Yongchao Lü (University of Cincinnati)

On the classification of 4d rank1 N=2 SCFT by mass deformation

I will report on a systematic approach to the classification of four dimensional N=2 superconformal field theories (SCFTs) with a one dimensional moduli space of Coulomb vacua with planar topology. The geometric structure of the Coulomb branch encodes ultraviolet conformal field theory data: the relevant mass deformations of the UV N=2 SCFTs are mapped to the complex deformations of singular Coulomb branch geometries. Our results go beyond the standard lore of the ADE classification, and a richer pattern of flavor symmetries is revealed corresponding to different deformations.

We have constructed explicit Seiberg-Witten (SW) curves and one-forms for each possible regular deformation. Further physical consistency conditions are obtained by considering N=2 RG flows, and certain SW geometries are ruled out by our conjecture about the absence of dangerously irrelevant operators in N=2 field theories. Along this way, we have discovered several new rank-1 N=2 SCFTs.

The structure of the Higgs branch and enhanced Coulomb branches (also known as mixed branches) of these N=2 SCFTs is also examined in terms of N=2 chiral ring relations and N=2 S-dualities. The related data (i.e., the dimension of the Higgs branch factor of enhanced Coulomb branches ) is used to compute the conformal and flavor central charges by a refined version of Shapere and Tachikawa's topological twisting argument.