Quenched equals annealed at leading order in the colored SYK model

We consider a colored version of the SYK model, that is we distinguish the $D$ vector fermionic fields involved in the interaction by a color. We obtain the full $1\mathrm{/}N$ series of both the quenched and annealed free energies of the model and show that at leading order the two are identical. The results can be used to study systematically the $1\mathrm{/}N$ corrections to this leading order behavior.