N=2 central charge bounds from 2d chiral algebras

We study protected correlation functions in 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 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 N = 2 SCFTs given by Kodaira's classification.