Semi-local Cosmic Strings and the Cosmological Constant Problem

TL;DR

This paper investigates semi-local cosmic strings in a 3D N=2 supergravity model, demonstrating supersymmetry's role in stability and exploring the implications for the cosmological constant problem without requiring Bose-Fermi degeneracy.

Contribution

It provides a concrete example of supersymmetric cosmic strings stabilizing solutions and clarifies the relationship between supersymmetry and the vanishing cosmological constant in three dimensions.

Findings

Supersymmetry ensures stability of semi-local cosmic strings.

Charged Killing spinors exist on solutions saturating the Bogomolnyi bound.

The cosmological constant vanishes without Bose-Fermi degeneracy.

Abstract

We study the cosmological constant problem in a three-dimensional N=2 supergravity theory with gauge group SU[2]_{global}xU[1]_{local}. The model we consider is known to admit string-like configurations, the so-called semi-local cosmic strings. We show that the stability of these solutions is provided by supersymmetry through the existence of a lower bound for the energy, even though the manifold of the Higgs vacuum does not contain non-contractible loops. Charged Killing spinors do exist over configurations that saturate the Bogomolnyi bound, as a consequence of an Aharonov-Bohm-like effect. Nevertheless, there are no physical fermionic zero modes on these backgrounds. The exact vanishing of the cosmological constant does not imply, then, Bose-Fermi degeneracy. This provides a non-trivial example of the recent claim made by Witten on the vanishing of the cosmological constant in three dimensions without unphysical degeneracies.