c − a from the superconformal index

Abstract

Abstract: We present a prescription for obtaining the difference of the central charges, c−a, of a four dimensional superconformal quantum field theory from its single-trace index. The formula is derived from a one-loop holographic computation, but is expected to be valid independent of holography. We demonstrate the prescription with several holographic and non-holographic examples. As an application of our formula, we show the AdS/CFT matching of c − a for arbitrary toric quiver CFTs without adjoint matter that are dual to smooth Sasaki-Einstein 5-manifolds.