$N=2$ Superconformal Field Theories in $4$ Dimensions and A-D-E Classification

TL;DR

This paper constructs new 4D N=2 superconformal field theories by tuning moduli parameters to critical points, revealing an A-D-E classification similar to 2D SCFTs, based on exact solutions of supersymmetric gauge theories.

Contribution

It introduces a novel classification of 4D N=2 SCFTs using A-D-E types, derived from exact solutions and critical point analysis.

Findings

N=2 critical points classified by A-D-E types

New classes of SCFTs constructed from pure gauge theories

Connection between 4D and 2D SCFT classifications

Abstract

Making use of the exact solutions of the $N=2$ supersymmetric gauge theories we construct new classes of superconformal field theories (SCFTs) by fine-tuning the moduli parameters and bringing the theories to critical points. In the case of SCFTs constructed from pure gauge theories without matter $N=2$ critical points seem to be classified according to the A-D-E classification as in the two-dimensional SCFTs.