nLab super 2-brane in 4d

Contents

Context

String theory

Super-Geometry

Idea
Related entries

The Brane molecule

References

Idea

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

Related entries

The brane scan.

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

$\stackrel{d}{=}$	$p =$	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 ${}_{top}$
6		F1 ${}_{little}$ , S1 ${}_{sd}$		S3
5			*
4		*	*
3		*

(The first columns follow the exceptional spinors table.)

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

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

The Brane molecule

Furthermore, there exists a more general classification of possible supermembranes in spacetime with $S$ spatial dimensions and $T$ time dimensions, appearing in (Blencowe-Duff 88). In this sense, the brane scan is but the $T=1$ 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.

The brane molecule without assuming super Poincare invariance.

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)
brane bouquet

References

The action functional is apparently originally due to

A. Achúcarro, Jerome Gauntlett, K. Itoha, Paul Townsend, World-volume supersymmetry from spacetime supersymmetry of the four-dimensional supermembrane, Nuclear Physics B Volume 314, Issue 1, 20 February 1989, Pages 129–157 (doi:10.1016/0550-3213(89)90115-6)

Further dicussion of the coupling to the d=4 N=1 supergravity background:

Burt Ovrut, Daniel Waldram, Membranes and Three-form Supergravity, Nucl.Phys. B506 (1997) 236-266 (arXiv:hep-th/9704045)
Maria P. Garcia del Moral, J. M. Pena, Alvaro Restuccia, $\mathcal{N}=1$ 4D Supermembrane from $11D$ , JHEP0807 039 (2008) [arXiv:0709.4632]
M. Huebscher, P. Meessen, T. Ortin, Domain walls and instantons in $N=1$ , $d=4$ supergravity, JHEP 1006:001,2010 (arXiv:0912.3672)
Igor Bandos, Carlos Meliveo, Supermembrane interaction with dynamical $D=4$ $N=1$ supergravity. Superfield Lagrangian description and spacetime equations of motion (arXiv:1205.5885)
Carlos Meliveo, On Supermembrane in $D=4$ , multiple M0-brane in $D=11$ and Supersymmetric Higher Spin Theories (arXiv:1312.3512)

nLab super 2-brane in 4d

Context

String theory

Ingredients

Critical string models

Extended objects

Topological strings

Backgrounds

Phenomenology

Super-Geometry

Background

Introductions

Superalgebra

Supergeometry

Supersymmetry

Supersymmetric field theory

Applications

Contents

Idea

Related entries

The Brane molecule

References