Towards the classification of rank-$r$ $\mathcal{N}=2$ SCFTs. Part I: twisted partition function and central charge formulae

TL;DR

This paper provides explicit formulas for calculating the central charges of four-dimensional $ =2$ SCFTs from Coulomb branch data, revealing properties of flavor symmetry and establishing a UV-IR flavor condition, with applications to rank-2 theories.

Contribution

It introduces general formulas for central charges of $ =2$ SCFTs at any rank based on Coulomb branch quantities and explores flavor symmetry behavior and UV-IR relations.

Findings

Derived explicit formulas for $a$ and $c$ central charges.

Discovered properties of flavor symmetry in $ =2$ SCFTs.

Applied techniques to rank-2 SCFTs, including new theories.

Abstract

We derive explicit formulae to compute the $a$ and $c$ central charges of four dimensional $\mathcal{N}=2$ superconformal field theories (SCFTs) directly from Coulomb branch related quantities. The formulae apply at arbitrary rank. We also discover general properties of the low-energy limit behavior of the flavor symmetry of $\mathcal{N}=2$ SCFTs which culminate with our $\mathcal{N}=2$ UV-IR simple flavor condition. This is done by determining precisely the relation between the integrand of the partition function of the topologically twisted version of the 4d $\mathcal{N}=2$ SCFTs and the singular locus of their Coulomb branches. The techniques developed here are extensively applied to many rank-2 SCFTs, including new ones, in a companion paper.