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

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.

19 pages. v2: minor changes, reference added. v3: minor clarifications, published version. v4: a typo in Table 2 fixed

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