nLab super-orbifold

Idea

A super-orbifold is an orbifold in supergeometry, hence like a supermanifold but possibly with singularities of the form of fixed points of local actions on the supermanifold by finite groups.

Examples

Moduli space of super-Riemann surfaces

Just like the moduli space of Riemann surfaces is an orbifold, so the moduli space of super-Riemann surfaces is a super-orbifold (e.g. Rabin 87, LeBrun-Rothstein 88, Witten 12, Codogni-Viviani 17).

References

Super-orbifolds as target spaces in superstring theory (orbi-superspace):

• Jaemo Park, Soo-Jong Reym, Supertwistor Orbifolds: Gauge Theory Amplitudes and Topological Strings, JHEP 0412:017, 2004 (arXiv:hep-th/0411123)

• Matthias Gaberdiel, Dan Israel, Eliezer Rabinovici, D-branes at multicritical points, JHEP 0804:086, 2008 [arXiv:0803.0291]

and in M-theory:

• John Huerta, Hisham Sati, Urs Schreiber, Real ADE-equivariant (co)homotopy and Super M-branes, Communications in Mathematical Physics 371: 425. (2019) (arXiv:1805.05987, doi:10.1007/s00220-019-03442-3)

The moduli space of super Riemann surfaces as a super-orbifold:

• Jeffrey Rabin, Supermanifolds and Super Riemann Surfaces, In: H.C. Lee et. al (eds.) Super Field Theories, NATO Science Series (Series B: Physics), vol 160. Springer (1987) (doi:10.1007/978-1-4613-0913-0_34, pdf)

• Claude LeBrun, Mitchell Rothstein, Moduli of super Riemann surfaces, Comm. Math. Phys. Volume 117, Number 1 (1988), 159-176 (euclid:cmp/1104161598)

• Edward Witten, Notes On Super Riemann Surfaces And Their Moduli, Pure and Applied Mathematics Quarterly Volume 15 (2019) Number 1 Special Issue on Super Riemann Surfaces and String Theory (arXiv:1209.2459, doi:10.4310/PAMQ.2019.v15.n1.a2)

• Giulio Codogni, Filippo Viviani, Moduli and Periods of Supersymmetric Curves, Adv. Theor. Math. Phys. 23 (2019) 2, 345-402 (arXiv:1706.04910, doi:10.4310/ATMP.2019.v23.n2.a2)