Physics and Astronomy Colloquium

Quantum Field Theory (QFT) is the common language of particle physicists, cosmologists, and condensed matter physicists. Even so, many fundamental aspects of QFT remain poorly understood. I discuss some of the recent progress made by my research group in understanding QFT using the geometry of extra dimensions predicted by string theory, highlighting in particular the special role of seemingly "exotic" higher-dimensional supersymmetric QFTs with no length scales known as six-dimensional superconformal field theories (6D SCFTs). We have recently classified all examples of such 6D SCFTs, and are now using this to extract observables from strongly correlated systems in theories with D>4 and D≤4 spacetime dimensions. Along the way, I will also highlight the remarkable interplay between physical and mathematical structures in the study of such systems.