Towards an UV fixed point in CDT gravity

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.

Critical Reflections on Asymptotically Safe Gravity

“…In practice, evidence for several [231,232] second-order phase transition lines/points exists in numerical simulations, both in spherical and toroidal spatial topology. The large-scale spatial topology does not appear to impact the phase structure [233], but can actually improve the numerical efficiency of the studies, as observed in [234]. The higher-order transition can be approached from a phase in which several geometric indicators (spatial volume of the geometry as a function of time [235]; Hausdorff dimension and spectral dimension [236]) signal the emergence of a spacetime with semi-classical geometric properties.…”

Renormalization in Quantum Theories of Geometry

“…The diagram is surprisingly complicated and part of it is still under investigation. We refer to the original articles for a careful discussion [27][28][29][30][31][32]40]. What is important for the present discussion is that in phase C dS in Figure 1, which we denote the de Sitter-phase, geometries with continuum-like properties are found.…”

“…The path integral is then performed over these Euclidean piecewise linear geometries. It turns out that the phase diagram of CDT is highly non-trivial and possesses phase transition lines of both first and second order [27][28][29][30][31][32][33]. We will provide some details below.…”

The higher-order phase transition in toroidal CDT

“…In our case the number of time slices was equal T = 4, the numerical constant governing the magnitude of volume fluctuations was fixed at = 0.00002 and measurements were performed every 10 7 attempted Monte Carlo moves (such that the measured N 4,1 volume could differ from the targetN 4,1 volume). 5 In our analysis we will focus on the behaviour of four order parameters which have previously been successfully used in phase transition studies both in the spherical [18,28,29] and the toroidal [19,30,31] CDT, 6…”

“…11 In the toroidal CDT one was also able to make MC simulations in the most interesting region of the CDT parameter space, namely in the vicinity of the two "triple" points where the A − B − C and the B − C − C b phases meet (see the CDT phase diagram in figure 1), which was not possible in the spherical CDT where MC simulations got effectively "frozen" in this region of the phase diagram. As a result in the toroidal CDT one observes the direct B − C transition which was classified to be the first-order transition, albeit with some atypical properties suggesting a possible higher-order transition [31]. Summing up, we have shown that the B − C b transition is the higher order transition which most likely makes the B − C − C b "triple" point the higher order transition point even though the B − C and the C − C b transitions are possibly the first-order transitions.…”