The Action of the (free) $(4,0)$-theory

Understand

The $(4,0)$ theory in six dimensions is an exotic theory of supergravity that has been argued to emerge as the strong coupling limit of theories having $N=8$ supergravity as their low energy effective theory in five spacetime dimensions.

• It has maximal supersymmetry and is superconformal.
• Very little is known about this intriguing theory.
• While the spectrum of fields occurring in its description has been given and their equations of motion in the absence of interactions have been written down, no action principle has been formulated, even in the free case.