Abstract
Asymptotically nonlocal field theories interpolate between Lee-Wick theories with multiple propagator poles, and ghost-free nonlocal theories. Previous work on asymp- totically nonlocal scalar, Abelian, and non-Abelian gauge theories has demonstrated the existence of an emergent regulator scale that is hierarchically smaller than the lightest Lee-Wick partner, in a limit where the Lee-Wick spectrum becomes dense and decoupled. We generalize this construction to linearized gravity, and demonstrate the emergent regula- tor scale in three examples: by studying the resolution of the singularity (i) at the origin in the classical solution for the metric of a point particle, and (ii) in the nonrelativistic gravitational potential computed via a one-graviton exchange amplitude; (iii) we also show how this derived scale regulates the one-loop graviton contribution to the self energy of a real scalar field. We comment briefly on the generalization of our approach to the full, nonlinear theory of gravity.
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References
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 [Erratum ibid. 6 (1972) 2721] [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, The Lee-Wick standard model, Phys. Rev. D 77 (2008) 025012 [arXiv:0704.1845] [INSPIRE].
C.D. Carone and R.F. Lebed, A higher-derivative Lee-Wick standard model, JHEP 01 (2009) 043 [arXiv:0811.4150] [INSPIRE].
T.G. Rizzo, Searching for Lee-Wick gauge bosons at the LHC, JHEP 06 (2007) 070 [arXiv:0704.3458] [INSPIRE].
J.R. Espinosa, B. Grinstein, D. O’Connell and M.B. Wise, Neutrino masses in the Lee-Wick standard model, Phys. Rev. D 77 (2008) 085002 [arXiv:0705.1188] [INSPIRE].
T.R. Dulaney and M.B. Wise, Flavor changing neutral currents in the Lee-Wick standard model, Phys. Lett. B 658 (2008) 230 [arXiv:0708.0567] [INSPIRE].
F. Krauss, T.E.J. Underwood and R. Zwicky, The process gg → h0 → γγ in the Lee-Wick standard model, Phys. Rev. D 77 (2008) 015012 [Erratum ibid. 83 (2011) 019902] [arXiv:0709.4054] [INSPIRE].
Z. Fodor et al., New Higgs physics from the lattice, PoS LATTICE2007 (2007) 056 [arXiv:0710.3151] [INSPIRE].
T.G. Rizzo, Unique identification of Lee-Wick gauge bosons at linear colliders, JHEP 01 (2008) 042 [arXiv:0712.1791] [INSPIRE].
E. Alvarez, L. Da Rold, C. Schat and A. Szynkman, Electroweak precision constraints on the Lee-Wick Standard Model, JHEP 04 (2008) 026 [arXiv:0802.1061] [INSPIRE].
T.E.J. Underwood and R. Zwicky, Electroweak precision data and the Lee-Wick standard model, Phys. Rev. D 79 (2009) 035016 [arXiv:0805.3296] [INSPIRE].
B. Fornal, B. Grinstein and M.B. Wise, Lee-Wick theories at high temperature, Phys. Lett. B 674 (2009) 330 [arXiv:0902.1585] [INSPIRE].
C.D. Carone and R. Primulando, Constraints on the Lee-Wick Higgs sector, Phys. Rev. D 80 (2009) 055020 [arXiv:0908.0342] [INSPIRE].
C.D. Carone, R. Ramos and M. Sher, LHC constraints on the Lee-Wick Higgs sector, Phys. Lett. B 732 (2014) 122 [arXiv:1403.0011] [INSPIRE].
A. Accioly et al., Investigations in the Lee-Wick electrodynamics, Mod. Phys. Lett. A 26 (2011) 1985 [INSPIRE].
T. Figy and R. Zwicky, The other Higgses, at resonance, in the Lee-Wick extension of the standard model, JHEP 10 (2011) 145 [arXiv:1108.3765] [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].
