On Large N Expansion of the Sphere Free Energy

TL;DR

This paper derives formulas for the 1/N corrections to the sphere free energy in conformal theories with 4-fermion interactions and the scalar O(N) model, confirming their accuracy through epsilon-expansion comparisons.

Contribution

It introduces new formulas for 1/N corrections to sphere free energy in certain conformal theories and validates them against epsilon-expansion results.

Findings

Formulas agree with epsilon-expansion in various dimensions.

Large N results match Pade-resummed epsilon-expansion in d=3.

Provides a unified approach for corrections in conformal theories.

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.