Carlos I. Perez-Sanchez
May 03, 2021
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, 2021] 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. 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.
Keywords:finite almost-commutative manifolds, noncommutative geometry, Gauge theory, random noncommutative geometry, quantum gravity