Q torus in N=2 supersymmetric QED

We construct "flying saucer" solitons in supersymmetric N=2 gauge theory, which is known to support Bogomol'nyi-Prasad-Sommerfield domain walls with a U(1) gauge field localized on its worldvolume. We demonstrate that this model supports exotic particlelike solitons with the shape of a torus. Q tori, and also 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.