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

Understand

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.