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On Large N Expansion of the Sphere Free Energy
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On Large N Expansion of the Sphere Free Energy
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We propose formulas for the $1/N$ 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 $\epsilon$ near various integer dimensions we find a perfect agreement with results obtained using $\epsilon$-expansion technique. In $d=3$, the large $N$ results with the $1/N$ correction included are in good agreement with the Pade resummed $\epsilon$-expansion.
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Local CFTs extremise $F$
Local CFTs lie at the extrema of the sphere free energy tilde F for nonlocal CFT lines, and maximize it when unitary.
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