Signature change of the metric in CDT quantum gravity?

Abstract

Abstract: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.

Spectrum of the Laplace-Beltrami operator and the phase structure of causal dynamical triangulations

“…Furthermore, the maximal slice in the C b phase is typically observed to be of B-type, with a volume ranging in a narrow interval which is separated from the volumes of the other slices. This alternating distribution of spatial volumes has been indeed one of the first signals of the presence of the new phase [3,4].…”

“…Among the various results, we will show that the different phases can be characterized by the presence or absence of a gap in the spectrum of the LB operator, as it happens for the spectrum of the Dirac operator in strong interactions, and we will give an interpretation of this fact in terms of the geometrical properties of the slices. The presence/absence of a gap will also serve to better characterize the two different classes of spatial slices which are found in the recently discovered bifurcation phase [3][4][5][6]. Moreover, we will show how the spectrum can be used to derive an effective dimensionality of the triangulations at different length scales, and to investigate quantities useful to characterize the critical behavior expected around a possible secondorder transition point.…”

“…With this prescription, simplexes in the same class (according to the above definition) not only are equivalent topologically, but also geometrically, so that the expression of the discretized action greatly simplifies. Indeed, at the end of the day, 4 the standard fourdimensional action employed in CDT simulations with S 3 topology of the slices and periodic time conditions becomes a functional of the triangulation T , and takes the relatively simple form…”

“…where N 0 counts the total number of vertices, N 4 counts the total number of pentachorons, and N 41 is the sum of the total numbers of type (4,1) and type (1,4) pentachorons, while k 4 , k 0 and Δ are free dimensionless parameters, related to the Cosmological constant, the Newton constant, and the freedom in the choice of the time/space asymmetry parameter α (see Ref. [1] for more details).…”

FuzzyCP2spacetimes

“…Signature change is known to be a possible feature of both classical and quantum gravity. [19]- [28] The region bounded by the singular latitudes has Lorentzian signature, and describes a closed two-dimensional space-time. The two singular latitudes behave as cosmological singularities, which get resolved at finite N .…”