We study the effective transfer matrix within the semiclassical and bifurcation phases of CDT quantum gravity. We find that for sufficiently large lattice volumes the kinetic term of the effective transfer matrix has a different sign in each of the two phases. We argue that this sign change can be viewed as a Wick rotation of the metric. We discuss the likely microscopic mechanism responsible for the bifurcation phase transition, and propose an order parameter that can potentially be used to determine the precise location and order of the transition. Using the effective transfer matrix we approximately locate the position of the bifurcation transition in some region of coupling constant space, allowing us to present an updated version of the CDT phase diagram.
J.F. Donoghue, Introduction to the effective field theory description of gravity, gr-qc/9512024.
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].
M.H. Goroff and A. Sagnotti, The ultraviolet behavior of Einstein gravity, Nucl. Phys. B 266 (1986) 709 [INSPIRE].
S. Weinberg, General relativity, an Einstein centenary survey, Cambridge University Press, Cambridge U.K. (1997).
J. Ambjorn, B. Durhuus and T. Jonsson, Quantum geometry. A statistical field theory approach, Camrbidge University Press, Cambridge U.K. (1997).
T. Regge, General relativity without coordinates, Nuovo Cim. 19 (1961) 558 [INSPIRE].
J. Hartle and S. Hawking, Wave function of the universe, Phys. Rev. D 28 (1983) 2960 [INSPIRE].
J Gizbert-Studnicki, The effective action in four-dimensional CDT, Ph.D. thesis, Jagiellonian University, Poland (2014).
T. Cailleteau, J. Mielczarek, A. Barrau and J. Grain, Anomaly-free scalar perturbations with holonomy corrections in loop quantum cosmology, Class. Quant. Grav. 29 (2012) 095010 [arXiv:1111.3535] [INSPIRE].
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ArXiv ePrint: 1503.08580
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Ambjørn, J., Coumbe, D.N., Gizbert-Studnicki, J. et al. Signature change of the metric in CDT quantum gravity?. J. High Energ. Phys. 2015, 33 (2015). https://doi.org/10.1007/JHEP08(2015)033
- Models of Quantum Gravity
- Lattice Models of Gravity