nLab supersphere

Idea

In the context of supergeometry, the supersphere $S^{n \vert m}$ is the supersubmanifold of the superspace $\mathbb{R}^{n+1 \vert m}$ of points at a fixed distance from the origin.

Coset representations

• The supersphere $S^{2|2}$ is the super coset space $UOSp(1|2)/U(1)$.

• The supersphere $S^{r-1|2s}$ is the super coset space $OSp(r|2s)/OSp(r-1|2s)$ of orthosymplectic groups (GJS 18).

Related concepts

• super Klein geometry

References

• Etienne Granet, Jesper Lykke Jacobsen, Hubert Saleur, Spontaneous symmetry breaking in 2D supersphere sigma models and applications to intersecting loop soups, (arXiv:1810.07807)