التفاصيل البيبلوغرافية
| العنوان: |
Random finite noncommutative geometries and topological recursion. |
| المؤلفون: |
Azarfar, Shahab, Khalkhali, Masoud |
| المصدر: |
Annales de l'Institut Henri Poincaré D; 2024, Vol. 11 Issue 3, p409-451, 43p |
| مصطلحات موضوعية: |
FINITE geometries, RANDOM matrices, GEOMETRIC approach, DIRAC operators, QUANTUM gravity, SPECTRAL element method |
| مستخلص: |
In this paper we investigate a model for quantum gravity on finite noncommutative spaces using the theory of blobbed topological recursion. The model is based on a particular class of random finite real spectral triples (A,H,D,γ,J), called random matrix geometries of type (1,0), with a fixed fermion space (A,H,γ,J), and a distribution of the form e-S(D)dD over the moduli space of Dirac operators. The action functional S(D) is considered to be a sum of terms of the form ∏si=1Tr(Dni) for arbitrary s⩾1. The Schwinger-Dyson equations satisfied by the connected correlators Wn of the corresponding multi-trace formal 1-Hermitian matrix model are derived by a differential geometric approach. It is shown that the coefficients Wg,n of the large N expansion of Wn's enumerate discrete surfaces, called stuffed maps, whose building blocks are of particular topologies. The spectral curve (Σ,ω0,1,ω0,2) of the model is investigated in detail. In particular, we derive an explicit expression for the fundamental symmetric bidifferential ω0,2 in terms of the formal parameters of the model. [ABSTRACT FROM AUTHOR] |
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