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)
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.
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).
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 :
Discussion of triple-membrane junction-shaped black brane-solutions to 11-dimensional supergravity is in
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
Last revised on May 17, 2018 at 05:05:59. See the history of this page for a list of all contributions to it.