5d and 6d SCFTs Have No Weak Coupling Limit

TL;DR

This paper proves that five- and six-dimensional superconformal field theories cannot reach weak coupling limits, indicating that their holographic duals in superstring theory also lack tensionless limits, impacting the understanding of M5-branes.

Contribution

It establishes the non-existence of weak coupling limits in 5d and 6d SCFTs using superconformal algebra representation theory, with implications for holography and M-brane actions.

Findings

No weak coupling limit exists in 5d and 6d SCFTs

Superstring theories on AdS6 and AdS7 lack tensionless limits

Implications for the existence of an action for M5-branes

Abstract

We prove that there does not exist any weak coupling limit in the space of superconformal field theories in five and six dimensions, based on an analysis of 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 our result on the existence of an action for coincident M5-branes.