Topology induced first-order phase transitions in lattice quantum gravity

Abstract

Causal Dynamical Triangulations (CDT) is a lattice formulation of quantum gravity, suitable for Monte-Carlo simulations which have been used to study the phase diagram of the model. It has four phases characterized by different dominant geometries, denoted phase A, B, C and Cb. In this article we analyse the A − B and the B − C phase transitions in the case where the topology of space is that of the three-torus. This completes the phase diagram of CDT for such a spatial topology. We observe that the order of a phase transition of spacetime geometries can depend on the topology of spacetime.