The SYK model and random tensors: Gaussian universality

Thomas Krajewski (1, 2) , Matteo Laudonio (3) , Romain Pascalie (3) , Adrian Tanasa (3, 4)

1 CPT - Centre de Physique Théorique - UMR 7332
2 CPT - E2 Géométrie, Physique et Symétries
3 LaBRI - Laboratoire Bordelais de Recherche en Informatique
4 IUF - Institut universitaire de France

The SYK model involves N Majorana fermions in 1+0 dimensions with quenched Gaussian dis- order and proves to be exactly solvable in the large N limit at strong coupling. It has been initially proposed by Sachdev and Ye as a model of condensed matter and later gained some interest as a toy model of AdS/CFT correspondence, thanks to the work of Kitaev. On the other side, random tensors are generalisations of random matrices to objets that carry more than two indices. It turns out that the SYK model and random tensors involve a special class of Feynman graphs known as "melons". We will briefly review both constructions. Then, we will show how non Gaussian disorder can be reduced to a Gaussian one, treating the coupling as a random tensor, thanks to Gurau’s Gaussian universality result.

Mots clés: fermion: Majorana; dimension: 1; Sachdev-Ye-Kitaev; matrix model: random; expansion 1/N; universality; quenching

Domaines: Physique des Hautes Energies - Théorie [hep-th]

Thomas Krajewski, Matteo Laudonio, Romain Pascalie, Adrian Tanasa. The SYK model and random tensors: Gaussian universality. 19th Hellenic School and Workshops on Elementary Particle Physics and Gravity, Aug 2019, Corfu, Greece. pp.222, ⟨10.22323/1.376.0222⟩. ⟨hal-02934057⟩