superalgebra and (synthetic ) supergeometry
black hole spacetimes | vanishing angular momentum | positive angular momentum |
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vanishing charge | Schwarzschild spacetime | Kerr spacetime |
positive charge | Reissner-Nordstrom spacetime | Kerr-Newman spacetime |
A supergeometric analog of anti-de Sitter spacetime. By the discussion at supersymmetry – Classification – Superconformal and super anti de Sitter symmetry this includes the following coset superspacetimes (super Klein geometries):
super anti de Sitter spacetime | |
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4 | |
5 | |
7 |
(Here denotes orthosymplectic super Lie groups.)
In particular for (see e.g. Section 3 of Kuzenko & Tartaglino-Mazzucchelli 2022):
Also notice that the de Sitter spacetime (not anti-de Sitter) does not have a standard extension to supergeometry, but see arXiv:1610.01566.
General discussion:
Leonardo Castellani, Riccardo D'Auria, Pietro Fré, sections II.2.6, II.3.2 and II.3.3 in Supergravity and Superstrings - A Geometric Perspective, World Scientific (1991)
Antoine Van Proeyen, sections 4.5, 4.7 of Tools for supersymmetry (arXiv:hep-th/9910030)
Sergei Kuzenko, Gabriele Tartaglino-Mazzucchelli, Supertwistor realisations of AdS superspaces, The European Physical Journal C 82 2 (2022) 146 [doi:10.1140/epjc/s10052-022-10072-y, arXiv:2108.03907]
The super 3-cocycle for the Green-Schwarz superstring on is originally due to
However, a supersymmetric trivialization of this cocycle seems to have been obtained in
(according to arxiv:1808.04470, p. 5 and equation (5.5), but check).
See also the references at Green-Schwarz sigma-model – References – AdS backgrounds
Last revised on March 8, 2024 at 14:54:26. See the history of this page for a list of all contributions to it.