The effective kinetic term in CDT

Abstract

We report on recently performed simulations of Causal Dynamical Triangulations (CDT) in 2+1 dimensions aimed at studying its effective dynamics in the continuum limit. Two pieces of evidence from completely different measurements are presented suggesting that three-dimensional CDT is effectively described by an action with kinetic term given by a modified Wheeler-De Witt metric. These observations could strengthen an earlier observed connection between CDT and Horava-Lifshitz gravity. One piece of evidence comes from measurements of the modular parameter in CDT simulations with spatial topology of a torus, the other from measurements of local metric fluctuations close to a fixed spatial boundary.

Publication
J. Phys.: Conf. Ser. 360, 012038 (2012)
Date

Citations

  1. Ambjørn, Jan, et al. “Nonperturbative quantum gravity.” Physics Reports 519.4-5 (2012): 127-210.
  2. Anderson, Christian, et al. “Quantizing Hořava-Lifshitz gravity via causal dynamical triangulations.” Physical Review D 85.4 (2012): 044027.
  3. Ambjørn, Jan, et al. “Quantum gravity via causal dynamical triangulations.” Springer Handbook of Spacetime. Springer, Berlin, Heidelberg, 2014. 723-741.
  4. Koslowski, Tim A. “Shape dynamics and effective field theory.” International Journal of Modern Physics A 28.13 (2013): 1330017.
  5. Benedetti, Dario, and Joe Henson. “Spacetime condensation in (2+ 1)-dimensional CDT from a Hořava–Lifshitz minisuperspace model.” Classical and Quantum Gravity 32.21 (2015): 215007.
  6. Cooperman, Joshua H., and Jonah M. Miller. “A first look at transition amplitudes in (2+ 1)-dimensional causal dynamical triangulations.” Classical and Quantum Gravity 31.3 (2014): 035012.
  7. Loll, R., and L. Pires. “Role of the extra coupling in the kinetic term in Ho ř ava-Lifshitz gravity.” Physical Review D 90.12 (2014): 124050.
  8. Ambjørn, Jan, et al. “The phase structure of Causal Dynamical Triangulations with toroidal spatial topology.” arXiv preprint arXiv:1802.10434 (2018).
  9. Budd, T.. Non-perturbative quantum gravity: a conformal perspective. Diss. Utrecht University, 2012.
  10. Loll, R., and L. Pires. “More on Little Lambda in Horava-Lifshitz Gravity.” arXiv preprint arXiv:1407.1259 (2014).
  11. Benedetti, Dario, and James P. Ryan. “Capturing the phase diagram of (2+ 1)-dimensional CDT using a balls-in-boxes model.” Classical and Quantum Gravity 34.10 (2017): 105012.
  12. Miller, Jonah. Selected Problems in Computational Gravity. Diss. 2017.
  13. Baytas, Bekir, Martin Bojowald, Sean Crowe, and Jakub Mielczarek. “Minisuperspace results for causal dynamical triangulations.” arXiv preprint arXiv:1905.11843 (2019).
  14. Eichhorn, A., Pereira, A.D. and Pithis, A.G., 2020. The phase diagram of the multi-matrix model with ABAB-interaction from functional renormalization. arXiv preprint arXiv:2009.05111.
  15. Brunekreef, J. and Loll, R. “On the Nature of Spatial Universes in 3D Lorentzian Quantum Gravity”. arXiv preprint arXiv:2208.12718 (2022).