Abstract
The validity of the Coleman mechanism, which automatically tunes the fundamental constants, is examined in two-dimensional and four-dimensional quantum gravity theories. First, we consider two-dimensional Euclidean quantum gravity on orientable closed manifolds coupled to conformal matter of central charge c ≤ 1. The proper time Hamiltonian of this system is known to be written as a field theory of noncritical strings, which can also be viewed as a third quantization in two dimensions. By directly counting the number of random surfaces with various topologies, we find that the contribution of the baby universes is too small to realize the Coleman mechanism. Next, we consider four-dimensional Lorentzian gravity. Based on the difference between the creation of the mother universe from nothing and the annihilation of the mother universe into nothing, we introduce a non-Hermitian effective Hamiltonian for the multiverse. We show that Coleman’s idea is satisfied in this model and that the cosmological constant is tuned to be nearly zero. Potential implications for phenomenology are also discussed.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
S.R. Coleman, Why There Is Nothing Rather Than Something: A Theory of the Cosmological Constant, Nucl. Phys. B 310 (1988) 643 [INSPIRE].
I.R. Klebanov, L. Susskind and T. Banks, Wormholes and the Cosmological Constant, Nucl. Phys. B 317 (1989) 665 [INSPIRE].
S.B. Giddings and A. Strominger, Axion Induced Topology Change in Quantum Gravity and String Theory, Nucl. Phys. B 306 (1988) 890 [INSPIRE].
H. Kawai, Low energy effective action of quantum gravity and the naturalness problem, Int. J. Mod. Phys. A 28 (2013) 1340001 [INSPIRE].
A. Hebecker, T. Mikhail and P. Soler, Euclidean wormholes, baby universes, and their impact on particle physics and cosmology, Front. Astron. Space Sci. 5 (2018) 35 [arXiv:1807.00824] [INSPIRE].
W. Fischler and L. Susskind, A wormhole catastrophe, Phys. Lett. B 217 (1989) 48 [INSPIRE].
J. Polchinski, The Phase of the Sum Over Spheres, Phys. Lett. B 219 (1989) 251 [INSPIRE].
W. Fischler, I.R. Klebanov, J. Polchinski and L. Susskind, Quantum Mechanics of the Googolplexus, Nucl. Phys. B 327 (1989) 157 [INSPIRE].
H. Kawai and T. Okada, Asymptotically Vanishing Cosmological Constant in the Multiverse, Int. J. Mod. Phys. A 26 (2011) 3107 [arXiv:1104.1764] [INSPIRE].
H. Kawai and T. Okada, Solving the Naturalness Problem by Baby Universes in the Lorentzian Multiverse, Prog. Theor. Phys. 127 (2012) 689 [arXiv:1110.2303] [INSPIRE].
Y. Hamada, H. Kawai and K. Kawana, Evidence of the Big Fix, Int. J. Mod. Phys. A 29 (2014) 1450099 [arXiv:1405.1310] [INSPIRE].
Y. Hamada, H. Kawai and K. Kawana, Weak Scale From the Maximum Entropy Principle, PTEP 2015 (2015) 033B06 [arXiv:1409.6508] [INSPIRE].
Y. Hamada, H. Kawai and K. Kawana, Natural solution to the naturalness problem: The universe does fine-tuning, PTEP 2015 (2015) 123B03 [arXiv:1509.05955] [INSPIRE].
G. Penington, Entanglement Wedge Reconstruction and the Information Paradox, JHEP 09 (2020) 002 [arXiv:1905.08255] [INSPIRE].
A. Almheiri, N. Engelhardt, D. Marolf and H. Maxfield, The entropy of bulk quantum fields and the entanglement wedge of an evaporating black hole, JHEP 12 (2019) 063 [arXiv:1905.08762] [INSPIRE].
G. Penington, S.H. Shenker, D. Stanford and Z. Yang, Replica wormholes and the black hole interior, JHEP 03 (2022) 205 [arXiv:1911.11977] [INSPIRE].
A. Almheiri, T. Hartman, J. Maldacena, E. Shaghoulian and A. Tajdini, Replica Wormholes and the Entropy of Hawking Radiation, JHEP 05 (2020) 013 [arXiv:1911.12333] [INSPIRE].
A. Almheiri, T. Hartman, J. Maldacena, E. Shaghoulian and A. Tajdini, The entropy of Hawking radiation, Rev. Mod. Phys. 93 (2021) 035002 [arXiv:2006.06872] [INSPIRE].
S. Raju, Lessons from the information paradox, Phys. Rept. 943 (2022) 1 [arXiv:2012.05770] [INSPIRE].
A. Lyons and S.W. Hawking, Wormholes in string theory, Phys. Rev. D 44 (1991) 3802 [INSPIRE].
P. Betzios and O. Papadoulaki, Liouville theory and Matrix models: A Wheeler DeWitt perspective, JHEP 09 (2020) 125 [arXiv:2004.00002] [INSPIRE].
