A membrane sigma-model topological quantum field theory that is roughly related to topological M-theory as the M2-brane is related to M-theory and to the topological string (A-model/B-model) as the M2-brane is related to the string and to the topological M5-brane as the M2-brane is related to the M5-brane.
The target space of the topological membrane is a G2-manifold, the action functional is governed by the higher holonomy of the compatible supergravity C-field over the membrane worldvolume.
According to (Bao-Bengtsson-Cederwall-Nillson 05, equation (2.14)) the topological -brane is the super 2-brane which exists in according to the brane scan, which says that the super Poincare Lie algebra in carries an exceptional Lie algebra cocycle of degree , hence admits the Green-Schwarz action functional for a super 2-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) |
Table of branes appearing in supergravity/string theory (for classification see at brane scan).
Giulio Bonelli, Alessandro Tanzini, Maxim Zabzine, On topological M-theory (arXiv:hep-th/0509175)
Ling Bao, Topological membranes, Nucl. Phys. Proc. Suppl. 171 (2007) 259-260 (inspire)
In the context of exceptional generalized geometry:
Last revised on June 9, 2017 at 17:50:55. See the history of this page for a list of all contributions to it.