N = 2 $$ mathcal{N}=2 $$ central charge bounds from 2 d chiral algebras

We study protected correlation functions in $$ mathcal{n}=2 $$ scft whose description is captured by a two-dimensional chiral algebra. our analysis implies a new analytic bound for the c-anomaly as a function of the flavor central charge k, valid for any theory with a flavor symmetry. combining our result with older bounds in the literature puts strong constraints on the parameter space of $$ mathcal{n}=2 $$ theories. in particular, it singles out a special set of models whose value of c is uniquely fixed once k is given. this set includes the canonical rank one $$ mathcal{n}=2 $$ scfts given by kodaira’s classification.