nLab super 1-brane in 4d



String theory




By the old brane scan there is a Green-Schwarz sigma-model for a superstring on 4d super-Minkowski spacetime.

Due to the 4d Fierz identity

Γ aψ(ψ¯Γ aψ)=0 \Gamma_a \psi \left( \overline{\psi} \Gamma^a \psi\right) \;= 0\;

(e.g. Ravera 18, (A.17))

Being of codimension=2, this 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.



Discussion relating to the analog of the DF-algebra/M-theory super Lie algebra in 4d supergravity is in

Last revised on December 24, 2021 at 15:58:02. See the history of this page for a list of all contributions to it.