Coloured combinatorial maps and quartic bi-tracial 2-matrix ensembles from noncommutative geometry
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| Format: | Preprint |
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2023
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| _version_ | 1866914884313153536 |
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| author | Khalkhali, Masoud Pagliaroli, Nathan |
| author_facet | Khalkhali, Masoud Pagliaroli, Nathan |
| contents | We compute the first twenty moments of three convergent quartic bi-tracial 2-matrix ensembles in the large $N$ limit. These ensembles are toy models for Euclidean quantum gravity originally proposed by John Barrett and collaborators. A perturbative solution is found for the first twenty moments using the Schwinger-Dyson equations and properties of certain bi-colored unstable maps associated to the model. We then apply a result of Guionnet et al. to show that the perturbative and convergent solution coincide for a small neighbourhood of the coupling constants. For each model we compute an explicit expression for the free energy, critical points, and critical exponents in the large $N$ limit. In particular, the string susceptibility is found to be $γ=1/2$, hinting that the associated universality class of the model is the continuous random tree. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2312_10530 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Coloured combinatorial maps and quartic bi-tracial 2-matrix ensembles from noncommutative geometry Khalkhali, Masoud Pagliaroli, Nathan Mathematical Physics High Energy Physics - Theory Operator Algebras Quantum Algebra We compute the first twenty moments of three convergent quartic bi-tracial 2-matrix ensembles in the large $N$ limit. These ensembles are toy models for Euclidean quantum gravity originally proposed by John Barrett and collaborators. A perturbative solution is found for the first twenty moments using the Schwinger-Dyson equations and properties of certain bi-colored unstable maps associated to the model. We then apply a result of Guionnet et al. to show that the perturbative and convergent solution coincide for a small neighbourhood of the coupling constants. For each model we compute an explicit expression for the free energy, critical points, and critical exponents in the large $N$ limit. In particular, the string susceptibility is found to be $γ=1/2$, hinting that the associated universality class of the model is the continuous random tree. |
| title | Coloured combinatorial maps and quartic bi-tracial 2-matrix ensembles from noncommutative geometry |
| topic | Mathematical Physics High Energy Physics - Theory Operator Algebras Quantum Algebra |
| url | https://arxiv.org/abs/2312.10530 |