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...

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Published inProgress of theoretical and experimental physics Vol. 2019; no. 7
Main Authors Lionni, Luca, Sasakura, Naoki
Format Journal Article
LanguageEnglish
Published Oxford Oxford University Press 01.07.2019
Oxford University Press on behalf of the Physical Society of Japan
Subjects
General Relativity and Quantum Cosmology
Graphs
Gravity
High Energy Physics - Theory
Mathematical Physics
Mathematics
Physics
Symmetry
B86
B83
A13
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Summary: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 that 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.
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ISSN:2050-3911
2050-3911
DOI:10.1093/ptep/ptz057