From noncommutative geometry to random matrix theory

Author:

Hessam Hamed,Khalkhali MasoudORCID,Pagliaroli Nathan,Verhoeven Luuk S

Abstract

Abstract We review recent progress in the analytic study of random matrix models suggested by noncommutative geometry. One considers fuzzy spectral triples where the space of possible Dirac operators is assigned a probability distribution. These ensembles of Dirac operators are constructed as toy models of Euclidean quantum gravity on finite noncommutative spaces and display many interesting properties. The ensembles exhibit spectral phase transitions, and near these phase transitions they show manifold-like behavior. In certain cases one can recover Liouville quantum gravity in the double scaling limit. We highlight examples where bootstrap techniques, Coulomb gas methods, and Topological Recursion are applicable.

Publisher

IOP Publishing

Subject

General Physics and Astronomy,Mathematical Physics,Modeling and Simulation,Statistics and Probability,Statistical and Nonlinear Physics

Reference90 articles.

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1. Double scaling limits of Dirac ensembles and Liouville quantum gravity;Journal of Physics A: Mathematical and Theoretical;2023-05-09

2. Computing the spectral action for fuzzy geometries: from random noncommutative geometry to bi-tracial multimatrix models;Journal of Noncommutative Geometry;2022-12-29

3. BV quantization of dynamical fuzzy spectral triples;Journal of Physics A: Mathematical and Theoretical;2022-11-25

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