Solitons and Domain Walls in Odd Dimensions

TL;DR

This work analyzes the existence of smooth solitons and domain walls in odd-dimensional SUSY theories, both with and without gravity. It shows that in non-gravitational settings fermion zero-modes can be chiral when a mass term $M(r)$ changes sign, but in odd-dimensional supergravity the Goldstino spectrum becomes ill-behaved if the superpotential $W$ changes sign, since Goldstino modes diverge as $W\to 0$. The authors derive the Bogomolnyi equations for domain walls, employ the Nester tensor to establish stability bounds, and demonstrate that a sign change in $W$ is incompatible with smooth domain walls between SUSY vacua in these theories. Consequently, Randall-Sundrum-type smooth domain walls are ruled out in broad classes of odd-dimensional supergravities, impacting brane-world constructions and AdS/CFT interpretations in this setting.

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.