Three-Dimensional Supergravity and the Cosmological Constant

TL;DR

This paper explores a novel mechanism in 2+1-dimensional supergravity where local supersymmetry ensures a zero cosmological constant through a unique cancellation involving vortex solitons, despite the absence of bose-fermi degeneracy.

Contribution

It demonstrates a new implementation of supersymmetry in a (2+1)-dimensional abelian Higgs model coupled to supergravity, revealing a unique cancellation mechanism affecting soliton properties.

Findings

Half of the supersymmetries are preserved in vortex solitons.

Existence of covariantly constant spinors due to phase cancellations.

Bose-fermi degeneracy is absent in the soliton spectrum.

Abstract

Witten has argued that in $2+1$ dimensions local supersymmetry can ensure the vanishing of the cosmological constant without requiring the equality of bose and fermi masses. We find that this mechanism is implemented in a novel fashion in the (2+1)-dimensional supersymmetric abelian Higgs model coupled to supergravity. The vortex solitons are annihilated by half of the supersymmetry transformations. The covariantly constant spinors required to define these supersymmetries exist by virtue of a surprising cancellation between the Aharonov-Bohm phase and the phase associated with the holonomy of the spin connection. However the other half of the supersymmetry transformations, whose actions ordinarily generate the soliton supermultiplet, are not well-defined and bose-fermi degeneracy is consequently absent in the soliton spectrum.