nLab 3-brane in 6d

Contents

Idea

There is supposed to be a $(p=3)$ -brane in 6-dimensional super-spacetime given by the Green-Schwarz action functional induced by the exceptional super Lie algebra $(3+2)$ -cocycle on $\mathfrak{siso}(5,1)$ (Hughes-Liu-Polchinski 86).

Since this brane has codimension 2, it is a defect brane.

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):

(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 original construction is in

James Hughes, Jun Liu, Joseph Polchinski, Supermembranes, Physics Letters B Volume 180, Issue 4, 20 November 1986, Pages 370–374 (spire)

Discussion building on that includes

Martin Rocek, Arkady Tseytlin, Partial breaking of global D=4 supersymmetry, constrained superfields, and 3-brane actions, Phys.Rev.D59:106001, 1999 (arXiv:hep-th/9811232)

The relevant cocycle for discussion as a Green-Schwarz sigma-model is given in

Discussion of the 3-brane in 6d explicitly as a black brane in an M5-brane/NS5-brane worldvolume is due to

Paul Howe, Neil Lambert, Peter West, The Threebrane Soliton of the M-Fivebrane, Phys. Lett. B419 (1998) 79-83 (arXiv:hep-th/9710033)

and the understanding of this configuration as resulting from two intersecting M5-branes is due to

George Papadopoulos, Paul Townsend, Intersecting M-branes, Phys. Lett. B380 (1996) 273 (arXiv:hep-th/9603087)
Arkady Tseytlin, Harmonic superpositions of M-branes, Nucl. Phys. B475 (1996) 149 (arXiv:hep-th/9604035, doi:10.1016/0550-3213(96)00328-8)

with a matrix model-description in:

Shamit Kachru, Yaron Oz, Zheng Yin, Matrix Description of Intersecting M5 Branes JHEP 9811:004, (1998) (arXiv:hep-th/9803050)

For more on this see

Joaquim Gomis, David Mateos, Joan Simón, Paul Townsend, Brane-Intersection Dynamics from Branes in Brane Backgrounds, Phys. Lett. B430 (1998) 231-236 (arXiv:hep-th/9803040)