A random matrix model with non-pairwise contracted indices

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.

arXiv comment42 pages, many figures

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Cited by in corpus (7)

• Numerical and analytical analyses of a matrix model with non-pairwise contracted indices
• Phases of a matrix model with non-pairwise index contractions
• Splitting-merging transitions in tensor-vectors systems in exact large-$N$ limits
• Symmetry enhancement in a two-logarithm matrix model and the canonical tensor model
• Phase profile of the wave function of canonical tensor model and emergence of large spacetimes
• Emergence of Lie group symmetric classical spacetimes in canonical tensor model
• Counting tensor rank decompositions