Non-Lagrangian theories and six-dimensional superconformal theories

4 problems

• Do all six-dimensional superconformal theories arise from F-theory

  Open

  A catalog of six-dimensional theories was built from geometric constructions in string theory. Whether every such theory appears in the catalog is unknown.

• Intrinsic definition of the six-dimensional (2,0) theory

  Open

  The six-dimensional $(2,0)$ theory, the version with the maximum amount of supersymmetry, is defined only as a limit of a stack of M5-branes, membrane-like objects of M-theory. A definition that stands on its own is missing.

• Microscopic origin of $N^3$ degrees of freedom on M5-branes

  Open

  A stack of $N$ M5-branes behaves as if it carried about $N^3$ independent quantities, while a stack of $N$ ordinary D-branes carries about $N^2$. Which objects supply the $N^3$ is unknown.

• Classification of rank-2 four-dimensional $N=2$ superconformal theories

  Partially resolved

  Four-dimensional theories with extra supersymmetry (a symmetry pairing each force particle with a matter particle) can be sorted by the shape of their space of vacua. The sorting is complete only for the simplest case, with one complex dimension.