$c-a$ from the $N=1$ superconformal index

Understand

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.