4D Simplicial Quantum Gravity Research Articles

Grand-canonical simulation of 4D simplicial quantum gravity

A thorough numerical examination for the field theory of 41) quantum gravity (QG) with a special emphasis on the conformal mode dependence has been studied. More clearly than before, we obtain the string susceptibility exponent of the partition function by using the Grand-Canonical Monte-Carlo method. Taking thorough care of the update method, the simulation is made for 4D Euclidean simplicial manifold coupled to N x scalar fields and N A U(1) gauge fields. The numerical results suggest that 4D simplicial quantum gravity (SQG) can be reached to the continuum theory of 41) QG. We discuss the significant property of 4D SQG.

Clear evidence of a continuum theory of 4D Euclidean simplicial quantum gravity

Four-dimensional (4D) simplicial quantum gravity coupled to both scalar fields ( N X ) and gauge fields ( N A ) has been studied using Monte-Carlo simulations. The matter dependence of the string susceptibility exponent γ (4) is estimated. Furthermore, we compare our numerical results with Background-Metric-Indepenent (BMI) formulation conjectured to describe the quantum field theory of gravity in 4D. The numerical results suggest that the 4D simplicial quantum gravity is related to the conformal gravity in 4D. Therefore, we propose a phase structure in detail with adding both scalar and gauge fields and discuss the possibility and the property of a continuum theory of 4D Euclidean simplicial quantum gravity.

Geometry of 4-d simplicial quantum gravity with a U(1) gauge field

The geometry of 4D simplicial quantum gravity with a U(1) gauge field is studied numerically. The phase diagram shows a continuous transition when gravity is coupled with a U(1) gauge field. At the critical point measurements of the curvature distribution of S 4 space shows an inflated geometry with homogeneous and symmetric nature. Also, by choosing a 4-simplex and fixing the scalar curvature geometry of the space is measured.

Recent analytical results in 4D-dynamical triangulations

We briefly discuss some recent analytical results in 4D simplicial quantum gravity: (i) The characterization of the singular structures sampling a neighborhood of the critical point; (ii) The transition between weak and strong coupling as driven by the dynamics of a polymeric interface; (iii) The possible connection between triangulations counting and the geometry of the moduli space of singular Euclidean structures on 4D manifolds.

Phase transition of 4D simplicial quantum gravity with U (1) gauge field

The phase transition of 4D simplicial quantum gravity coupled to U (1) gauge fields is studied using Monte-Carlo simulations. The phase transition of the dynamical triangulation model with a vector field ( N V = 1) is smooth compared with pure gravity ( N V = 0). The node susceptibility (χ) is studied by the finite size scaling method. At the critical point, the node distribution has a sharp peak in contrast to the double peak in pure gravity. From the numerical results, we expect that 4D simplicial quantum gravity with U (1) vector fields has a higher order phase transition than 1st order, which means the possibility to take the continuum limit at the critical point.

Phase Transition of 4D Simplicial Quantum Gravity with U(1) Gauge Field

Phase Transition of 4D Simplicial Quantum Gravity with U(1) Gauge Field

Recent Development of 4D Simplicial Quantum Gravity

Recent Development of 4D Simplicial Quantum Gravity

Further evidence of a smooth phase in 4D simplicial quantum gravity

Four-dimensional (4D) simplicial quantum gravity coupled to U(1) gauge fields has been studied using Monte-Carlo simulations. A negative string susceptibility exponent is observed beyond the phase-transition point, even if the number of vector fields ( N V ) is 1. We find a scaling relation of the boundary volume distributions in this new phase. This scaling relation suggests a fractal structure similar to that of 2D quantum gravity. Furthermore, evidence of a branched polymer-like structure is suggested far into the weak-coupling region, even for N V > 1. As a result, we propose new phase structures and discuss the possibility of taking the continuum limit in a certain region between the crumpled and branched polymer phases.

