nLab
super 2-brane in 4d

Contents

Context

String theory

Super-Geometry

Contents

Idea

By the brane scan there exists a classical (pre-quantum) Green-Schwarz super p-brane sigma model for p=2p =2 (supermembrane) with target space being d=4d = 4 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 N=(1,1)N=(1,1) 3d supergravity.

The brane scan.

The Green-Schwarz type super pp-brane sigma-models (see at table of branes for further links and see at The brane bouquet for the full classification):

=d\stackrel{d}{=}p=p =123456789
11M2M5
10D0F1, D1D2D3D4NS5, D5D6D7D8D9
9*\ast
8*\ast
7M2 top{}_{top}
6F1 little{}_{little}, S1 sd{}_{sd}S3
5*\ast
4**
3*

(The first columns follow the exceptional spinors table.)

The corresponding exceptional super L-∞ algebra cocycles (schematically, without prefactors):

=d\stackrel{d}{=}p=p =123456789
11Ψ 2E 2\Psi^2 E^2 on sIso(10,1)Ψ 2E 5+Ψ 2E 2C 3\Psi^2 E^5 + \Psi^2 E^2 C_3 on m2brane
10Ψ 2E 1\Psi^2 E^1 on sIso(9,1)B 2 2+B 2Ψ 2+Ψ 2E 2B_2^2 + B_2 \Psi^2 + \Psi^2 E^2 on StringIIA\cdots on StringIIBB 2 3+B 2 2Ψ 2+B 2Ψ 2E 2+Ψ 2E 4B_2^3 + B_2^2 \Psi^2 + B_2 \Psi^2 E^2 + \Psi^2 E^4 on StringIIAΨ 2E 5\Psi^2 E^5 on sIso(9,1)B 2 4++Ψ 2E 6B_2^4 + \cdots + \Psi^2 E^6 on StringIIA\cdots on StringIIBB 2 5++Ψ 2E 8B_2^5 + \cdots + \Psi^2 E^8 in StringIIA\cdots on StringIIB
9Ψ 2E 4\Psi^2 E^4 on sIso(8,1)
8Ψ 2E 3\Psi^2 E^3 on sIso(7,1)
7Ψ 2E 2\Psi^2 E^2 on sIso(6,1)
6Ψ 2E 1\Psi^2 E^1 on sIso(5,1)Ψ 2E 3\Psi^2 E^3 on sIso(5,1)
5Ψ 2E 2\Psi^2 E^2 on sIso(4,1)
4Ψ 2E 1\Psi^2 E^1 on sIso(3,1)Ψ 2E 2\Psi^2 E^2 on sIso(3,1)
3Ψ 2E 1\Psi^2 E^1 on sIso(2,1)

References

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, N=1N=1 4D Supermembrane from 11D11D, JHEP0807:039,2008 (arXiv:0709.4632)

  • M. Huebscher, P. Meessen, T. Ortin, Domain walls and instantons in N=1N=1, d=4d=4 supergravity, JHEP 1006:001,2010 (arXiv:0912.3672)

  • Igor Bandos, Carlos Meliveo, Supermembrane interaction with dynamical D=4D=4 N=1N=1 supergravity. Superfield Lagrangian description and spacetime equations of motion (arXiv:1205.5885)

  • Carlos Meliveo, On Supermembrane in D=4D=4, multiple M0-brane in D=11D=11 and Supersymmetric Higher Spin Theories (arXiv:1312.3512)

See also

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 January 15, 2019 at 09:13:07. See the history of this page for a list of all contributions to it.