nLab triple membrane junction

Idea

Among the possible $\frac{1}{8}$-BPS states of 11-dimensional supergravity/M-theory is one where three black M2-branes jointly intersect at equal angles (Tseytlin 96)

$$M2 \perp M2 \perp M2 \,.$$

This is the lift to M-theory of 3-string junctions in type IIB string theory (Krogh-Lee 97, Ramadevi 99), see at string network.

Properties

Triple generalization of Chan-Paton factors

Since black M2-branes may also end on M5-branes, in an M-theory lift of how strings end on D-branes as quanta of super Yang-Mills theory, there was the suggestion that this points to a generalization of gauge theories where matrix Lie algebras (matrices of Chan-Paton factors) are enhanced to some kind of higher or hypermatrix structure (FLST 10).

Gauge enhancement at ADE-Singularities

If one accepts the traditional story of the M-theory lift of gauge enhancement on D6-branes, in terms of M2-branes wrapping 2-spheres that touch along the shape of a Dynkin diagram blowup of an ADE-singularity,

graphics grabbed from HSS18

then such triple membrane junctions must correspond to blowups of the dihedral, tetrahedral, octahedral or icosahedral ADE-singularities, since in these cases the Dynkin diagram has a triple junction node :

Related concepts

brane intersections/bound states/wrapped branes/polarized branes

• D-branes and anti D-branes form bound states by tachyon condensation, thought to imply the classification of D-brane charge by K-theory

• intersecting D-branes/fuzzy funnels:

  • Dp-D(p+2)-brane bound state and Yang-Mills monopoles

    • D0-D2 brane bound state

    • D1-D3 brane bound state

    • D2-D4 brane bound state

    • D3-D5 brane bound state

    • D4-D6 brane bound state

    • D6-D8-brane bound state

  • Dp-D(p+4)-brane bound state and Yang-Mills instantons

    • D0-D4 brane bound state

    • D1-D5 brane bound state

    • D2-D6 brane bound state

    • D3-D7 brane bound state

    • D4-D8 brane bound state

    • D5-D9 brane bound state

      small instanton

• Dp-D(p+6) brane bound state

  • D0-D6 brane bound state

  • D1-D7 brane bound state

  • D2-D8 brane bound state

• NS5-D4-D2 bound states

• Hanany-Witten effect

S-duality$\,$bound states:

• (p,q)-string

• (p,q)5-branes

• string network

• 5-brane web

intersecting$\,$M-branes:

• M5-MO9 brane bound state

• M2-M5 brane bound state

  • M-string, E-string

• membrane triple junction

References

Discussion of triple-membrane junction-shaped black brane-solutions to 11-dimensional supergravity is in

• Arkady Tseytlin, Harmonic superpositions of M-branes, Nucl. Phys. B475:149-163, 1996 (arxiv:hep-th/9604035)

Lift of and relation to string networks is discussed in

• Morten Krogh, Sangmin Lee, String Network from M-theory, Nucl. Phys. B516:241-254, 1998 (arXiv:hep-th/9712050)

• P. Ramadevi, Supergravity Solution for Three-String Junction in M-Theory, JHEP 0006 (2000) 005 (arXiv:hep-th/9906247)

Possible relation to hypermatrices is discussed in

• Yuhan Fang, Shir Levkowitz, Hisham Sati, Daniel Thompson, Hypermatrix factors for string and membrane junctions, J. Phys. A43: 505401, 2010 (arXiv:1001.5166)