# A random matrix model with non-pairwise contracted indices

## TL;DR

This paper introduces a random matrix model with complex index contractions, analyzes its dominant graph structures, and applies findings to a quantum gravity-related tensor model, supporting its quantum probabilistic interpretation.

## Contribution

It develops a detailed diagrammatic analysis of a novel random matrix model with mixed index contractions and explores its implications for tensor models in quantum gravity.

## Key findings

- Identification of dominant graph structures in large dimension limits
- Application to a tensor model relevant to quantum gravity
- Support for the quantum probabilistic interpretation of the tensor model

## Abstract

We consider a random matrix model with both pairwise and non-pairwise contracted indices. The partition function of the matrix model is similar to that appearing in some replicated systems with random tensor couplings, such as the p-spin spherical model for the spin glass. We analyze the model using Feynman diagrammatic expansions, and provide an exhaustive characterization of the graphs which dominate when the dimensions of the pairwise and (or) non-pairwise contracted indices are large. We apply this to investigate the properties of the wave function of a toy model closely related to a tensor model in the Hamilton formalism, which is studied in a quantum gravity context, and obtain a result in favor of the consistency of the quantum probabilistic interpretation of this tensor model.