Among the allowed representations of extended supersymmetry in six dimensions there are exotic chiral multiplets that, instead of a graviton, contain mixed-symmetry spin-2 tensor fields.
Notably, the N = (4, 0) multiplet has a four index exotic graviton and when compactified on a circle,
the 6d (4,0) multiplets give rise to the same degrees of freedom as five-dimensional supergravity theories with the same number of supersymmetries.
It was conjectured that an interacting theory based on this multiplet could arise as a strong coupling limit of M-theory compactified on T6.
In this talk, I will review the above conjecture and present some recent studies on these multiplets in terms of anomalies,
higher-form symmetries, gauge quantisations and swampland conjectures.