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

Léonard Ferdinand (1) , Razvan Gurau (2, 3, 4) , Carlos I. Perez-Sanchez (2) , Fabien Vignes-Tourneret (5)

1 IJCLab - Laboratoire de Physique des 2 Infinis Irène Joliot-Curie
2 Institut für Theoretische Physik [Heidelberg]
3 CPHT - Centre de Physique Théorique [Palaiseau]
4 Perimeter Institute for Theoretical Physics [Waterloo]
5 PSPM - Probabilités, statistique, physique mathématique

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.

Domains: Mathematics [math]; Mathematical Physics [math-ph]

Léonard Ferdinand, Razvan Gurau, Carlos I. Perez-Sanchez, Fabien Vignes-Tourneret. Borel summability of the 1/N expansion in quartic O(N)-vector models. 2022. ⟨hal-03781144⟩