superalgebra and (synthetic ) supergeometry
According to the brane scan of super -branes there exists a supermembrane propagating on 4+1 dimensional super Minkowski spacetime (being of codimension=2, this is a defect brane):
The brane scan.
The Green-Schwarz type super -brane sigma-models (see at table of branes for further links and see at The brane bouquet for the full classification):
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | ||
---|---|---|---|---|---|---|---|---|---|---|
11 | M2 | M5 | ||||||||
10 | D0 | F1, D1 | D2 | D3 | D4 | NS5, D5 | D6 | D7 | D8 | D9 |
9 | * | |||||||||
8 | * | |||||||||
7 | M2 | |||||||||
6 | F1, S1 | S3 | ||||||||
5 | * | |||||||||
4 | * | * | ||||||||
3 | * |
(The first columns follow the exceptional spinors table.)
The corresponding exceptional super L-∞ algebra cocycles (schematically, without prefactors):
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | ||
---|---|---|---|---|---|---|---|---|---|---|
11 | on sIso(10,1) | on m2brane | ||||||||
10 | on sIso(9,1) | on StringIIA | on StringIIB | on StringIIA | on sIso(9,1) | on StringIIA | on StringIIB | in StringIIA | on StringIIB | |
9 | on sIso(8,1) | |||||||||
8 | on sIso(7,1) | |||||||||
7 | on sIso(6,1) | |||||||||
6 | on sIso(5,1) | on sIso(5,1) | ||||||||
5 | on sIso(4,1) | |||||||||
4 | on sIso(3,1) | on sIso(3,1) | ||||||||
3 | on sIso(2,1) |
Furthermore, there exists a more general classification of possible supermembranes in spacetime with spatial dimensions and time dimensions, appearing in (Blencowe-Duff 88). In this sense, the brane scan is but the branch of the brane molecule. The objects appearing here are expected to be related to other generalizations of string theory. See D=12 supergravity and bosonic M-theory.
Compare:
Miles Blencowe, Mike Duff, Supermembranes and the Signature of Space-time, Nucl. Phys. B310 (1988) 387-404 (spire:262142, 10.1016/0550-3213(88)90155-1, pdf)
Minkyu Park, Masaki Shigemori, Codimension-2 Solutions in Five-Dimensional Supergravity, JHEP 1510 (2015) 011 (arXiv:1505.05169)
Masaki Shigemori, Interpolating between multi-center microstate geometries, JHEP 09 (2021) 010 (arXiv:2105.11639)
S. Bellucci, N. Kozyrev, S. Krivonos, A. Yeranyan, Supermembrane in : component action, Journal of High Energy Physics volume 2014 142 (2014) (arXiv:1312.0231, doi:10.1007%2FJHEP05%282014%29142)
Last revised on December 24, 2021 at 15:57:43. See the history of this page for a list of all contributions to it.