
A. Vilenkin, Classical and quantum cosmology of the Starobinsky inflationary model, Phys. Rev. D 32 (1985) 2511 [INSPIRE].
K.-I. Maeda, Inflation as a transient attractor in R2 cosmology, Phys. Rev. D 37 (1988) 858 [INSPIRE].
L. Modesto and L. Rachwał, Super-renormalizable and finite gravitational theories, Nucl. Phys. B 889 (2014) 228 [arXiv:1407.8036] [INSPIRE].
L. Modesto and L. Rachwał, Universally finite gravitational and gauge theories, Nucl. Phys. B 900 (2015) 147 [arXiv:1503.00261] [INSPIRE].
L. Modesto and L. Rachwał, Nonlocal quantum gravity: A review, Int. J. Mod. Phys. D 26 (2017) 1730020 [INSPIRE].
J. Julve and M. Tonin, Quantum gravity with higher derivative terms, Nuovo Cim. B 46 (1978) 137 [INSPIRE].
A.O. Barvinsky and G.A. Vilkovisky, The generalized Schwinger-DeWitt technique in gauge theories and quantum gravity, Phys. Rept. 119 (1985) 1 [INSPIRE].
I.G. Avramidi and A.O. Barvinsky, Asymptotic freedom in higher-derivative quantum gravity, Phys. Lett. B 159 (1985) 269 [INSPIRE].
I.L. Shapiro and J. Sola, On the possible running of the cosmological ‘constant’, Phys. Lett. B 682 (2009) 105 [arXiv:0910.4925] [INSPIRE].
E.S. Fradkin and A.A. Tseytlin, Renormalizable asymptotically free quantum theory of gravity, Nucl. Phys. B 201 (1982) 469 [INSPIRE].
A. Eichhorn, A. Held and C. Wetterich, Quantum-gravity predictions for the fine-structure constant, Phys. Lett. B 782 (2018) 198 [arXiv:1711.02949] [INSPIRE].
F. Englert, C. Truffin and R. Gastmans, Conformal invariance in quantum gravity, Nucl. Phys. B 117 (1976) 407 [INSPIRE].
G. ’t Hooft, A class of elementary particle models without any adjustable real parameters, Found. Phys. 41 (2011) 1829 [arXiv:1104.4543] [INSPIRE].
L. Modesto and L. Rachwał, Finite conformal quantum gravity and nonsingular spacetimes, arXiv:1605.04173 [INSPIRE].
Acknowledgments
L.R. thanks the Department of Physics, UFJF, for the warm hospitality. G.C., L.M. and L.R. are supported by grant PID2020-118159GB-C41 funded by MCIN/AEI/10.13039/501100011033. L.M. is also supported by the Basic Research Program of the Science, Technology, and Innovation Commission of Shenzhen Municipality (grant no. JCYJ2018030-2174206969).
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Calcagni, G., Giacchini, B.L., Modesto, L. et al. Renormalizability of nonlocal quantum gravity coupled to matter. J. High Energ. Phys. 2023, 34 (2023). https://doi.org/10.1007/JHEP09(2023)034
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DOI: https://doi.org/10.1007/JHEP09(2023)034