nLab superspace


This entry is about the concept in supergeometry. For the concept in gravity/cosmology see at Wheeler superspace.





Physicists often refer to spaces in supergeometry, such as supermanifolds or super schemes, as superspaces. Hence a superspace can be an affine superspace (the affine counterpart of the super vector space over real or complex numbers), superscheme, supermanifold, etc.

Mostly however “superspace” is used for superspacetimes, and here mostly for super Minkowski spacetimes.


The concept of superspace in physics (together with that of superfields) is due to

(which considered superspace of dimension d=4d = 4 with number of supersymmetries N=2N = 2, hence the supermanifold 4|4+4\mathbb{R}^{4\vert \mathbf{4}+ \mathbf{4}}, or rather the super Minkowski spacetime 3,1|4+4\mathbb{R}^{3,1\vert \mathbf{4}+ \mathbf{4}})

Textbook accounts:

specifically for D=4 supergravity:

Further review:

Discussion of superspace within philosophy of physics:

  • Tushar Menon, Taking up superspace – the spacetime structure of supersymmetric field theory (philsci:14682, pdf,)

Last revised on November 22, 2022 at 04:37:05. See the history of this page for a list of all contributions to it.