D. Anselmi, Fakeons and Lee-Wick models, JHEP 02 (2018) 141 [arXiv:1801.00915] [INSPIRE].
P. Chin and E.T. Tomboulis, Nonlocal vertices and analyticity: Landau equations and general Cutkosky rule, JHEP 06 (2018) 014 [arXiv:1803.08899] [INSPIRE].
J. Boos and C.D. Carone, Asymptotic nonlocality, Phys. Rev. D 104 (2021) 015028 [arXiv:2104.11195] [INSPIRE].
J. Boos and C.D. Carone, Asymptotic nonlocality in gauge theories, Phys. Rev. D 104 (2021) 095020 [arXiv:2109.06261] [INSPIRE].
J. Boos and C.D. Carone, Asymptotic nonlocality in non-Abelian gauge theories, Phys. Rev. D 105 (2022) 035034 [arXiv:2112.05270] [INSPIRE].
G.V. Efimov, Non-local quantum theory of the scalar field, Commun. Math. Phys. 5 (1967) 42 [INSPIRE].
N.V. Krasnikov, Nonlocal gauge theories, Theor. Math. Phys. 73 (1987) 1184 [INSPIRE].
Y.V. Kuzmin, Convergent nonlocal gravitation (in RUSSIAN), Sov. J. Nucl. Phys. 50 (1989) 1011 [INSPIRE].
E.T. Tomboulis, Superrenormalizable gauge and gravitational theories, hep-th/9702146 [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].
A. Ghoshal, A. Mazumdar, N. Okada and D. Villalba, Stability of infinite-derivative Abelian Higgs models, Phys. Rev. D 97 (2018) 076011 [arXiv:1709.09222] [INSPIRE].
L. Buoninfante, G. Lambiase and A. Mazumdar, Ghost-free infinite-derivative quantum field theory, Nucl. Phys. B 944 (2019) 114646 [arXiv:1805.03559] [INSPIRE].
J. Boos, Effects of nonlocality in gravity and quantum theory, Ph.D. thesis, Alberta University, Canada(2020) [arXiv:2009.10856] [INSPIRE].
A. Ghoshal, A. Mazumdar, N. Okada and D. Villalba, Nonlocal non-Abelian gauge theory: Conformal invariance and β-function, Phys. Rev. D 104 (2021) 015003 [arXiv:2010.15919] [INSPIRE].
E. Tomboulis, 1/N expansion and renormalization in quantum gravity, Phys. Lett. B 70 (1977) 361 [INSPIRE].
E. Tomboulis, Renormalizability and asymptotic freedom in quantum gravity, Phys. Lett. B 97 (1980) 77 [INSPIRE].
L. Modesto and I.L. Shapiro, Superrenormalizable quantum gravity with complex ghosts, Phys. Lett. B 755 (2016) 279 [arXiv:1512.07600] [INSPIRE].
L. Modesto, Super-renormalizable or finite Lee-Wick quantum gravity, Nucl. Phys. B 909 (2016) 584 [arXiv:1602.02421] [INSPIRE].
A. Pais and G.E. Uhlenbeck, On field theories with nonlocalized action, Phys. Rev. 79 (1950) 145 [INSPIRE].
G. Dvali, Black holes and large-N species solution to the hierarchy problem, Fortsch. Phys. 58 (2010) 528 [arXiv:0706.2050] [INSPIRE].
L. Buoninfante, A. Ghoshal, G. Lambiase and A. Mazumdar, Transmutation of nonlocal scale in infinite-derivative field theories, Phys. Rev. D 99 (2019) 044032 [arXiv:1812.01441] [INSPIRE].
K. Hinterbichler, Theoretical aspects of massive gravity, Rev. Mod. Phys. 84 (2012) 671 [arXiv:1105.3735] [INSPIRE].
M. Park, Quantum aspects of massive gravity II: non-Pauli-Fierz theory, JHEP 10 (2011) 130 [arXiv:1011.4266] [INSPIRE].
S. Talaganis, T. Biswas and A. Mazumdar, Towards understanding the ultraviolet behavior of quantum loops in infinite-derivative theories of gravity, Class. Quant. Grav. 32 (2015) 215017 [arXiv:1412.3467] [INSPIRE].
