Abstract
We explore an extended coupling constant space of 4d regularized Euclidean quantum gravity, defined via the formalism of dynamical triangulations. We add a measure term which can also serve as a generalized higher curvature term and determine the phase diagram and the geometries dominating in the various regions. A first order phase transition line is observed, but no second order transition point is located. As a consequence we cannot attribute any continuum physics interpretation to the so-called crinkled phase of 4d dynamical triangulations.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
J. Ambjørn and J. Jurkiewicz, Four-dimensional simplicial quantum gravity, Phys. Lett. B 278 (1992)42 [INSPIRE].
M. Agishtein and A.A. Migdal, Simulations of four-dimensional simplicial quantum gravity, Mod. Phys. Lett. A 7 (1992) 1039 [INSPIRE].
M. Agishtein and A.A. Migdal, Critical behavior of dynamically triangulated quantum gravity in four-dimensions, Nucl. Phys. B 385 (1992) 395 [hep-lat/9204004] [INSPIRE].
S. Weinberg, Ultraviolet divergences in quantum theories of gravitation, in General relativity: Einstein centenary survey, S.W. Hawking and W. Israel eds., Cambridge University Press, Cambridge U.K. (1979).
H. Kawai and M. Ninomiya, Renormalization group and quantum gravity, Nucl. Phys. B 336 (1990)115 [INSPIRE].
H. Kawai, Y. Kitazawa and M. Ninomiya, Scaling exponents in quantum gravity near two-dimensions, Nucl. Phys. B 393 (1993) 280 [hep-th/9206081] [INSPIRE].
H. Kawai, Y. Kitazawa and M. Ninomiya, Ultraviolet stable fixed point and scaling relations in (2 + ϵ)-dimensional quantum gravity, Nucl. Phys. B 404 (1993) 684 [hep-th/9303123] [INSPIRE].
H. Kawai, Y. Kitazawa and M. Ninomiya, Renormalizability of quantum gravity near two-dimensions, Nucl. Phys. B 467 (1996) 313 [hep-th/9511217] [INSPIRE].
T. Aida, Y. Kitazawa, H. Kawai and M. Ninomiya, Conformal invariance and renormalization group in quantum gravity near two-dimensions, Nucl. Phys. B 427 (1994) 158 [hep-th/9404171] [INSPIRE].
M. Reuter, Nonperturbative evolution equation for quantum gravity, Phys. Rev. D 57 (1998) 971 [hep-th/9605030] [INSPIRE].
A. Codello, R. Percacci and C. Rahmede, Investigating the ultraviolet properties of gravity with a wilsonian renormalization group equation, Annals Phys. 324 (2009) 414 [arXiv:0805.2909] [INSPIRE].
M. Reuter and F. Saueressig, Functional renormalization group equations, asymptotic safety and quantum einstein gravity, arXiv:0708.1317 [INSPIRE].
M. Niedermaier and M. Reuter, The asymptotic safety scenario in quantum gravity, Living Rev. Rel. 9 (2006) 5.
D.F. Litim, Fixed points of quantum gravity, Phys. Rev. Lett. 92 (2004) 201301 [hep-th/0312114] [INSPIRE].
P. Bialas, Z. Burda, A. Krzywicki and B. Petersson, Focusing on the fixed point of 4D simplicial gravity, Nucl. Phys. B 472 (1996) 293 [hep-lat/9601024] [INSPIRE].
B.V. de Bakker, Further evidence that the transition of 4D dynamical triangulation is first order, Phys. Lett. B 389 (1996) 238 [hep-lat/9603024] [INSPIRE].
S.M. Catterall, J.B. Kogut, R.L. Renken and G. Thorleifsson, Simplicial gravity in dimension greater than two, Nucl. Phys. (Proc. Suppl.) B 53 (1997) 756 [hep-lat/9608042] [INSPIRE].
K.S. Stelle, Renormalization of higher derivative quantum gravity, Phys. Rev. D 16 (1977) 953 [INSPIRE].
K.S. Stelle, Classical gravity with higher derivatives, Gen. Rel. Grav. 9 (1978) 353 [INSPIRE].
M.R. Niedermaier, Gravitational fixed points from perturbation theory, Phys. Rev. Lett. 103 (2009) 101303 [INSPIRE].
A. Codello and R. Percacci, Fixed points of higher derivative gravity, Phys. Rev. Lett. 97 (2006)221301 [hep-th/0607128] [INSPIRE].
D. Benedetti, P.F. Machado and F. Saueressig, Asymptotic safety in higher-derivative gravity, Mod. Phys. Lett. A 24 (2009) 2233 [arXiv:0901.2984] [INSPIRE].
D. Benedetti, P.F. Machado and F. Saueressig, Taming perturbative divergences in asymptotically safe gravity, Nucl. Phys. B 824 (2010) 168 [arXiv:0902.4630] [INSPIRE].
J. Ambjørn, J. Jurkiewicz and C.F. Kristjansen, Quantum gravity, dynamical triangulations and higher derivative regularization, Nucl. Phys. B 393 (1993) 601 [hep-th/9208032] [INSPIRE].
T. Regge, General relativity without coordinates, Nuovo Cim. 19 (1961) 558 [INSPIRE].
S. Bilke et al., 4D simplicial quantum gravity: Matter fields and the corresponding effective action, Phys. Lett. B 432 (1998) 279 [hep-lat/9804011] [INSPIRE].
S. Bilke et al., 4D simplicial quantum gravity interacting with gauge matter fields, Phys. Lett. B 418 (1998) 266 [hep-lat/9710077] [INSPIRE].
