nLab supersphere

Idea

Superspheres are supergeometric analogs of spheres.

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 super Lie groups (GJS 18).

Related concepts

• super Klein geometry

• fuzzy superspheres

References

In the context of instantons in supersymemtric quantum field theory:

• Aiyalam P. Balachandran, A. Pinzul, B. Qureshi: SUSY anomalies break $\mathcal{N}=2$ to $\mathcal{N}=1$: The supersphere and the fuzzy supersphere, Journal of High Energy Physics 2005 12 (2005) [arXiv:10.1088/1126-6708/2005/12/002, arXiv:hep-th/0506037]

In relation to Brownian loop soup models:

• Etienne Granet, Jesper Lykke Jacobsen, Hubert Saleur, Spontaneous symmetry breaking in 2D supersphere sigma models and applications to intersecting loop soups, J. Phys. A: Math. Theor. 52 345001 (2019) [doi:10.1088/1751-8121/ab2aaa, arXiv:1810.07807]