Supersymmetric Q Solitons of Arbitrary Genus

TL;DR

This paper constructs novel supersymmetric solitons called 'Flying Saucer' solitons with arbitrary genus in N=2 gauge theory, demonstrating their stability and properties through multiple theoretical frameworks.

Contribution

It introduces a new class of supersymmetric solitons with arbitrary topology, supported by electric and magnetic fields, and provides multiple proofs of their existence and characteristics.

Findings

Existence of supersymmetric Q solitons with arbitrary genus.

Q tori are related to Hopf Skyrmions in the sigma-model.

Multiple theoretical frameworks confirm the stability and properties of these solitons.

Abstract

We construct "Flying Saucer" solitons in supersymmetric N=2 gauge theory which is known to support BPS domain walls with a U(1) gauge field localized on its worldvolume. We demonstrate that this model supports exotic particle-like solitons whose topology is largely arbitrary: closed orientable surfaces in three-dimensional space which can have arbitrary genus. In particular, we focus on Q tori. Q tori and similar solitons of higher genera are obtained by folding the domain wall into an appropriate surface. Nontrivial cycles on the domain wall worldvolume (handles) are stabilized by crossed electric and magnetic fields inside the folded domain wall. Three distinct frameworks are used to prove the existence of these Flying Saucer solitons and study their properties: the worldvolume description (including the Dirac-Born-Infeld action), the bulk theory description in the sigma-model limit, and the bulk theory description in the thin-edge approximation. In the sigma-model framework the Q torus is shown to be related to the Hopf Skyrmion studied previously.