Nonperturbative sum over topologies in 2D Lorentzian quantum gravity

TL;DR

This paper explores a nonperturbative approach to summing over topologies in 2D Lorentzian quantum gravity, demonstrating that microscopic wormholes can reduce the effective cosmological constant without requiring fundamental discreteness.

Contribution

It introduces a nonperturbative implementation of the sum over topologies in 1+1D quantum gravity within the CDT framework, showing finite wormhole density in the continuum limit.

Findings

Infinitesimal wormholes decrease the effective cosmological constant.

The model yields a finite microscopic wormhole density without fundamental discreteness.

Sum over topologies is well-defined with causality-preserving restrictions.

Abstract

The recent progress in the Causal Dynamical Triangulations (CDT) approach to quantum gravity indicates that gravitation is nonperturbatively renormalizable. We review some of the latest results in 1+1 and 3+1 dimensions with special emphasis on the 1+1 model. In particular we discuss a nonperturbative implementation of the sum over topologies in the gravitational path integral in 1+1 dimensions. The dynamics of this model shows that the presence of infinitesimal wormholes leads to a decrease in the effective cosmological constant. Similar ideas have been considered in the past by Coleman and others in the formal setting of 4D Euclidean path integrals. A remarkable property of the model is that in the continuum limit we obtain a finite space-time density of microscopic wormholes without assuming fundamental discreteness. This shows that one can in principle make sense out of a gravitational path integral including a sum over topologies, provided one imposes suitable kinematical restrictions on the state-space that preserve large scale causality.