图论确定晶格化理论空间模型中的无质量模
Graph-theoretic determination of massless modes in latticized theory-space models
AI总结：
本文提出图论方法分析晶格化理论空间模型中费米子质量谱，通过将费米子质量项映射为二分图，确定无质量模数量及波函数支持区域，方法独立于模型参数。
摘要：
本文介绍了一种图论方法，用于分析晶格化理论空间模型中的费米子质量谱，包括源自维度解构的链模型。费米子质量项被映射为二分图，其中场作为顶点，非零质量项作为边。无质量模的数量由关联图的最大匹配的基数确定。此外，这些模的波函数支持受限于从暴露或未匹配顶点可达的偶长度最大匹配交替路径，由Dulmage-Mendelsohn分解表征。这些结果仅依赖于晶格化理论空间的拓扑结构，与模型参数无关。该方法使系统构造具有指定无质量模数量和局部化性质的晶格化模型成为可能。
英文摘要：
A graph-theoretic method is introduced for analyzing 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 characterized 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 localization properties of massless modes.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
