On Large N Expansion of the Sphere Free Energy

Abstract

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.

25 pages, 6 figures, v2: minor corrections, references added

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Cited by in corpus (6)

• The critical O(N) CFT: Methods and conformal data
• Entanglement entropy of the large $N$ Wilson-Fisher conformal field theory
• RG flows on $S^d$ and Hamiltonian truncation
• A note on sphere free energy of $p$-form gauge theory and Hodge duality
• Sphere free energy of scalar field theories with cubic interactions
• 3d Large $N$ Vector Models at the Boundary