In recent years string theory-inspired techniques, such as geometric engineering, have greatly enriched the toolbox available to study strongly-coupled and non-Lagrangian theories in various dimensions. In the realm of 6d superconformal field theories (SCFTs), a classification in terms of basic building blocks that generalize usual bifundamental matter, termed “conformal matter theories”, has been presented via F-theoretic setups. These blocks can then be systematically fused to form more complicated theories, that classify 6d SCFTs via generalized quivers. In this talk we start tackling an analogous classification problem for 5d SCFTs, relying on M-theory geometric engineering on singular Calabi-Yau threefolds. We present a novel “atomic” classification for 5d SCFTs with flavor symmetry of type GxG, with G an ADE algebra; we show how the elementary 5d SCFT “atoms” can be fused to produce arbitrarily long “molecules”, and finally we apply this technique to exhibit new 5d dualities. The talk is based on https://arxiv.org/pdf/2311.04984.pdf.

King’s College London