# On multimatrix models motivated by random noncommutative geometry II: A Yang-Mills-Higgs matrix model

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