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

Abstract

Four-dimensional (4D) simplicial quantum gravity coupled to U(1) gauge fields has been studied using MonteCarlo simulations. A negative string susceptibility exponent is observed beyond the phase-transition point, even if the number of vector fields (NV ) 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 NV > 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.

Dynamics of the conformal mode and simplicial gravity

“…Such branched polymer configurations have been seen in simulations of 4D DTs and have led to the speculation that these represent regularizations of this conformal factor gravity. If so, it should be possible to enter the Liouville-like phase by the addition of suitable massless fields -preliminary numerical evidence indeed hints at this [4,5]. If this were so the simulations could be used to both measure Q 2 graviton and to do nonperturbative studies of relevance to cosmology [6].…”

Phase Structure of Four-Dimensional Simplicial Quantum Gravity with a U(1) Gauge Field

“…Recently, the phase structure with vector fields has been studied numerically, 19), 18) and a region with negative string susceptibility exponents has been found. Encouraged by this observation, we investigate the nature of the phase transition by measuring the susceptibility using the method of finite size scaling and the scaling property using the boundary volume distribution of the mother universe.…”

“…Thus, we have found that the obscure transition at κ o 2 is very smooth (more smooth than the cross-over) and that it is similar to that of the c = 1 barrier in two-dimensional quantum gravity. 18) In two-dimensions, the c = 1 barrier is known as an obscure transition, separating the fractal phase (c ≤ 1 and γ 2D st < 0) and the branched polymer phase (c > 1 and γ 2D st > 0). As claimed by Antoniadis et al, 15) the quantum field theory of gravity with conformal invariance can be described by conformal field theory with central charge Q 2 and a threshold value Q 2 ≈ 8.…”