Abstract
We show that classically scale invariant gravity coupled to a single scalar field can undergo dimensional transmutation and generate an effective Einstein-Hilbert action for gravity, coupled to a massive dilaton. The same theory has an ultraviolet fixed point for coupling constant ratios such that all couplings are asymptotically free. However the catchment basin of this fixed point does not include regions of coupling constant parameter space compatible with locally stable dimensional transmutation. In a companion paper, we will explore whether this more desirable outcome does obtain in more complicated theories with non-Abelian gauge interactions.
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M.B. Einhorn and D.R.T. Jones, Naturalness and dimensional transmutation in classically scale-invariant gravity, JHEP 03 (2015) 047 [arXiv:1410.8513] [INSPIRE].
S.R. Coleman and E.J. Weinberg, Radiative corrections as the origin of spontaneous symmetry breaking, Phys. Rev. D 7 (1973) 1888 [INSPIRE].
I.L. Buchbinder, Mechanism for induction of Einstein gravitation, Sov. Phys. J. 29 (1986) 220 [INSPIRE].
G. Cognola and I.L. Shapiro, Back reaction of vacuum and the renormalization group flow from the conformal fixed point, Class. Quant. Grav. 15 (1998) 3411 [hep-th/9804119] [INSPIRE].
I.L. Shapiro and A.G. Zheksenaev, Gauge dependence in higher derivative quantum gravity and the conformal anomaly problem, Phys. Lett. B 324 (1994) 286 [INSPIRE].
M.B. Einhorn and D.R.T. Jones, Induced Gravity II: Grand Unified Theories, in preparation.
E.S. Fradkin and A.A. Tseytlin, Renormalizable asymptotically free quantum theory of gravity, Phys. Lett. B 104 (1981) 377 [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. B 159 (1985) 269 [INSPIRE].
I.G. Avramidi, Heat kernel and quantum gravity, Lect. Notes Phys. M 64 (2000) 1 [INSPIRE].
I.L. Buchbinder, S.D. Odintsov and I.L. Shapiro, Effective action in quantum gravity, IOP Publishing, Bristol U.K. (1992).
A. Salvio and A. Strumia, Agravity, JHEP 06 (2014) 080 [arXiv:1403.4226] [INSPIRE].
M.B. Einhorn and D.R.T. Jones, Gauss-Bonnet coupling constant in classically scale-invariant gravity, Phys. Rev. D 91 (2015) 084039 [arXiv:1412.5572] [INSPIRE].
T.P. Cheng, E. Eichten and L.-F. Li, Higgs Phenomena in Asymptotically Free Gauge Theories, Phys. Rev. D 9 (1974) 2259 [INSPIRE].
I.L. Buchbinder, J.J. Wolfengaut, I.L. Shapiro, V.B. Vologodsky and O.K. Kalashnikov, Asymptotically free grand unification models with quantum R 2 gravitation, Sov. J. Nucl. Phys. 49 (1989) 544 [INSPIRE].
I.L. Buchbinder, O.K. Kalashnikov, I.L. Shapiro, V.B. Vologodsky and J.J. Wolfengaut, The stability of asymptotic freedom in grand unified models coupled to R 2 gravity, Phys. Lett. B 216 (1989) 127 [INSPIRE].
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ArXiv ePrint: 1511.01481
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Einhorn, M.B., Jones, D.R.T. Induced gravity I: real scalar field. J. High Energ. Phys. 2016, 19 (2016). https://doi.org/10.1007/JHEP01(2016)019
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DOI: https://doi.org/10.1007/JHEP01(2016)019