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# 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).

The scan.

The super $p$- (see at for further links and see at for the full classification):

$\stackrel{d}{=}$$p =$123456789
11
10, ,
9$\ast$
8$\ast$
7${}_{top}$
6${}_{little}$, ${}_{sd}$
5$\ast$
4
3

(The first columns follow the .)

The corresponding exceptional (schematically, without prefactors):

$\stackrel{d}{=}$$p =$123456789
11$\Psi^2 E^2$ on (10,1)$\Psi^2 E^5 + \Psi^2 E^2 C_3$ on
10$\Psi^2 E^1$ on (9,1)$B_2^2 + B_2 \Psi^2 + \Psi^2 E^2$ on $\cdots$ on $B_2^3 + B_2^2 \Psi^2 + B_2 \Psi^2 E^2 + \Psi^2 E^4$ on $\Psi^2 E^5$ on (9,1)$B_2^4 + \cdots + \Psi^2 E^6$ on $\cdots$ on $B_2^5 + \cdots + \Psi^2 E^8$ in $\cdots$ on
9$\Psi^2 E^4$ on (8,1)
8$\Psi^2 E^3$ on (7,1)
7$\Psi^2 E^2$ on (6,1)
6$\Psi^2 E^1$ on (5,1)$\Psi^2 E^3$ on (5,1)
5$\Psi^2 E^2$ on (4,1)
4$\Psi^2 E^1$ on (3,1)$\Psi^2 E^2$ on (3,1)
3$\Psi^2 E^1$ on (2,1)

## References

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

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

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

For more on this see

Last revised on May 14, 2018 at 03:44:42. See the history of this page for a list of all contributions to it.