5d SCFTs and their gauge theory phases

<!--HTML-->In this talk I will revist the geometric engineering of five-dimensional supersymmetric conformal field theories (SCFTs) in M-theory after Intrilligator, Morrison and Seiberg. This esablishes a conjectural map assigning to each local isolated Calabi-Yau three-fold singularity a five-dimensional superconformal field theory. Focusing on the toric case, I will discuss applications of IIA/M-theory fiberwise duality to characterizing the possible gauge theory phases of these systems. This geometric setup clarifies the notion of “UV duality” for such theories. Along the way, I will provide a slightly revised gauge theoretical expression for the 5d prepotential, accounting correctly for the 5d parity anomaly. Based on the preprint arXiv:1812.10451, with Cyril Closset and Vivek Saxena.