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3-brane in 6d

Context

String theory

Ingredients

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Critical string models

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Extended objects

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Topological strings

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Backgrounds

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Phenomenology

Contents

Idea

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

The scan.

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

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

(The first columns follow the .)

The corresponding exceptional (schematically, without prefactors):

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