Diagrammatic proof of the large $N$ melonic dominance in the SYK model

Valentin Bonzom (1) , Victor Nador (2) , Adrian Tanasa (2)

1 LIPN - Laboratoire d'Informatique de Paris-Nord
2 LaBRI - Laboratoire Bordelais de Recherche en Informatique

A crucial result on the celebrated Sachdev–Ye–Kitaev model is that its large N limit is dominated by melonic graphs. In this letter, we offer a rigorous, diagrammatic proof of that result by direct, combinatorial analysis of its Feynman graphs.

Mots clés: Sachdev-Ye-Kitaev model; melonic graphs; tensor models; Sachdev–Ye–Kitaev model; Melonic graphs; Tensor models; Sachdev-Ye-Kitaev; Feynman graph; model: tensor; expansion 1/N; AdS/CFT correspondence; condensed matter; random; two-point function

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

Valentin Bonzom, Victor Nador, Adrian Tanasa. Diagrammatic proof of the large $N$ melonic dominance in the SYK model. Lett.Math.Phys., 2019, 109 (12), pp.2611-2624. ⟨10.1007/s11005-019-01194-8⟩. ⟨hal-01871799⟩