J. Ambjørn, Y. Sato and Y. Watabiki, Wormholes, a fluctuating cosmological constant and the Coleman mechanism, Phys. Lett. B 815 (2021) 136152 [arXiv:2101.00478] [INSPIRE].
C. Teitelboim, Gravitation and Hamiltonian Structure in Two Space-Time Dimensions, Phys. Lett. B 126 (1983) 41 [INSPIRE].
R. Jackiw, Lower Dimensional Gravity, Nucl. Phys. B 252 (1985) 343 [INSPIRE].
V.G. Knizhnik, A.M. Polyakov and A.B. Zamolodchikov, Fractal Structure of 2D Quantum Gravity, Mod. Phys. Lett. A 3 (1988) 819 [INSPIRE].
F. David, Conformal Field Theories Coupled to 2D Gravity in the Conformal Gauge, Mod. Phys. Lett. A 3 (1988) 1651 [INSPIRE].
J. Distler and H. Kawai, Conformal Field Theory and 2D Quantum Gravity, Nucl. Phys. B 321 (1989) 509 [INSPIRE].
F. David, Planar Diagrams, Two-Dimensional Lattice Gravity and Surface Models, Nucl. Phys. B 257 (1985) 45 [INSPIRE].
V.A. Kazakov, Bilocal Regularization of Models of Random Surfaces, Phys. Lett. B 150 (1985) 282 [INSPIRE].
D.V. Boulatov, V.A. Kazakov, I.K. Kostov and A.A. Migdal, Analytical and Numerical Study of the Model of Dynamically Triangulated Random Surfaces, Nucl. Phys. B 275 (1986) 641 [INSPIRE].
J. Ambjørn, B. Durhuus and J. Fröhlich, Diseases of Triangulated Random Surface Models, and Possible Cures, Nucl. Phys. B 257 (1985) 433 [INSPIRE].
V.A. Kazakov, A.A. Migdal and I.K. Kostov, Critical Properties of Randomly Triangulated Planar Random Surfaces, Phys. Lett. B 157 (1985) 295 [INSPIRE].
E. Brézin and V.A. Kazakov, Exactly Solvable Field Theories of Closed Strings, Phys. Lett. B 236 (1990) 144 [INSPIRE].
M.R. Douglas and S.H. Shenker, Strings in Less Than One-Dimension, Nucl. Phys. B 335 (1990) 635 [INSPIRE].
D.J. Gross and A.A. Migdal, Nonperturbative Two-Dimensional Quantum Gravity, Phys. Rev. Lett. 64 (1990) 127 [INSPIRE].
H. Kawai, Quantum gravity and random surfaces, Nucl. Phys. B Proc. Suppl. 26 (1992) 93 [INSPIRE].
P.H. Ginsparg and G.W. Moore, Lectures on 2-D gravity and 2-D string theory, in Theoretical Advanced Study Institute (TASI 92): From Black Holes and Strings to Particles, pp. 277–469 (1993) [hep-th/9304011] [INSPIRE].
P. Di Francesco, P.H. Ginsparg and J. Zinn-Justin, 2-D Gravity and random matrices, Phys. Rept. 254 (1995) 1 [hep-th/9306153] [INSPIRE].
Y. Nakayama, Liouville field theory: A Decade after the revolution, Int. J. Mod. Phys. A 19 (2004) 2771 [hep-th/0402009] [INSPIRE].
N. Ishibashi and H. Kawai, String field theory of noncritical strings, Phys. Lett. B 314 (1993) 190 [hep-th/9307045] [INSPIRE].
M. Fukuma, N. Ishibashi, H. Kawai and M. Ninomiya, Two-dimensional quantum gravity in temporal gauge, Nucl. Phys. B 427 (1994) 139 [hep-th/9312175] [INSPIRE].
H. Kawai, N. Kawamoto, T. Mogami and Y. Watabiki, Transfer matrix formalism for two-dimensional quantum gravity and fractal structures of space-time, Phys. Lett. B 306 (1993) 19 [hep-th/9302133] [INSPIRE].
S.B. Giddings and A. Strominger, Baby Universes, Third Quantization and the Cosmological Constant, Nucl. Phys. B 321 (1989) 481 [INSPIRE].
M. Ikehara, N. Ishibashi, H. Kawai, T. Mogami, R. Nakayama and N. Sasakura, String field theory in the temporal gauge, Phys. Rev. D 50 (1994) 7467 [hep-th/9406207] [INSPIRE].
N. Ishibashi and H. Kawai, String field theory of c ≤ 1 noncritical strings, Phys. Lett. B 322 (1994) 67 [hep-th/9312047] [INSPIRE].
