Solitons and Domain Walls in Odd Dimensions

TL;DR

This paper investigates the existence of smooth soliton and domain wall solutions in odd-dimensional supergravity theories, concluding that smooth domain walls between supersymmetric vacua generally do not exist due to divergence issues.

Contribution

It provides a theoretical analysis showing the non-existence of smooth supersymmetric domain walls in a broad class of odd-dimensional supergravities.

Findings

Smooth soliton solutions can exist in odd dimensions.

Smooth domain walls between supersymmetric vacua are generally absent.

Divergence of Goldstino modes prevents smooth domain walls when the superpotential changes sign.

Abstract

We discuss the existance of smooth soliton solutions which interpolate between supersymmetric vacua in odd-dimensional theories. In particular we apply this analysis to a wide class of supergravities to argue against the existence of smooth domain walls interpolating between supersymmetric vacua. We find that if the superpotential changes sign then any Goldstino modes will diverge.