superalgebra and (synthetic ) supergeometry
By the brane scan there exists a classical (pre-quantum) Green-Schwarz super p-brane sigma model for (supermembrane) with target space being dimensional super Minkowski spacetime with N=1 supersymmetry, or more generally a superspacetime which is a super Cartan geometry solving the equations of motion of d=4 N=1 supergravity. (The literature traditionally knows this as the “4d supermembrane”.)
Its double dimensional reduction is the super 1-brane in 3d (see there) for 3d supergravity.
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) |
The action functional is apparently originally due to
Further dicussion of the coupling to the d=4 N=1 supergravity background includes
Burt Ovrut, Daniel Waldram, Membranes and Three-form Supergravity, Nucl.Phys. B506 (1997) 236-266 (arXiv:hep-th/9704045)
M. P. Garcia del Moral, J. M. Pena, A. Restuccia, 4D Supermembrane from , JHEP0807:039,2008 (arXiv:0709.4632)
M. Huebscher, P. Meessen, T. Ortin, Domain walls and instantons in , supergravity, JHEP 1006:001,2010 (arXiv:0912.3672)
Igor Bandos, Carlos Meliveo, Supermembrane interaction with dynamical supergravity. Superfield Lagrangian description and spacetime equations of motion (arXiv:1205.5885)
Carlos Meliveo, On Supermembrane in , multiple M0-brane in and Supersymmetric Higher Spin Theories (arXiv:1312.3512)
See also
Discussion of coupling of the super 2-brane in 4d to D=4 N=1 super Yang-Mills theory:
On membranes in D=4 supergravity (super 2-brane in 4d):
Discussion of strongly coupled 4d physics akin to 11d M-theory with its M2-brane includes
(on possible solutions to the cosmological constant problem).
Last revised on May 24, 2020 at 12:19:46. See the history of this page for a list of all contributions to it.