P. Saad, S.H. Shenker and D. Stanford, JT gravity as a matrix integral, arXiv:1903.11115 [INSPIRE].
S. Hirano and T. Kuroki, Replica wormholes from Liouville theory, JHEP 01 (2022) 094 [arXiv:2109.12539] [INSPIRE].
T.G. Mertens and G.J. Turiaci, Defects in Jackiw-Teitelboim Quantum Gravity, JHEP 08 (2019) 127 [arXiv:1904.05228] [INSPIRE].
T.G. Mertens and G.J. Turiaci, Liouville quantum gravity — holography, JT and matrices, JHEP 01 (2021) 073 [arXiv:2006.07072] [INSPIRE].
G.J. Turiaci, M. Usatyuk and W.W. Weng, 2D dilaton-gravity, deformations of the minimal string, and matrix models, Class. Quant. Grav. 38 (2021) 204001 [arXiv:2011.06038] [INSPIRE].
K. Okuyama and K. Sakai, FZZT branes in JT gravity and topological gravity, JHEP 09 (2021) 191 [arXiv:2108.03876] [INSPIRE].
P. Gregori and R. Schiappa, From Minimal Strings towards Jackiw-Teitelboim Gravity: On their Resurgence, Resonance, and Black Holes, arXiv:2108.11409 [INSPIRE].
S.S. Gubser and I.R. Klebanov, Scaling functions for baby universes in two-dimensional quantum gravity, Nucl. Phys. B 416 (1994) 827 [hep-th/9310098] [INSPIRE].
D. Weingarten, A Lattice Field Theory for Interacting Strings, Phys. Lett. B 90 (1980) 280 [INSPIRE].
T. Eguchi and H. Kawai, Planar Random Surfaces on the Lattice, Phys. Lett. B 114 (1982) 247 [INSPIRE].
H. Kawai and Y. Okamoto, Entropy of Planar Random Surfaces on the Lattice, Phys. Lett. B 130 (1983) 415 [INSPIRE].
J. Ambjørn, B. Durhuus, J. Fröhlich and P. Orland, The Appearance of Critical Dimensions in Regulated String Theories, Nucl. Phys. B 270 (1986) 457 [INSPIRE].
J. Polchinski, A Two-Dimensional Model for Quantum Gravity, Nucl. Phys. B 324 (1989) 123 [INSPIRE].
S.R. Das, A. Dhar, A.M. Sengupta and S.R. Wadia, New Critical Behavior in d = 0 Large N Matrix Models, Mod. Phys. Lett. A 5 (1990) 1041 [INSPIRE].
B. Durhuus, Multispin systems on a randomly triangulated surface, Nucl. Phys. B 426 (1994) 203 [hep-th/9402052] [INSPIRE].
I.R. Klebanov, Touching random surfaces and Liouville gravity, Phys. Rev. D 51 (1995) 1836 [hep-th/9407167] [INSPIRE].
J.L.F. Barbón, K. Demeterfi, I.R. Klebanov and C. Schmidhuber, Correlation functions in matrix models modified by wormhole terms, Nucl. Phys. B 440 (1995) 189 [hep-th/9501058] [INSPIRE].
J. Ambjørn, T. Budd and Y. Makeenko, Generalized multicritical one-matrix models, Nucl. Phys. B 913 (2016) 357 [arXiv:1604.04522] [INSPIRE].
R.P. Geroch, Topology in general relativity, J. Math. Phys. 8 (1967) 782 [INSPIRE].
A. Vilenkin, Creation of Universes from Nothing, Phys. Lett. B 117 (1982) 25 [INSPIRE].
S.R. Coleman, Black Holes as Red Herrings: Topological Fluctuations and the Loss of Quantum Coherence, Nucl. Phys. B 307 (1988) 867 [INSPIRE].
S. Weinberg, The Cosmological constant problems, in 4th International Symposium on Sources and Detection of Dark Matter in the Universe (DM 2000), pp. 18–26 (2000) [astro-ph/0005265] [INSPIRE].
Y. Hamada, H. Kawai and K.-y. Oda, Minimal Higgs inflation, PTEP 2014 (2014) 023B02 [arXiv:1308.6651] [INSPIRE].
Y. Hamada, H. Kawai, K.-y. Oda and S.C. Park, Higgs inflation from Standard Model criticality, Phys. Rev. D 91 (2015) 053008 [arXiv:1408.4864] [INSPIRE].
Y. Hamada, H. Kawai, K. Kawana, K.-y. Oda and K. Yagyu, Minimal scenario of criticality for electroweak scale, neutrino masses, dark matter, and inflation, Eur. Phys. J. C 81 (2021) 962 [arXiv:2102.04617] [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2210.05134
Rights and permissions
Open Access . This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Hamada, Y., Kawai, H. & Kawana, K. Baby universes in 2d and 4d theories of quantum gravity. J. High Energ. Phys. 2022, 100 (2022). https://doi.org/10.1007/JHEP12(2022)100
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP12(2022)100