Abstract
We perform a detailed investigation of the phase structure and the semiclassical effective action of (2+1)-dimensional Causal Dynamical Triangulations (CDT) quantum gravity using computer simulations. On the one hand, we study the effect of enlarging the ensemble of triangulations by relaxing the simplicial manifold conditions in a controlled way. On the other hand, we cast a first look at CDT geometries with spatial topology beyond that of the sphere or torus. We measure the phase structure of the model for several triangulation ensembles and spatial topologies, finding evidence that the phase structure is qualitatively unaffected by these generalizations. Furthermore, we determine the effective action for the spatial volumes of the system, again varying the simplicial manifold conditions and the spatial topology. In all cases where we were able to gather sufficient statistics, we found the resulting effective action to be consistent with a minisuperspace action derived from continuum Einstein gravity, although more work is needed to confirm this conclusion. We interpret our overall results as evidence that 1) partially relaxing simplicial manifold conditions or changing the spatial genus does not affect the continuum limit of 3D CDT and that 2) increasing the spatial genus of the system likely does not influence the leading-order terms in the emergent effective action.
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J. Ambjørn, A. Görlich, J. Jurkiewicz, and R. Loll, Nonperturbative quantum gravity, Phys. Rept. 519 (2012) 127 [arXiv:1203.3591] [INSPIRE].
R. Loll, Quantum gravity from causal dynamical triangulations: a review, Class. Quant. Grav. 37 (2020), no. 1 013002 [arXiv:1905.08669] [INSPIRE].
J. Ambjørn and R. Loll, Nonperturbative Lorentzian quantum gravity, causality and topology change, Nucl. Phys. B 536 (1998) 407 [hep-th/9805108] [INSPIRE].
J. Ambjørn, J. Jurkiewicz, and R. Loll, Nonperturbative 3 − D Lorentzian quantum gravity, Phys. Rev. D 64 (2001) 044011 [hep-th/0011276] [INSPIRE].
J. Ambjørn, J. Jurkiewicz, and R. Loll, Dynamically triangulating Lorentzian quantum gravity, Nucl. Phys. B 610 (2001) 347 [hep-th/0105267] [INSPIRE].
J. Ambjørn, S. Jordan, J. Jurkiewicz, and R. Loll, A second-order phase transition in CDT, Phys. Rev. Lett. 107 (2011) 211303 [arXiv:1108.3932] [INSPIRE].
J. Ambjørn, S. Jordan, J. Jurkiewicz, and R. Loll, Second- and First-Order Phase Transitions in CDT, Phys. Rev. D 85 (2012) 124044 [arXiv:1205.1229] [INSPIRE].
J. Ambjørn, J. Jurkiewicz, and R. Loll, Emergence of a 4 − D world from causal quantum gravity, Phys. Rev. Lett. 93 (2004) 131301 [hep-th/0404156] [INSPIRE].
J. Ambjørn et al., CDT quantum toroidal spacetimes: an overview, Universe 7 (2021) 79 [arXiv:2103.15610] [INSPIRE].
J. Ambjørn, A. Görlich, J. Jurkiewicz, and R. Loll, Planckian birth of the quantum de Sitter universe, Phys. Rev. Lett. 100 (2008) 091304 [arXiv:0712.2485] [INSPIRE].
J. Ambjørn, A. Görlich, J. Jurkiewicz, and R. Loll, The Nonperturbative Quantum de Sitter Universe, Phys. Rev. D 78 (2008) 063544 [arXiv:0807.4481] [INSPIRE].
N. Klitgaard and R. Loll, How round is the quantum de Sitter universe?, Eur. Phys. J. C 80 (2020), no. 10 990 [arXiv:2006.06263] [INSPIRE].
F. David, Planar diagrams, two-dimensional lattice gravity and surface models, Nucl. Phys. B 257 (1985) 45.
V.A. Kazakov, I.K. Kostov, and A.A. Migdal, Critical properties of randomly triangulated planar random surfaces, Phys. Lett. B 157 (1985) 295.
B. Durhuus, J. Fröhlich and T. Jónsson, Critical behaviour in a model of planar random surfaces, Nucl. Phys. B 240 (1984) 453.
J. Ambjørn, B. Durhuus, T. Jonsson and O. Jonsson, Quantum geometry: a statistical field theory approach, Cambridge University Press, Cambridge U.K. (1997).
J. Ambjørn, J. Jurkiewicz, and R. Loll, Semiclassical universe from first principles, Phys. Lett. B 607 (2005) 205 [hep-th/0411152] [INSPIRE].
J. Ambjørn, J. Jurkiewicz, and R. Loll, Reconstructing the universe, Phys. Rev. D 72 (2005) 064014 [hep-th/0505154] [INSPIRE].
S. Carlip, Quantum gravity in 2 + 1 dimensions, Cambridge Monographs on Mathematical Physics, Cambridge University Press, Cambridge U.K. (1998).
T.G. Budd, The effective kinetic term in CDT, J. Phys. Conf. Ser. 36 (2012) 012038 [arXiv:1110.5158] [INSPIRE].
T.G. Budd and R. Loll, Exploring torus universes in causal dynamical triangulations, Phys. Rev. D 88 (2013) 024015 [arXiv:1305.4702] [INSPIRE].
