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

Abstract We derive explicit formulae to compute the a and c central charges of four dimensional N $$ \mathcal{N} $$ = 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 N $$ \mathcal{N} $$ = 2 SCFTs which culminate with our N $$ \mathcal{N} $$ = 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 N $$ \mathcal{N} $$ = 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. This manuscript is dedicated to the memory of Rayshard Brooks, George Floyd, Breonna Taylor and the countless black lives taken by US police forces and still awaiting justice. Our hearts are with our colleagues of color who suffer daily the consequences of this racist world.