Abstract
AbstractWe continue the study of fuzzy geometries inside Connes’ spectral formalism and their relation to multimatrix models. In this companion paper to Pérez-Sánchez (Ann Henri Poincaré 22:3095–3148, 2021, arXiv:2007.10914), we propose a gauge theory setting based on noncommutative geometry, which—just as the traditional formulation in terms of almost-commutative manifolds—has the ability to also accommodate a Higgs field. However, in contrast to ‘almost-commutative manifolds’, the present framework, which we call gauge matrix spectral triples, employs only finite-dimensional algebras. In a path-integral quantization approach to the Spectral Action, this allows to state Yang–Mills–Higgs theory (on four-dimensional Euclidean fuzzy space) as an explicit random multimatrix model obtained here, whose matrix fields exactly mirror those of the Yang–Mills–Higgs theory on a smooth manifold.
Funder
fundacja na rzecz nauki polskiej
European Research Council
Deutsche Forschungsgemeinschaft
Publisher
Springer Science and Business Media LLC
Subject
Mathematical Physics,Nuclear and High Energy Physics,Statistical and Nonlinear Physics
Reference58 articles.
1. Azarfar, S., Khalkhali, M.: Random Finite Noncommutative Geometries and Topological Recursion (2019). arXiv:1906.09362
2. Barrett, J.W.: A Lorentzian version of the non-commutative geometry of the standard model of particle physics. J. Math. Phys. 48, 012303 (2007)
3. Barrett, J.W.: Matrix geometries and fuzzy spaces as finite spectral triples. J. Math. Phys. 56(8), 082301 (2015)
4. Benedetti, D., Carrozza, S., Toriumi, R., Valette, G.: Multiple Scaling Limits of $${\text{U}} (N)^2 \times {\text{ O }} (D)$$ Multi-Matrix Models (2020). arXiv:2003.02100
5. Barrett, J.W., Druce, P., Glaser, L.: Spectral estimators for finite non-commutative geometries. J. Phys. A 52(27), 275203 (2019)
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