Notes on tensor models and tensor field theories

  • Razvan G. Gurau

    Ecole Polytechnique, Palaiseau, France; Perimeter Institute for Theoretical Physics, Waterloo, Canada
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Abstract

Tensor models and tensor field theories admit a expansion and a melonic large limit which is simpler than the planar limit of random matrices and richer than the large 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 expansion, as well as recent developments. These notes are loosely bases on four lectures given at the Journées de physique mathématique Lyon 2019: Random tensors and SYK models.

Cite this article

Razvan G. Gurau, Notes on tensor models and tensor field theories. Ann. Inst. Henri Poincaré Comb. Phys. Interact. 9 (2022), no. 1, pp. 159–218

DOI 10.4171/AIHPD/117