Taming the cosmological constant in 2D causal quantum gravity with topology change
arXiv:hep-th/0507012 · doi:10.1016/j.nuclphysb.2006.06.033
Abstract
As shown in previous work, there is a well-defined nonperturbative gravitational path integral including an explicit sum over topologies in the setting of Causal Dynamical Triangulations in two dimensions. In this paper we derive a complete analytical solution of the quantum continuum dynamics of this model, obtained uniquely by means of a double-scaling limit. We show that the presence of infinitesimal wormholes leads to a decrease in the effective cosmological constant, reminiscent of the suppression mechanism considered by Coleman and others in the four-dimensional Euclidean path integral. Remarkably, in the continuum limit we obtain a finite spacetime density of microscopic wormholes without assuming fundamental discreteness. This shows that one can in principle make sense of a gravitational path integral which includes a sum over topologies, provided suitable causality restrictions are imposed on the path integral histories.
19 pages, 4 figures. Comments on general covariance added. To be published in Nucl. Phys. B
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