Divisibility conjecture for the index of holomorphic N=1 SCFTs

Let $V$ be a holomorphic $\mathcal N=1$ superconformal field theory of central charge $c=12k$, and let $Z_{RR}(V)$ be its supersymmetric index. Index divisibility conjecture. The integer $Z_{RR}(V)$ is divisible by

$$\frac{24}{\gcd(k,24)}.$$

This follows in the source from the preceding Stolz–Teichner prediction together with the known image of $\pi_n\mathrm{TMF}$ in integral modular forms; the source presents it as a consequence of the conjectural description.