Y.-D. Li, L. Modesto and L. Rachwał, Exact solutions and spacetime singularities in nonlocal gravity, JHEP 12 (2015) 173 [arXiv:1506.08619] [INSPIRE].
L. Modesto and L. Rachwał, Nonlocal quantum gravity: A review, Int. J. Mod. Phys. D 26 (2017) 1730020 [INSPIRE].
K.S. Stelle, Classical gravity with higher derivatives, Gen. Rel. Grav. 9 (1978) 353 [INSPIRE].
I. Quandt and H.-J. Schmidt, The Newtonian limit of fourth and higher-order gravity, Astron. Nachr. 312 (1991) 97 [gr-qc/0109005] [INSPIRE].
L. Modesto, T. de Paula Netto and I.L. Shapiro, On Newtonian singularities in higher-derivative gravity models, JHEP 04 (2015) 098 [arXiv:1412.0740] [INSPIRE].
N. Burzillà, B.L. Giacchini, T.P. Netto and L. Modesto, Higher-order regularity in local and nonlocal quantum gravity, Eur. Phys. J. C 81 (2021) 462 [arXiv:2012.11829] [INSPIRE].
A.A. Tseytlin, On singularities of spherically symmetric backgrounds in string theory, Phys. Lett. B 363 (1995) 223 [hep-th/9509050] [INSPIRE].
P. Nicolini, A. Smailagic and E. Spallucci, Noncommutative geometry inspired Schwarzschild black hole, Phys. Lett. B 632 (2006) 547 [gr-qc/0510112] [INSPIRE].
L. Modesto, J.W. Moffat and P. Nicolini, Black holes in an ultraviolet complete quantum gravity, Phys. Lett. B 695 (2011) 397 [arXiv:1010.0680] [INSPIRE].
J. Edholm, A.S. Koshelev and A. Mazumdar, Behavior of the Newtonian potential for ghost-free gravity and singularity-free gravity, Phys. Rev. D 94 (2016) 104033 [arXiv:1604.01989] [INSPIRE].
B.L. Giacchini, On the cancellation of Newtonian singularities in higher-derivative gravity, Phys. Lett. B 766 (2017) 306 [arXiv:1609.05432] [INSPIRE].
J. Boos, V.P. Frolov and A. Zelnikov, Gravitational field of static p-branes in linearized ghost-free gravity, Phys. Rev. D 97 (2018) 084021 [arXiv:1802.09573] [INSPIRE].
A. Akil et al., Semiclassical spacetimes at super-Planckian scales from delocalized sources, arXiv:2211.01657 [INSPIRE].
M.E. Peskin and D.V. Schroeder, An introduction to quantum field theory, Addison-Wesley, Reading, U.S.A. (1995) [INSPIRE].
I. Antoniadis, J. Iliopoulos and T.N. Tomaras, Gauge invariance in quantum gravity, Nucl. Phys. B 267 (1986) 497 [INSPIRE].
P.T. Mackay and D.J. Toms, Quantum gravity and scalar fields, Phys. Lett. B 684 (2010) 251 [arXiv:0910.1703] [INSPIRE].
V.P. Frolov and A. Zelnikov, Head-on collision of ultrarelativistic particles in ghost-free theories of gravity, Phys. Rev. D 93 (2016) 064048 [arXiv:1509.03336] [INSPIRE].
Acknowledgments
We thank the NSF for support under Grants PHY-1819575 and PHY-2112460.
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Boos, J., Carone, C.D. Asymptotically nonlocal gravity. J. High Energ. Phys. 2023, 17 (2023). https://doi.org/10.1007/JHEP06(2023)017
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DOI: https://doi.org/10.1007/JHEP06(2023)017