Phases of simplicial quantum gravity

Abstract

Recent results for simplicial quantum gravity are reviewed. Models are considered in which the topology is fixed, and the edge lengths are varied while the coordination number is held fixed (‘Regge calculus’). As expected on the basis of universality, in two dimensions the results for pure gravity critical exponents are found to be in agreement with the conformal field theory predictions. The effects of both higher derivative terms and gravitational measure contributions are investigated in detail, as well as the inclusion of a D-component scalar field. For sufficiently large D a phase transition is found, leading from the Liouville phase into a branched polymer phase. The results suggest universal critical behavior, and are in good agreement with recent results obtained with the dynamical triangulation models. While no phase transition is found for pure gravity in two dimensions, a phase transition between a ‘rough’ and a ‘smooth’ phase of spacetime is found in both three and four dimensions, in agreement with the results of the 2+ c-expansion in the continuum. In both cases the transition appears to be continuous (suggesting therefore the existence of a lattice continuum limit), and the critical exponents can be estimated. While fluctuations in the local volumes are responsible for critical behavior in two dimensions, in three and four dimensions it is instead the fluctuations in the local curvature that diverge at the critical point.