Phase structure and graviton propagators in lattice formulations of four-dimensional quantum gravity

Abstract

We examine the phase structure of standard Regge calculus in four dimensions and compare our Monte Carlo results with those of the -Regge model as well as with another formulation of lattice gravity derived from group-theoretical considerations. Within all of the three models of quantum gravity we find an extension of the well-defined phase to negative gravitational couplings and a new phase transition. In contrast to the well known transition at positive coupling there is evidence for a continuous phase transition which is essential for a continuum limit. We calculate two-point functions between geometrical quantities at the corresponding critical point and estimate the masses of the respective interaction particles.