J. Ambjørn, J. Jurkiewicz, R. Loll, and G. Vernizzi, Lorentzian 3D gravity with wormholes via matrix models, JHEP 09 (2001) 022 [hep-th/0106082] [INSPIRE].
J. Ambjørn, G. Thorleifsson, and M. Wexler, New critical phenomena in 2D quantum gravity, Nucl. Phys. B 439 (1995) 187 [hep-lat/9411034] [INSPIRE].
W.T. Tutte, A census of planar triangulations, Canad. J. Math. 14 (1962) 21.
E. Brézin, C. Itzykson, G. Parisi and J.B. Zuber, Planar diagrams, Commun. Math. Phys. 59 (1978) 35.
J. Brunekreef and R. Loll, On the nature of spatial universes in 3D lorentzian quantum gravity, arXiv:2208.12718 [INSPIRE].
J. Ambjørn, J. Jurkiewicz, and R. Loll, Computer simulations of 3D Lorentzian quantum gravity, Nucl. Phys. B Proc. Suppl. 94 (2001) 689 [hep-lat/0011055] [INSPIRE].
J. Ambjørn, J. Jurkiewicz, and R. Loll, 3D Lorentzian, dynamically triangulated quantum gravity, Nucl. Phys. B Proc. Suppl. 106 (2002) 980 [hep-lat/0201013] [INSPIRE].
J. Brunekreef, D. Németh, and A. Görlich, JorenB/3d-cdt: first release, Zenodo, (2022).
J. Ambjørn, J. Jurkiewicz, and R. Loll, Renormalization of 3 − D quantum gravity from matrix models, Phys. Lett. B 581 (2004) 255 [hep-th/0307263] [INSPIRE].
D. Benedetti, R. Loll, and F. Zamponi, (2 + 1)-dimensional quantum gravity as the continuum limit of causal dynamical triangulations, Phys. Rev. D 76 (2007) 104022 [arXiv:0704.3214] [INSPIRE].
D. Benedetti and J.P. Ryan, Capturing the phase diagram of (2 + 1)-dimensional CDT using a balls-in-boxes model, Class. Quant. Grav. 34 (2017) 105012 [arXiv:1612.09533] [INSPIRE].
D. Benedetti and J. Henson, Spectral geometry as a probe of quantum spacetime, Phys. Rev. D 80 (2009) 124036 [arXiv:0911.0401] [INSPIRE].
J. Ambjørn, J. Jurkiewicz, and R. Loll, Spectral dimension of the universe, Phys. Rev. Lett. 95 (2005) 171301 [hep-th/0505113] [INSPIRE].
S. Jordan and R. Loll, Causal dynamical triangulations without preferred foliation, Phys. Lett. B 724 (2013) 155 [arXiv:1305.4582] [INSPIRE].
S. Jordan and R. Loll, de Sitter universe from causal dynamical triangulations without preferred foliation, Phys. Rev. D 88 (2013) 044055 [arXiv:1307.5469] [INSPIRE].
C. Anderson, S.J. Carlip, J.H. Cooperman, P. Hořava, R.K. Kommu, and P.R. Zulkowski, Quantizing Hořava-Lifshitz gravity via causal dynamical triangulations, Phys. Rev. D 85 (2012) 044027 [arXiv:1111.6634] [INSPIRE].
J.H. Cooperman and J. Miller, A first look at transition amplitudes in (2 + 1)-dimensional causal dynamical triangulations, Class. Quant. Grav. 31 (2014), no. 3 035012 [arXiv:1305.2932] [INSPIRE].
J. Ambjørn, R. Loll, W. Westra, and S. Zohren, Putting a cap on causality violations in CDT, JHEP 12 (2007) 017 [arXiv:0709.2784] [INSPIRE].
J. Ambjørn, J. Gizbert-Studnicki, A.T. Görlich, J. Jurkiewicz, and R. Loll, The transfer matrix method in four-dimensional causal dynamical triangulations, AIP Conf. Proc. 1514 (2013), no. 1 67–72 [arXiv:1302.2210] [INSPIRE].
N. Goldenfeld, Lectures on phase transitions and the renormalization group, CRC Press, Boca Raton U.S.A. (2019).
J. Ambjørn, J. Gizbert-Studnicki, A. Görlich, and J. Jurkiewicz, The effective action in 4-dim CDT. The transfer matrix approach, JHEP 06 (2014) 034 [arXiv:1403.5940] [INSPIRE].
J. Ambjørn, Z. Drogosz, J. Gizbert-Studnicki, A. Görlich, J. Jurkiewicz, and D. Nemeth, Impact of topology in causal dynamical triangulations quantum gravity, Phys. Rev. D 94 (2016) 044010 [arXiv:1604.08786] [INSPIRE].
J. Ambjørn, J. Gizbert-Studnicki, A. Görlich, K. Grosvenor, and J. Jurkiewicz, Four-dimensional CDT with toroidal topology, Nucl. Phys. B 922 (2017) 226 [arXiv:1705.07653] [INSPIRE].
M. Jungerman and G. Ringel, Minimal triangulations on orientable surfaces, Acta Math. 145 (1980) 121.
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Brunekreef, J., Németh, D. The phase structure and effective action of 3D CDT at higher spatial genus. J. High Energ. Phys. 2022, 212 (2022). https://doi.org/10.1007/JHEP09(2022)212
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DOI: https://doi.org/10.1007/JHEP09(2022)212