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• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeSep 19th 2011

earlier today I had created a stub for anti de Sitter spacetime

• CommentRowNumber2.
• CommentAuthorDavid_Corfield
• CommentTimeDec 13th 2016

Presumably super anti de Sitter spacetime

A supergeometric analog of de Sitter spacetime.

is missing an ’anti’.

Can you have plain ’super de Sitter’? If so, I guess that wants an entry.

By the way, aren’t I supposed to get the impression from anti de Sitter spacetime of an $(n-1, 2)$ signature, as at anti de Sitter group?

Up to isometry, the anti de Sitter spacetime of dimension $d + 1$ is the pseudo-Riemannian manifold whose underlying manifold is the submanifold of the Cartesian space $\mathbb{R}^{d+2}$ that solves the equation

$\sum_{i = 1}^{d+1} (x^i)^2 - (x^{d+2})^2 = 0$
• CommentRowNumber3.
• CommentAuthorUrs
• CommentTimeDec 13th 2016

Woops. All fixed now.

Regarding super de Sitter: not in the usual sense, but see arXiv:1610.01566

• CommentRowNumber4.
• CommentAuthorDavid_Corfield
• CommentTimeDec 15th 2016
• (edited Dec 15th 2016)

Is this right yet? Don’t we need two coordinates of negative sign in the signature?

From here (2.30)

$-x_0^2 + \sum_{i = 1}^{d-1} x^2_i - x^2_{d+1} = -R^2$

(why no $d$-coordinate?)

From here

an $n + 1$ dimensional flat spacetime with signature $(n - 1, 2)$, i.e. the set of points $(X_1, X_2, \ldots , X_{n+1})$ satisfying $(X_1)^2 + (X_2)^2 + \ldots + (X_{n-1})^2 - (X_n)^2 - (X_{n+1})^2 = -1$.

• CommentRowNumber5.
• CommentAuthorDavid_Corfield
• CommentTimeDec 16th 2016

I gave what I think is the right definition, and mentioned the more general case of $(p, q)$ signature.

• CommentRowNumber6.
• CommentAuthorUrs
• CommentTimeNov 15th 2018

Discussion of thermal Wick rotation on global anti-de Sitter spacetime (which is already periodic in real time) to Euclidean field theory with periodic imaginary time is in

• CommentRowNumber7.
• CommentAuthorUrs
• CommentTimeNov 20th 2019

• CommentRowNumber8.
• CommentAuthorUrs
• CommentTimeMay 6th 2020