Fermionic Minimal Models

We show that there is a fermionic minimal model, i.e., a $1+1\mathrm{D}$ conformal field theory which contains operators of half-integral spins in its spectrum, for each $c=1–6/m(m+1)$, $m\ge 3$. This generalizes the Majorana fermion for $c=1/2$, $m=3$ and the smallest $\mathcal{N}=1$ supersymmetric minimal model for $c=7/10$, $m=4$. We provide explicit Hamiltonians on Majorana chains realizing these fermionic minimal models.