$c-a$ from the $N=1$ superconformal index
Arash Arabi Ardehali, James T. Liu, Phillip Szepietowski
TL;DR
This paper introduces a new method to compute the difference c-a of central charges in 4D superconformal theories using the single-trace index, applicable to both holographic and non-holographic cases.
Contribution
A novel formula derived from holographic computations that allows calculation of c-a from the superconformal index, validated on various examples.
Findings
Successfully computes c-a for multiple theories
Matches c-a values with holographic duals in AdS/CFT correspondence
Applicable to toric quiver CFTs without adjoint matter
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.
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