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 Poincaré] 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.

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

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• A Lorentzian version of the non-commutative geometry of the standard model of particle physics
• Spectral truncations in noncommutative geometry and operator systems
• Reconstruction of manifolds in noncommutative geometry
• Particle Physics from Almost Commutative Spacetimes
• A universal Dirac operator and noncommutative spin bundles over fuzzy complex projective spaces
• Higher spin gauge theory on fuzzy $S_N^4$
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Cited by in corpus (6)

• From Noncommutative Geometry to Random Matrix Theory
• No Ward-Takahashi identity violation for an Abelian tensorial group field theories with closure constraint
• Dirac operators for matrix algebras converging to coadjoint orbits
• BV quantization of dynamical fuzzy spectral triples
• The loop equations for noncommutative geometries on quivers
• A ribbon graph derivation of the algebra of functional renormalization for random multi-matrices with multi-trace interactions