Classification of complete N=2 supersymmetric theories in 4 dimensions

Understand

We define the notion of a complete N=2 supersymmetric theory in 4 dimensions as a UV complete theory for which all the BPS central charges can be arbitrarily varied as we vary its Coulomb branch parameters, masses, and coupling constants.

• We classify all such theories whose BPS spectrum can be obtained via a quiver diagram.
• This is done using the 4d/2d correspondence and by showing that such complete N=2 theories map to quivers of finite mutation type.
• The list of such theories is given by the (generalized) Gaiotto theories consisting of two 5-branes wrapping Riemann surfaces with punctures, as well as 11 additional exceptional cases, which we identify.