Taste-splitting mass and edge modes in $3+1$ D staggered fermions

[2604.02078] Taste-splitting mass and edge modes in $3+1$ D staggered fermions Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search High Energy Physics - Lattice arXiv:2604.02078 (hep-lat) [Submitted on 2 Apr 2026 ( v1 ), last revised 15 Aug 2026 (this version, v4)] Title: Taste-splitting mass and edge modes in $3+1$ D staggered fermions Authors: Tatsuhiro Misumi , Tetsuya Onogi , Tatsuya Yamaoka View a PDF of the paper titled Taste-splitting mass and edge modes in $3+1$ D staggered fermions, by Tatsuhiro Misumi and 2 other authors View PDF HTML (experimental) Abstract: We investigate the symmetry structure of the $3+1$ D staggered fermion Hamiltonian and its implications for anomalies. Since the spin and flavor degrees of freedom of Dirac fermions are distributed over the lattice, in addition to the standard on-site mass term, the staggered fermion system also admits one-, two-, and three-link bilinear terms within a unit cube as local, charge conserving mass terms with different spin and flavor dependence. We identify the spin flavor structures of all those bilinear mass terms and determine the symmetries preserved by each of them. Among them, one of the one-link mass terms preserves a larger residual symmetry associated with conserved charges that generate the Onsager algebra. Motivated by this structure, we consider a kink profile of the one-link mass and analyze the resulting domain-wall system. In the low-energy limit, the $3+1$ D bulk becomes gapped, while two-flavor massless Dirac fermions appear as localized modes on the $2+1$ D domain wall. We show that the bulk conserved charges act on the wall as generators of a flavor $\mathrm{SU}(2)$ symmetry, and that no symmetric mass gap is allowed for the boundary theory when this $\mathrm{SU}(2)$ symmetry and space reflection symmetry are both imposed. This realizes the parity anomaly of the boundary theory and shows that the boundary flavor symmetry and anomaly descend from the ultraviolet staggered-fermion Hamiltonian rather than emerging only in the infrared. Comments: 28 pages, 2 figures, v2: minor corrections, v3: Appendix added presenting evidence for emanant SU(2) symmetry on the edge, v4: minor corrections Subjects: High Energy Physics - Lattice (hep-lat) ; Strongly Correlated Electrons (cond-mat.str-el); High Energy Physics - Theory (hep-th) Report number: OU-HET-1306 Cite as: arXiv:2604.02078 [hep-lat] (or arXiv:2604.02078v4 [hep-lat] for this version) https://doi.org/10.48550/arXiv.2604.02078 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Tatsuya Yamaoka [ view email ] [v1] Thu, 2 Apr 2026 14:10:06 UTC (45 KB) [v2] Mon, 11 May 2026 09:27:38 UTC (45 KB) [v3] Thu, 9 Jul 2026 14:23:35 UTC (46 KB) [v4] Sat, 15 Aug 2026 06:45:37 UTC (47 KB) Full-text links: Access Paper: View a PDF of the paper titled Taste-splitting mass and edge modes in $3+1$ D staggered fermions, by Tatsuhiro Misumi and 2 other authors View PDF HTML (experimental) TeX Source view license Current browse context: hep-lat < prev | next > new | recent | 2026-04 Change to browse by: cond-mat cond-mat.str-el hep-th References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... 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