The Geometry of the Elongated Phase in 4-D Simplicial Quantum Gravity

We discuss the elongated phase of 4D simplicial quantum gravity by exploiting recent analytical results. In particular using Walkup’s theorem we prove that the dominating configurations in the elongated phase are tree-like structures called “stacked spheres”. Such configurations can be mapped into branched polymers and baby universes arguments are used in order to analyse the critical behaviour of theory in the weak coupling regime.