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arXiv · 2508.17338

Comment on 'Gauge networks in noncommutative geometry'

Carlos I. Perez-Sanchez
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Abstract

The article (Gauge networks in noncommutative geometry, J. Geom. Phys. 75 : 71--91, 2014) that motivates this comment provides, in particular, one answer to the following natural question: what is noncommutative geometry on a lattice? In the context of spectral triples, Marcolli and van Suijlekom define in op. cit. a Dirac operator on the lattice and identify the corresponding Spectral Action with the lattice Yang-Mills--Higgs system. In this comment we show that the continuum limit of this theory is the Yang-Mills action functional, without a Higgs scalar. R\'esum\'e: Qu'est-ce que la g\'eom\'etrie non-commutative sur r\'eseau ? \`A cette question l'article ici comment\'e (Gauge networks in noncommutative geometry, J. Geom. Phys. 75 : 71--91, 2014) apporte une des r\'eponses possibles. Marcolli et van Suijlekom, travaillant dans le contexte des triplets spectraux, y construisent un op\'erateur de type Dirac pour le r\'eseau et d\'erivent une th\'eorie sur r\'eseau de type Yang-Mills--Higgs \`a partir de l'Action Spectrale. Ce commentaire montre que la limite continue de ce mod\`ele est la th\'eorie pure de Yang-Mills (sans aucun Higgs).

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Carlos I. Perez-Sanchez. 2025-08-24. Comment on 'Gauge networks in noncommutative geometry'. https://arxiv.org/abs/2508.17338

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