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We prove that there does not exist any weak coupling limit in the space ofsuperconformal field theories in five and six dimensions, based on an analysisof the representation theory of the corresponding superconformal algebras.Holographically, this implies that superstring theories on AdS$_6$ and AdS$_7$do not admit tensionless limits. Finally, we discuss the implications of ourresult on the existence of an action for coincident M5-branes.

5d and 6d SCFTs Have No Weak Coupling Limit