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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):
$\stackrel{d}{=}$ | $p =$ | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
---|---|---|---|---|---|---|---|---|---|---|
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):
$\stackrel{d}{=}$ | $p =$ | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
---|---|---|---|---|---|---|---|---|---|---|
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) |
The original construction is in
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
George Papadopoulos, Paul Townsend, Intersecting M-branes, Phys. Lett. B380 (1996) 273 (arXiv:hep-th/9603087)
Arkady Tseytlin, Nucl. Phys. B475 (1996) 149.
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.