Topology change in (2+1)-dimensional gravity with non-Abelian Higgs field

TL;DR

This paper explores how topology change occurs in (2+1)-dimensional gravity coupled with a non-Abelian Higgs field, using Morse theory to identify critical points where spacetime topology changes.

Contribution

It demonstrates that the Higgs potential acts as a Morse function, linking topology change to zeros of the Higgs field in (2+1)D gravity.

Findings

Topology change corresponds to zeros of the Higgs field.

Critical points feature degenerate metrics but bounded curvature.

Abstract

We study topology change in (2+1)D gravity coupling with non-Abelian SO(2,1) Higgs field from the point of view of Morse theory. It is shown that the Higgs potential can be identified as a Morse function. The critical points of the latter (i.e. loci of change of the spacetime topology) coincide with zeros of the Higgs field. In these critical points two-dimensional metric becomes degenerate, but the curvature remains bounded.