# nLab superspace

Contents

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

supersymmetry

# Contents

## Idea

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.

## References

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

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

A textbook account is

Further review:

• I. L. Buchbinder, S. M. Kuzenko, Ideas and methods of supersymmetry and supergravity; or A walk through superspace

• Albert Schwarz, On the definition of superspace Teoret. Mat. Fiz., 1984, Volume 60, Number 1, Pages 37–42 (Mi tmf5111), (russian original)

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 October 14, 2021 at 09:59:24. See the history of this page for a list of all contributions to it.