Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userScaling Structures in Four-dimensional Simplicial Gravity
226
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
Four-dimensional(4D) spacetime structures are investigated using the concept of the geodesic distance in the simplicial quantum gravity. On the analogy of the loop length distribution in 2D case, the scaling relations of the boundary volume distribution in 4D are discussed in various coupling regions i.e. strong-coupling phase, critical point and weak-coupling phase. In each phase the different scaling relations are found.
rate research
Read More
The statistical properties of dynamically triangulated manifolds (DT mfds) in terms of the geodesic distance have been studied numerically. The string susceptibility exponents for the boundary surfaces in three-dimensional DT mfds were measured numerically. For spherical boundary surfaces, we obtained a result consistent with the case of a two-dimensional spherical DT surface described by the matrix model. This gives a correct method to reconstruct two-dimensional random surfaces from three-dimensional DT mfds. Furthermore, a scaling property of the volume distribution of minimum neck baby universes was investigated numerically in the case of three and four dimensions, and we obtain a common scaling structure near to the critical points belonging to the strong coupling phase in both dimensions. We have evidence for the existence of a common fractal structure in three- and four-dimensional 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.
A model of simplicial quantum gravity in three dimensions is investigated numerically based on the technique of the dynamical triangulation (DT). We are concerned with the surfaces appearing on boundaries (i.e., sections) of three-dimensional DT manifold with $S^{3}$ topology. A new scaling behavior of genus distributions of boundary surfaces is found.Furthermore, these surfaces are compared with the random surfaces generated by the two-dimensional DT method which are well known as a correct discretized method of the two-dimensional quantum gravity.
The string susceptibility exponents of dynamically triangulated 2-dimensional surfaces with various topologies, such as a sphere, torus and double-torus, were calculated by the grand-canonical Monte Carlo method. These simulations were made for surfaces coupled to $d$-Ising spins ($d$=0,1,2,3,5). In each simulation the area of surface was constrained to within 1000 to 3000 of triangles, while maintaining the detailed-balance condition. The numerical results show excellent agreement with theoretical predictions as long as $d leq 2$.
The attempt of extending to higher dimensions the matrix model formulation of two-dimensional quantum gravity leads to the consideration of higher rank tensor models. We discuss how these models relate to four dimensional quantum gravity and the precise conditions allowing to associate a four-dimensional simplicial manifold to Feynman diagrams of a rank-four tensor model.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
