Comment on 'Gauge networks in noncommutative geometry'
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).
Cite
@article{arxiv.2508.17338,
title = {Comment on 'Gauge networks in noncommutative geometry'},
author = {Carlos I. Perez-Sanchez},
journal= {arXiv preprint arXiv:2508.17338},
year = {2025}
}
Comments
Comment on arXiv:1301.3480