J. Fröhlich, The statistical mechanics of surfaces, in Non-perturbative quantum field theory, J. Fröhlich ed., World Scientific, Singapore (1992); also in Proceedings, Applications of field theory to statistical mechanics , June 10–15, Sitges, Spain (1984).
J. Fröhlich, Survey of random surface theory, in the proceedings of Recent developments in quantum field theory, May 6–10, Copenaghen, Denmark (1985).
J. Ambjørn, B. Durhuus and J. Fröhlich, Diseases of triangulated random surface models and possible cures, Nucl. Phys. B 257 (1985) 433 [INSPIRE].
B. Bruegmann and E. Marinari, 4D simplicial quantum gravity with a nontrivial measure, Phys. Rev. Lett. 70 (1993) 1908 [hep-lat/9210002] [INSPIRE].
V.A. Kazakov, M. Staudacher and T. Wynter, Exact solution of discrete two-dimensional R 2 gravity, Nucl. Phys. B 471 (1996) 309 [hep-th/9601069] [INSPIRE].
D. Benedetti and R. Gurau, Phase transition in dually weighted colored tensor models, Nucl. Phys. B 855 (2012) 420 [arXiv:1108.5389] [INSPIRE].
J. Ambjørn, K. Anagnostopoulos and J. Jurkiewicz, Abelian gauge fields coupled to simplicial quantum gravity, JHEP 08 (1999) 016 [hep-lat/9907027] [INSPIRE].
S. Horata, H. Egawa, N. Tsuda and T. Yukawa, Phase structure of four-dimensional simplicial quantum gravity with a U(1) gauge field, Prog. Theor. Phys. 106 (2001) 1037 [hep-lat/0004021] [INSPIRE].
H. Egawa, S. Horata, N. Tsuda and T. Yukawa, Phase transition of 4D simplicial quantum gravity with U(1) gauge field, Nucl. Phys. Proc. Suppl. 83 (2000) 751 [hep-lat/9908048] [INSPIRE].
S. Horata, H.S. Egawa and T. Yukawa, Matter dependence of the string susceptibility exponent in four-dimensional simplicial quantum gravity, Prog. Theor. Phys. 108 (2002) 1171.
S. Horata, H. Egawa and T. Yukawa, Grand canonical simulation of 4D simplicial quantum gravity, Nucl. Phys. Proc. Suppl. 119 (2003) 921 [hep-lat/0209004] [INSPIRE].
J. Laiho and D. Coumbe, Evidence for asymptotic safety from lattice quantum gravity, Phys. Rev. Lett. 107 (2011) 161301 [arXiv:1104.5505] [INSPIRE].
J. Ambjørn, J. Jurkiewicz and R. Loll, Spectral dimension of the universe, Phys. Rev. Lett. 95 (2005) 171301 [hep-th/0505113] [INSPIRE].
J. Ambjørn, A. Görlich, J. Jurkiewicz and R. Loll, Nonperturbative quantum gravity, Phys. Rept. 519 (2012) 127 [arXiv:1203.3591] [INSPIRE].
J. Ambjørn, J. Jurkiewicz and R. Loll, Dynamically triangulating Lorentzian quantum gravity, Nucl. Phys. B 610 (2001) 347 [hep-th/0105267] [INSPIRE].
P. Hořava, Quantum gravity at a Lifshitz point, Phys. Rev. D 79 (2009) 084008 [arXiv:0901.3775] [INSPIRE].
P. Hořava and C.M. Melby-Thompson, General covariance in quantum gravity at a Lifshitz point, Phys. Rev. D 82 (2010) 064027 [arXiv:1007.2410] [INSPIRE].
S. Bilke and G. Thorleifsson, Simulating four-dimensional simplicial gravity using degenerate triangulations, Phys. Rev. D 59 (1999) 124008 [hep-lat/9810049] [INSPIRE].
M. Gross and S. Varsted, Elementary moves and ergodicity in D-dimensional simplicial quantum gravity, Nucl. Phys. B 378 (1992) 367 [INSPIRE].
J. Ambjørn, S. Jain, J. Jurkiewicz and C. Kristjansen, Observing 4D baby universes in quantum gravity, Phys. Lett. B 305 (1993) 208 [hep-th/9303041] [INSPIRE].
J. Ambjørn, S. Jain and G. Thorleifsson, Baby universes in 2D quantum gravity, Phys. Lett. B 307 (1993) 34 [hep-th/9303149] [INSPIRE].
J. Ambjørn and J. Jurkiewicz, Scaling in four-dimensional quantum gravity, Nucl. Phys. B 451 (1995) 643 [hep-th/9503006] [INSPIRE].
S. Catterall, J.B. Kogut and R. Renken, Phase structure of four-dimensional simplicial quantum gravity, Phys. Lett. B 328 (1994) 277 [hep-lat/9401026] [INSPIRE].
B.V. de Bakker and J. Smit, Curvature and scaling in 4D dynamical triangulation, Nucl. Phys. B 439 (1995) 239 [hep-lat/9407014] [INSPIRE].
B. de Bakker and J. Smit, Exploring curvature and scaling in 4D dynamical triangulation, Nucl. Phys. Proc. Suppl. 42 (1995) 719 [INSPIRE].
J. Smit, Continuum interpretation of the dynamical-triangulation formulation of quantum Einstein gravity, JHEP 08 (2013) 016 [arXiv:1304.6339] [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1307.2270
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License ( https://creativecommons.org/licenses/by/2.0 ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
About this article
Cite this article
Ambjørn, J., Glaser, L., Görlich, A. et al. Euclidian 4d quantum gravity with a non-trivial measure term. J. High Energ. Phys. 2013, 100 (2013). https://doi.org/10.1007/JHEP10(2013)100
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP10(2013)100