Central charges from the (N)=1 superconformal index.

Abstract

We present prescriptions for obtaining the central charges, a and c, of a four-dimensional superconformal quantum field theory from the superconformal index. At infinite N, for holographic theories dual to Sasaki-Einstein 5-manifolds the prescriptions give the O(1) parts of the central charges. This allows us, among other things, to show the exact AdS/CFT matching of a and c for arbitrary toric quiver CFTs without adjoint matter that are dual to smooth Sasaki-Einstein 5-manifolds. In addition, we include evidence from nonholographic theories for the applicability of these results outside of a holographic setting and away from the large-N limit.