superalgebra and (synthetic ) supergeometry
black hole spacetimes | vanishing angular momentum | positive angular momentum |
---|---|---|
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.3.2-3, II.5, and V.4.4 in: Supergravity and Superstrings - A Geometric Perspective, World Scientific (1991) [ch II.2: pdf, ch II.3: pdf, ch II.5: pdf, ch V.4: pdf]
Renata Kallosh, J. Rahmfeld, A. Rajaraman, Near Horizon Superspace, JHEP 9809:002 (1998) [arXiv:hep-th/9805217]
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]
Specifically on super- (super-near horizon geometry of black M2-branes as in AdS4/CFT3-duality):
Bernard de Wit, Kasper Peeters, Jan Plefka, Alexander Sevrin, The M-theory two-brane in and , Physics Letters B 443 1-4 (1998) 153-158 [doi:10.1016/S0370-2693(98)01340-9, inspire:474621, arXiv:hep-th/9808052]
Jaume Gomis, Dmitri Sorokin, Linus Wulff, The complete superspace for the type IIA superstring and D-branes, JHEP 0903:015 (2009) [arXiv:0811.1566]
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 April 23, 2024 at 15:54:37. See the history of this page for a list of all contributions to it.