Topology Changes by Quantum Tunneling in Four Dimensions

TL;DR

This paper explores topology-changing processes in 4D quantum gravity with negative cosmological constant, constructing explicit non-singular solutions and evaluating their amplitudes using hyperbolic geometry techniques.

Contribution

It introduces a novel method to explicitly construct non-singular instanton solutions for topology change in 4D quantum gravity.

Findings

Constructed a non-singular, finite-volume hyperbolic solution.

Evaluated topology change amplitude using WKB approximation.

Demonstrated the role of cusps in non-compact solutions.

Abstract

We investigate topology-changing processes in 4-dimensional quantum gravity with a negative cosmological constant. By playing the ``gluing-polytope game" in hyperbolic geometry, we explicitly construct an instanton-like solution without singularity. Because of cusps, this solution is non-compact but has a finite volume. Then we evaluate a topology change amplitude in the WKB approximation in terms of the volume of this solution.