Borel summability of the 1/N expansion in quartic O(N)-vector models

TL;DR

This paper proves that the 1/N expansion of a quartic O(N)-vector model's partition function and correlations is Borel summable along the real axis, uniformly in the coupling constant within a specific domain.

Contribution

It establishes Borel summability of the 1/N expansion for the quartic O(N)-vector model using the Loop Vertex Expansion, a novel rigorous result in this context.

Findings

Borel summability holds along the real axis.

Summability is uniform in the coupling constant within a cardioid domain.

The Loop Vertex Expansion is effectively used to prove these results.

Abstract

We consider a quartic O(N)-vector model. Using the Loop Vertex Expansion, we prove the Borel summability in 1/N along the real axis of the partition function and of the connected correlations of the model. The Borel summability holds uniformly in the coupling constant, as long as the latter belongs to a cardioid like domain of the complex plane, avoiding the negative real axis.