nLab super spacetime

Idea

A spacetime in supergeometry, used in some formulations of supergravity (see at D'Auria-Fre formulation of supergravity) and as target space for super-$p$-brane sigma-models (see at Green-Schwarz action functional).

Examples

• super Minkowski spacetime

• super anti de Sitter spacetime

• super-vielbein

• Green-Schwarz action functional

References

For more see the references at superspace.

• Veeravalli Varadarajan, section 7.4 of: Supersymmetry for mathematicians, Courant lecture notes in mathematics, American Mathematical Society Providence, R.I 2004

Explicit formulas for coframe fields on homogeneous (coset space) super-spacetimes of D=11 supergravity (such as super anti de Sitter spacetimes $AdS_{4,7} \times S^{7,4}$):

• Bernard de Wit, Kasper Peeters, Jan Plefka, Alexander Sevrin, Section 3 of: The M-theory two-brane in $AdS_4 \times S^7$ and $AdS_7 \times S^4$, Physics Letters B 443 1-4 (1998) 153-158 [doi:10.1016/S0370-2693(98)01340-9, inspire:474621, arXiv:hep-th/9808052]

following:

• Renata Kallosh, J. Rahmfeld, Arvind Rajaraman, Near Horizon Superspace, JHEP 9809:002 (1998) [arXiv:hep-th/9805217, doi:10.1088/1126-6708/1998/09/002]

Further discussion in:

• Piet Claus, Section 2 of Super M-brane actions in $adS_4 \times S^7$ and $adS_7 \times S^4$, Phys. Rev. D 59 (1999) 066003 [arXiv:hep-th/9809045, doi:10.1103/PhysRevD.59.066003]