Exploring Euclidean dynamical triangulations with a non-trivial measure term
- 516 Downloads
We investigate a nonperturbative formulation of quantum gravity defined via Euclidean dynamical triangulations (EDT) with a non-trivial measure term in the path integral. We are motivated to revisit this older formulation of dynamical triangulations by hints from renormalization group approaches that gravity may be asymptotically safe and by the emergence of a semiclassical phase in causal dynamical triangulations (CDT).
We study the phase diagram of this model and identify the two phases that are well known from previous work: the branched polymer phase and the collapsed phase. We verify that the order of the phase transition dividing the branched polymer phase from the collapsed phase is almost certainly first-order. The nontrivial measure term enlarges the phase diagram, allowing us to explore a region of the phase diagram that has been dubbed the crinkled region. Although the collapsed and branched polymer phases have been studied extensively in the literature, the crinkled region has not received the same scrutiny. We find that the crinkled region is likely a part of the collapsed phase with particularly large finite-size effects. Intriguingly, the behavior of the spectral dimension in the crinkled region at small volumes is similar to that of CDT, as first reported in arXiv:1104.5505, but for sufficiently large volumes the crinkled region does not appear to have 4-dimensional semiclassical features. Thus, we find that the crinkled region of the EDT formulation does not share the good features of the extended phase of CDT, as we first suggested in arXiv:1104.5505. This agrees with the recent results of arXiv:1307.2270, in which the authors used a somewhat different discretization of EDT from the one presented here.
KeywordsLattice Models of Gravity Models of Quantum Gravity
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.
- G. ’t Hooft and M.J.G. Veltman, One loop divergencies in the theory of gravitation, Annales Poincaré Phys. Theor. A 20 (1974) 69 [INSPIRE].
- S. Weinberg, Ultraviolet divergences in quantum theories of gravitation, in General relativity, an Einstein centenary survey, chapter 16, S.W. Hawking and W. Israel eds., Cambridge University Press, Cambridge U.K. (1979), pg. 790 [INSPIRE].
- M.E. Agishtein and A.A. Migdal, Three-dimensional quantum gravity as dynamical triangulation, Mod. Phys. Lett. A 6 (1991) 1863 [Erratum ibid. A 6 (1991) 2555] [INSPIRE].
- S. Warner, S. Catterall and R. Renken, Phase structure of 3D dynamical triangulations with a boundary, in Toward the theory of everything, MRST’98, Montreal Canada (1998), pg. 212 [INSPIRE].