Conformal modes in simplicial quantum gravity and the Weil-Petersson volume of moduli space (Q1394609)

One of the approaches to quantum gravity employs a path-integral formalism in which a sum over all metrics has to be performed. Recently there has been some progress in evaluating this sum using the method of dynamical triangulations. Especially simple, and mathematically tractable, is the situation in two spacetime dimensions. The present authors address this two-dimensional case. They prove that in the case of pure gravity the scaling properties of the set of dynamical triangulations is given by the asymptotics of the Weil-Petersson volume of the moduli space. They also add some speculations about the situation in the case where gravity is coupled to conformal matter.