Geometric constraints on the space of N=2 SCFTs III: enhanced Coulomb branches and central charges

TL;DR

This paper analyzes the geometric structures of rank-1 4D $ abla=2$ SCFTs, focusing on Coulomb, Higgs, and mixed branches, and computes their central charges to advance classification efforts.

Contribution

It introduces a systematic approach to understanding Higgs and mixed branch geometries and calculates central charges, enhancing the classification of rank-1 $ abla=2$ SCFTs.

Findings

Characterization of Higgs and mixed branch geometries

Calculation of conformal and flavor central charges

Summary of current classification status

Abstract

This is the third in a series of three papers on the systematic analysis of rank 1 four dimensional $\mathcal{N}=2$ SCFTs. In the first two papers we developed and carried out a strategy for classifying and constructing physical planar rank-1 Coulomb branch geometries of $\mathcal{N}=2$ SCFTs. Here we describe general features of the Higgs and mixed branch geometries of the moduli space of these SCFTs, and use this, along with their Coulomb branch geometry, to compute their conformal and flavor central charges. We conclude with a summary of the state of the art for rank-1 $\mathcal{N}=2$ SCFTs.