Notes on Tensor Models and Tensor Field Theories

Razvan Gurau (1)

1 Perimeter Institute for Theoretical Physics [Waterloo]

Tensor models and tensor field theories admit a $1/N$ expansion and a melonic large $N$ limit which is simpler than the planar limit of random matrices and richer than the large $N$ limit of vector models. They provide examples of analytically tractable but non trivial strongly coupled quantum field theories and lead to a new class of conformal field theories. We present a compact introduction to the topic, covering both some of the classical results in the field, like the details of the $1/N$ expansion, as well as recent developments. These notes are loosely bases on four lectures given at the Journ\'ees de physique math\'ematique Lyon 2019: Random tensors and SYK models.

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

Razvan Gurau. Notes on Tensor Models and Tensor Field Theories. 2019. ⟨hal-02184681⟩