Crumpled triangulations and critical points in 4D simplicial quantum gravity

We estimate analytically the critical coupling separating the weak and the strong coupling regime in 4D simplicial quantum gravity to be located at k 2 crit ⋍ 1.3093 . By carrying out a detailed geometrical analysis of the strong coupling phase we argue that the distribution of dynamical triangulations with singular vertices and singular edges, dominating in such a regime, is characterized by distinct subdominating peaks. The presence of such peaks generates volume-dependent pseudo-critical points: k 2 crit (N 4 = 32 000) ⋍ 1.25795,k 2 crit (N 4 = 48 000) ⋍ 1.26752 , k 2 crit (N 4 = 64 000) ⋍ 1.27466 , etc., which appear in good agreement with available Monte Carlo data. Under a certain scaling hypothesis we analytically characterize the (canonical) average value, c 1 ( N 4; k 2) = 〈 N 0〉/ N 4, and the susceptibility, c 2( N 4; k 2) = (〈 N 0 2〉 − 〈 N 0〉 2)/ N 4, associated with the vertex distribution of the 4D triangulations considered. Again, the resulting analytical expressions are found in quite a good agreement with their Monte Carlo counterparts.

The strong-coupling expansion in simplicial quantum gravity

We construct the strong-coupling series in 4d simplicial quantum gravity up to volume 38. It is used to calculate estimates for the string susceptibility exponent γ for various modifications of the theory. It provides a very efficient way to get a first view of the phase structure of the models.

4d Simplicial quantum gravity: matter fields and the corresponding effective action

Four-dimensional simplicial quantum gravity is modified either by coupling it to U (1) gauge fields or by introducing a measure weighted by the orders of the triangles. Strong coupling expansion and Monte Carlo simulations are used. Although the two modifications of the standard pure-gravity model are apparently very distinct, they produce strikingly similar results, as far as the geometry of random manifolds is concerned. In particular, for an appropriate choice of couplings, the branched polymer phase is replaced by a crinkled phase, characterized by the susceptibility exponent γ <0 and the fractal dimension d H >2. The quasi-equivalence between the two models is exploited to get further insight into the extended phase diagram of the theory.

Common structures in 2,3 and 4D simplicial quantum gravity

Two kinds of statistical properties of dynamical-triangulated manifolds (DT mfds) have been investigated. First, the surfaces appearing on the boundaries of 3D DT mfds were investigated. The string-susceptibility exponent of the boundary surfaces (∼ γ st ) of 3D DT mfds with S 3 topology near to the critical point was obtained by means of a MINBU (minimum neck baby universes) analysis; actually, we obtained ∼ γ st ≈ −0.5. Second, 3 and 4D DT mfds were also investigated by determining the string-susceptibility exponent near to the critical point from measuring the MINBU distributions. As a result, we found a similar behavior of the MINBU distributions in 3 and 4D DT mfds, and obtained γ st (3) ≈ γ st (4) ≈ 0. The existence of common structures in simplicial quantum gravity is also discussed.

4d simplicial quantum gravity interacting with gauge matter fields

The effect of coupling non-compact $U(1)$ gauge fields to four dimensional simplicial quantum gravity is studied using strong coupling expansions and Monte Carlo simulations. For one gauge field the back-reaction of the matter on the geometry is weak. This changes, however, as more matter fields are introduced. For more than two gauge fields the degeneracy of random manifolds into branched polymers does not occur, and the branched polymer phase seems to be replaced by a new phase with a negative string susceptibility exponent $\gamma$ and fractal dimension $d_H \approx 4$.

Scaling Behavior in 4D Simplicial Quantum Gravity

Scaling relations in four-dimensional simplicial quantum gravity are proposed using the concept of the geodesic distance. Based on the analogy of a loop length distribution in the two-dimensional case, the scaling relations of the boundary volume distribution in four dimensions are discussed in three regions: the strong-coupling phase, the critical point and the weak-coupling phase. In each phase a different scaling behavior is found.

4D simplicial quantum gravity with a nontrivial measure.

We study 4D simplicial quantum gravity in the dynamical triangulation approach with a nontrivial class of measures. We find that the measure contribution plays an important role, influencing the phase diagram and the nature of the (possible) critical theory. We discuss how the lattice theory could be used to fix the quantum measure in a nonambiguous way.