On Large N Expansion of the Sphere Free Energy

Grigory Tarnopolsky

doi:10.1103/physrevd.96.025017

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arXiv · 1609.09113

On Large N Expansion of the Sphere Free Energy

Grigory Tarnopolsky

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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.

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Grigory Tarnopolsky. 2016-09-28. On Large N Expansion of the Sphere Free Energy. https://doi.org/10.1103/physrevd.96.025017

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