  We utilize the integrality conjecture to show that the torus partition
function of a fermionic rational conformal theory in the Ramond-Ramond sector
becomes a constant when the bound $h^R \ge \frac{c}{24}$ is satisfied, where
$h^R$ denote the conformal weights of Ramond states and $c$ is the central
charge. The constant-valued Ramond-Ramond partition function strongly suggests
the presence of supersymmetry unless a given theory has free fermions. The
lower bound $h^R \ge \frac{c}{24}$ can then be identified with the unitarity
bound of $\mathcal{N}=1$ supersymmetry. We thus propose that, for rational CFTs
without free fermions, $(h^R-c/24) \geq 0$ can imply supersymmetry.
