Abstract
Abstract
In this paper we study ensembles of finite real spectral triples equipped with a path integral over the space of possible Dirac operators. In the noncommutative geometric setting of spectral triples, Dirac operators take the center stage as a replacement for a metric on a manifold. Thus, this path integral serves as a noncommutative analogue of integration over metrics, a key feature of a theory of quantum gravity. From these integrals in the so-called double scaling limit we derive critical exponents of minimal models from Liouville conformal field theory coupled with gravity. Additionally, the asymptotics of the partition function of these models satisfy differential equations such as Painlevé I, as a reduction of the KDV hierarchy, which is predicted by conformal field theory. This is all proven using well-established and rigorous techniques from random matrix theory.
Subject
General Physics and Astronomy,Mathematical Physics,Modeling and Simulation,Statistics and Probability,Statistical and Nonlinear Physics
Reference39 articles.
1. Generalized multicritical one-matrix models;Ambjorn;Nucl. Phys. B,2016
2. Matrix integrals & finite holography;Anninos;J. High Energy Phys.,2021
3. Random finite noncommutative geometries and topological recursion;Azarfar,2019
4. Matrix geometries and fuzzy spaces as finite spectral triples;Barrett;J. Math. Phys.,2015
5. Monte Carlo simulations of random non-commutative geometries;Barrett;J. Phys. A: Math. Theor.,2016
Cited by
1 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献