Constructive expansion for vector fields theories. I. Quartic models in low dimensions

Harold Erbin , Vincent Lahoche (1) , Mohamed Tamaazousti (1)

1 LIST (CEA) - Laboratoire d'Intégration des Systèmes et des Technologies

This paper is the first of a series aiming to use the loop vertex expansion (LVE) to recover or prove analyticity and Borel summability for generic vector models with bosonic or fermionic statistics in various dimensions. We consider both nonrelativistic and relativistic bosons and fermions coupled with a constant quartic tensor in zero-, one- and two-dimensional space, by limiting our investigations to the super-renormalizable models. This offers a unified perspective on classical constructive results, highlighting the usefulness of the LVE as a modern tool to address these questions and to tackle more challenging models in higher dimensions. Finally, we investigate the large N and massless limits along with quenching for fermions in one dimension. In particular, this work establishes the Borel summability of the Sachdev-Ye-Kitaev model.

Mots clés: model: vector; field theory: vector; boson: relativistic; fermion: vector; analytic properties; nonrelativistic; expansion 1/N; constructive; statistics; kinetic; O(N)

Domaines: Physique des Hautes Energies - Théorie [hep-th]; Physique Générale [physics.gen-ph]; Physique mathématique [math-ph]

Harold Erbin, Vincent Lahoche, Mohamed Tamaazousti. Constructive expansion for vector fields theories. I. Quartic models in low dimensions. Journal of Mathematical Physics, 2021, 62 (4), pp.043501. ⟨10.1063/5.0038599⟩. ⟨hal-02129902⟩