Topology change in ISO(2,1) Chern-Simons gravity

Details Topology change in ISO(2,1) Chern-Simons gravity Topology change in ISO(2,1) Chern-Simons gravity

1992-01-30

arxiv.org/abs/hep-th/9201075v1

Nucl.Phys. B377 (1992) 218-235

Physics

High Energy Physics

High Energy Physics - Theory

24 pages and 4 figures (not included)

Scientific paper

10.1016/0550-3213(92)90022-4

In 2+1 dimensional gravity, a dreibein and the compatible spin connection can represent a space-time containing a closed spacelike surface $\Sigma$ only if the associated SO(2,1) bundle restricted to $\Sigma$ has the same non-triviality (Euler class) as that of the tangent bundle of $\Sigma.$ We impose this bundle condition on each external state of Witten's topology-changing amplitude. The amplitude is non-vanishing only if the combination of the space topologies satisfies a certain selection rule. We construct a family of transition paths which reproduce all the allowed combinations of genus $g \ge 2$ spaces.

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