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Peer-reviewedCC BY 4.0Journal of High Energy Physics

Graph-theoretic determination of massless modes in latticized theory-space models

  • Ketan M. Patel1
  1. 1Physical Research Laboratory
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Abstract

A bstract : A graph-theoretic method is introduced for analysing fermion mass spectra in latticized theory-space models, including chain models arising from dimensional deconstruction. Fermion mass terms are mapped to bipartite graphs, with fields as vertices and nonvanishing mass terms as edges. The number of massless modes is shown to be fixed by the cardinality of a maximum matching of the associated graph. Moreover, the wave-function support of these modes is restricted to fields reachable from exposed or unmatched vertices by even-length maximum-matching-alternating paths, as characterised by the Dulmage-Mendelsohn decomposition. These results depend only on the topology of latticized theory space and are independent of model parameters. The method enables a systematic construction of latticized models with prescribed numbers and localisation properties of massless modes.

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Cite

BibTeXRIS
BibTeX
@article{patel2026graphtheoretic,
  title = {{Graph-theoretic determination of massless modes in latticized theory-space models}},
  author = {Ketan M. Patel},
  journal = {Journal of High Energy Physics},
  year = {2026},
  month = oct,
  doi = {10.1007/jhep10(2026)201},
  url = {https://link.springer.com/article/10.1007/JHEP10(2026)201},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Graph-theoretic determination of massless modes in latticized theory-space models
AU  - Ketan M. Patel
PY  - 2026
DA  - 2026/10/19
JO  - Journal of High Energy Physics
DO  - 10.1007/jhep10(2026)201
UR  - https://link.springer.com/article/10.1007/JHEP10(2026)201
AB  - A bstract : A graph-theoretic method is introduced for analysing fermion mass spectra in latticized theory-space models, including chain models arising from dimensional deconstruction. Fermion mass terms are mapped to bipartite graphs, with fields as vertices and nonvanishing mass terms as edges. The number of massless modes is shown to be fixed by the cardinality of a maximum matching of the associated graph. Moreover, the wave-function support of these modes is restricted to fields reachable from exposed or unmatched vertices by even-length maximum-matching-alternating paths, as characterised by the Dulmage-Mendelsohn decomposition. These results depend only on the topology of latticized theory space and are independent of model parameters. The method enables a systematic construction of latticized models with prescribed numbers and localisation properties of massless modes.
SN  - 1029-8479
ER  -