nLab 3-brane in 6d




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).

This is thought to be the intersection locus of two M5-branes (Papadopoulos & Townsend 1996, Tseytlin 1996, Howe, Lambert & West 1998, p. 2, Kachru, Oz & Yin 1998).

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

The brane scan.

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

=d\stackrel{d}{=}p=p =123456789
10D0F1, D1D2D3D4NS5, D5D6D7D8D9
7M2 top{}_{top}
6F1 little{}_{little}, S1 sd{}_{sd}S3

(The first columns follow the exceptional spinors table.)

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

=d\stackrel{d}{=}p=p =123456789
11Ψ 2E 2\Psi^2 E^2 on sIso(10,1)Ψ 2E 5+Ψ 2E 2C 3\Psi^2 E^5 + \Psi^2 E^2 C_3 on m2brane
10Ψ 2E 1\Psi^2 E^1 on sIso(9,1)B 2 2+B 2Ψ 2+Ψ 2E 2B_2^2 + B_2 \Psi^2 + \Psi^2 E^2 on StringIIA\cdots on StringIIBB 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 StringIIAΨ 2E 5\Psi^2 E^5 on sIso(9,1)B 2 4++Ψ 2E 6B_2^4 + \cdots + \Psi^2 E^6 on StringIIA\cdots on StringIIBB 2 5++Ψ 2E 8B_2^5 + \cdots + \Psi^2 E^8 in StringIIA\cdots on StringIIB
9Ψ 2E 4\Psi^2 E^4 on sIso(8,1)
8Ψ 2E 3\Psi^2 E^3 on sIso(7,1)
7Ψ 2E 2\Psi^2 E^2 on sIso(6,1)
6Ψ 2E 1\Psi^2 E^1 on sIso(5,1)Ψ 2E 3\Psi^2 E^3 on sIso(5,1)
5Ψ 2E 2\Psi^2 E^2 on sIso(4,1)
4Ψ 2E 1\Psi^2 E^1 on sIso(3,1)Ψ 2E 2\Psi^2 E^2 on sIso(3,1)
3Ψ 2E 1\Psi^2 E^1 on sIso(2,1)

The Brane molecule

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

It’s generalization featuring L-infinity-algebra extensions is the brane bouquet.



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

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

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

with a matrix model-description in:

For more on this see

See also

  • S. Bellucci, N. Kozyrev, S. Krivonos, A Sutulin, Component on-shell actions of supersymmetric 3-branes: I. 3-brane in D=6D = 6, Class. Quantum Grav. 32 (2015) 035025 (doi:10.1088/0264-9381/32/3/035025)

The relation to D=4 N=2 super Yang-Mills theory is discussed in

and via F-theory in

  • Robert de Mello Koch, Alastair Paulin-Campbell, Joao P. Rodrigues, Monopole Dynamics in 𝒩=2\mathcal{N}=2 super Yang-Mills Theory From a Threebrane Probe, Nucl. Phys. B559 (1999) 143-164 (arXiv:hep-th/9903207)

As M5-probe branes in an AdS7-CFT6 background (i.e. in the near horizon limit of black M5-branes):

Last revised on July 8, 2023 at 20:31:21. See the history of this page for a list of all contributions to it.