The Weak-Coupling Limit of Simplicial Quantum Gravity
نویسنده
چکیده
In the weak-coupling limit, κ0 → ∞, the partition function of simplicial quantum gravity is dominated by an ensemble of triangulations with the ratio N0/ND close to the upper kinematic limit. For a combinatorial triangulation of the D–sphere this limit is 1/D. Defining an ensemble of maximal triangulations, i.e. triangulations that have the maximal possible number of vertices for a given volume, we investigate the properties of this ensemble in three dimensions using both Monte Carlo simulations and a strong-coupling expansion of the partition function, both for pure simplicial gravity and a with a suitable modified measure. For the latter we observe a continuous phase transition to a crinkled phase and we investigate the fractal properties of this phase.
منابع مشابه
The Weak-Coupling Limit of 3D Simplicial Quantum Gravity
We investigate the weak-coupling limit, κ → ∞, of 3D simplicial gravity using Monte Carlo simulations and a Strong Coupling Expansion. With a suitable modification of the measure we observe a transition from a branched polymer to a crinkled phase. However, the intrinsic geometry of the latter appears similar to that of non-generic branched polymer, probable excluding the existence of a sensible...
متن کاملQuantum Gravity in Large Dimensions
Quantum gravity is investigated in the limit of a large number of space-time dimensions, using as an ultraviolet regularization the simplicial lattice path integral formulation. In the weak field limit the appropriate expansion parameter is determined to be 1/d. For the case of a simplicial lattice dual to a hypercube, the critical point is found at kc/λ = 1/d (with k = 1/8πG) separating a weak...
متن کاملOn the measure in simplicial gravity
Functional measures for lattice quantum gravity should agree with their continuum counterparts in the weak field, low momentum limit. After showing that the standard simplicial measure satisfies the above requirement, we prove that a class of recently proposed non-local measures for lattice gravity do not satisfy such a criterion, already to lowest order in the weak field expansion. We argue th...
متن کاملSimulating Four-Dimensional Simplicial Gravity using Degenerate Triangulations
We extend a model of four-dimensional simplicial quantum gravity to include degenerate triangulations in addition to combinatorial triangulations traditionally used. Relaxing the constraint that every 4-simplex is uniquely defined by a set of five distinct vertexes, we allow triangulations containing multiply connected simplexes and distinct simplexes defined by the same set of vertexes. We dem...
متن کامل4d 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 polyme...
متن کامل