Towards an UV fixed point in CDT gravity

J Ambjørn,A Görlich,J Jurkiewicz,D Németh,J Gizbert-Studnicki

doi:10.1007/jhep07(2019)166

Abstract

CDT is an attempt to formulate a non-perturbative lattice theory of quantum gravity. We describe the phase diagram and analyse the phase transition between phase B and phase C (which is the analogue of the de Sitter phase observed for the spherical spatial topology). This transition is accessible to ordinary Monte Carlo simulations when the topology of space is toroidal. We find that the transition is most likely first order, but with unusual properties. The end points of the transition line are candidates for second order phase transition points where an UV continuum limit might exist.

Highlights

JHEP07(2019)166 with the lattice regularization is whether or not diffeomorphism invariance is recovered when the lattice spacing goes to zero
We describe the phase diagram and analyse the phase transition between phase B and phase C
The analysis of the relevant coupling constant region was made possible by switching from spherical spatial topology to toroidal spatial topology

Summary

The phase structure of CDT

The phase diagram of the CDT model with a toroidal spatial topology permits us to investigate the properties of the model in an important range of the bare coupling constants, previously inaccessible to numerical measurements. Carlo evolution from the same small initial configuration as before, but using as the initial values of K4 the ones determined for the C or the B phase from earlier runs in the neighborhood of the transitions, corresponding to ∆clorwit(N41) or ∆chrigith(N41) respectively. This can be seen, where we show the values of K4crit(N41) plotted as a function of ∆crit(N41) On both sides of the hysteresis the dependence is approximately linear, which means that values of both pseudo-critical parameters (K4crit and ∆crit) scale in the same way with the lattice volume N41. The dependence of ∆crit on the lattice volume, ranging between N41 = 40k and N41 = 1600k is presented in figure 4 As it was explained above, the plot contains four sets of data corresponding to the four different points describing the hysteresis (see figure 2). On the scale used in this plot the green and blue curves practically overlap

Order parameters

Conclusion and discussion