6d superconformal field theories
The quantum field theories with the highest symmetries are the so called superconformal field theories (SCFT’s). They can exist in up to 6 spacetime dimensions and the 6d SCFT’s are believed to be fundamental for the construction of lower dimensional theories through compactification. A thorough understanding of these theories opens up the path to understanding many properties of ordinary quantum field theories through deformations. We start by defining 6d (2,0) SCFT’s and their fundamental properties. Then we proceed to give an overview of 6d (1,0) theories and the novel aspects they give rise to. The most general construction and classification of these theories is given in terms of geometric engineering in F-theory and we shall present a pedagogical overview of such constructions. Last but not least, we will turn our attention to compactifications on Riemann surfaces giving rise to 4d SCFT’s.