# Random Matrices and Holographic Tensor Models

## TL;DR

This paper investigates the spectral properties of holographic tensor models, revealing their connection to random matrix ensembles, symmetries, and periodicity, thus deepening understanding of their quantum chaotic behavior.

## Contribution

It extends the analysis of holographic tensor models by exploring uncolored cases, identifying symmetries, and linking their spectral features to specific random matrix ensembles.

## Key findings

- Density of states and spectral statistics match colored models
- Identification of spectral mirror and time-reversal symmetries
- Connection to Andreev ensembles and Bott periodicity

## Abstract

We further explore the connection between holographic $O(n)$ tensor models and random matrices. First, we consider the simplest non-trivial uncolored tensor model and show that the results for the density of states, level spacing and spectral form factor are qualitatively identical to the colored case studied in arXiv:1612.06330. We also explain an overall 16-fold degeneracy by identifying various symmetries, some of which were unavailable in SYK and the colored models. Secondly, and perhaps more interestingly, we systematically identify the Spectral Mirror Symmetry and the Time-Reversal Symmetry of both the colored and uncolored models for all values of $n$, and use them to identify the Andreev ensembles that control their random matrix behavior. We find that the ensembles that arise exhibit a refined version of Bott periodicity in $n$.