On the classification of 5d SCFTs

A bstract We determine all 5 d SCFTs upto rank three by studying RG flows of 5 d KK theories. Our analysis reveals the existence of new rank one and rank two 5 d SCFTs not captured by previous classifications. In addition to that, we provide for the first time a systematic and conjecturally complete classification of rank three 5 d SCFTs. Our methods are based on a recently studied geometric description of 5 d KK theories, thus demonstrating the utility of these geometric descriptions. It is straightforward, though computationally intensive, to extend this work and systematically classify 5 d SCFTs of higher ranks (greater than or equal to four) by using the geometric description of 5 d KK theories.