The Unreasonable Effectiveness of Geometry in Superconformal Field Theory
(University of Pennsylvania)
I will explain how certain physical properties of quantum field theories can be manifestly encoded in the geometric properties of the compactification space of a higher dimensional theory. I will focus on superconformal field theories where the correspondence can be made particularly explicit. I will start from the electric-magnetic duality of U(1) Maxwell theory and build up to recent work in 4d and 6d superconformal field theories. In particular, I will describe the vast zoo of 6d N=(1,0) SCFTs that can be constructed following this principle, and further what one can learn about their compactifications to four dimensions.