Classification of complete N=2 supersymmetric theories in 4 dimensions

TL;DR

This paper classifies all complete N=2 supersymmetric theories in four dimensions with a BPS spectrum describable by quivers, linking them to finite mutation type quivers and Gaiotto theories with additional exceptional cases.

Contribution

It provides a complete classification of such theories, identifying their correspondence with quivers of finite mutation type and extending known Gaiotto theories.

Findings

All theories map to quivers of finite mutation type.

The classification includes Gaiotto theories and 11 exceptional cases.

The approach uses 4d/2d correspondence and quiver mutation analysis.

Abstract

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.