On Large N Expansion of the Sphere Free Energy

We propose formulas for the $1\mathrm{/}N$ correction to the sphere free energy of theories with 4-fermion interactions, which are conformal for $d>2$. We also propose a formula for the scalar $O(N)$ model. Expanding these formulas in small $ϵ$ near various integer dimensions we find a perfect agreement with results obtained using $ϵ$-expansion technique. In $d=3$, the large $N$ results with the $1\mathrm{/}N$ correction included are in good agreement with the Pade resummed $ϵ$-expansion.