On multimatrix models motivated by random noncommutative geometry II: A Yang-Mills-Higgs matrix model
Abstract
We continue the study of fuzzy geometries inside Connes' spectral formalism and their relation to multimatrix models. In this companion paper to [arXiv 2007:10914, Ann. Henri Poincar\'e] 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 employs only finite dimensional algebras which we call gauge matrix spectral triples. 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 mirror those of the Yang-Mills--Higgs theory on a smooth manifold.
Keywords
Cite
@article{arxiv.2105.01025,
title = {On multimatrix models motivated by random noncommutative geometry II: A Yang-Mills-Higgs matrix model},
author = {Carlos I. Perez-Sanchez},
journal= {arXiv preprint arXiv:2105.01025},
year = {2022}
}
Comments
36 pages + appendix and references, some tables, three figures. V3. Corrected and slightly more general main result, updated references. V2: Discussion on gauge transformations added; re-defined field strength matrix (by incorporation of commutators of matrices that mimic the partial derivatives) leads now to a neat result