The Tensor Track V: Holographic Tensors

TL;DR

This paper reviews tensor models related to the NAdS$_2$/NCFT$_1$ holographic duality, focusing on quantum mechanical tensor models, their features, extensions, and comparisons with the SYK model.

Contribution

It provides a comprehensive overview of tensor models in holography, including new extensions and proposals for higher-dimensional generalizations and symmetry breaking.

Findings

Tensor models exhibit features similar to the SYK model.

Extensions include large D limit and symmetry breaking.

Proposals for higher-dimensional tensor models are discussed.

Abstract

We review the fast developing subject of tensor models for the NAdS$_2$/NCFT$_1$ holographic correspondence. We include a brief review of the Sachdev-Ye-Kitaev (SYK) model and then focus on the associated quantum mechanical tensor models (GW and CTKT). We examine their main features and how they compare with SYK. To end, we discuss different extensions: the large $D$ limit of matrix-tensor models, the large $N$ expansion of symmetric/antisymmetric tensors, the use of probes, the construction of a bilocal action for tensors, some attempts to extend the above models to higher dimensions and a proposal to break the tensor symmetry.