Formal Naive Dirac Operators and Graph Topology

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Détails bibliographiques
Auteur principal:	von Hippel, G. M.
Format:	Preprint
Publié:	2026
Sujets:	High Energy Physics - Lattice Mathematical Physics
Accès en ligne:	Acceder al recurso
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author	von Hippel, G. M.
author_facet	von Hippel, G. M.
contents	Motivated by a recent conjecture of Misumi and Yumoto relating the number of zero modes of lattice Dirac operators to the sum of the Betti numbers of the underlying spacetime manifold, we study formal naive Dirac operators on a class of graphs admitting such in terms of their zero modes. Our main result is that for graphs on which translations commute, the conjecture of Misumi and Yumoto can be shown and indeed can be strengthened to obtain bounds on the individual Betti numbers rather than merely on their sum. Interpretations of the zero modes in terms of graph quotients and of the representation theory of abelian groups are given, and connections with a homology theory for such graphs are highlighted.
format	Preprint
id	arxiv_https___arxiv_org_abs_2601_18576
institution	arXiv
publishDate	2026
record_format	arxiv
spellingShingle	Formal Naive Dirac Operators and Graph Topology von Hippel, G. M. High Energy Physics - Lattice Mathematical Physics Motivated by a recent conjecture of Misumi and Yumoto relating the number of zero modes of lattice Dirac operators to the sum of the Betti numbers of the underlying spacetime manifold, we study formal naive Dirac operators on a class of graphs admitting such in terms of their zero modes. Our main result is that for graphs on which translations commute, the conjecture of Misumi and Yumoto can be shown and indeed can be strengthened to obtain bounds on the individual Betti numbers rather than merely on their sum. Interpretations of the zero modes in terms of graph quotients and of the representation theory of abelian groups are given, and connections with a homology theory for such graphs are highlighted.
title	Formal Naive Dirac Operators and Graph Topology
topic	High Energy Physics - Lattice Mathematical Physics
url	https://arxiv.org/abs/2601.18576

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