Hidden Chiral Symmetry in Staggered Fermions and Weyl Semimetal Topology — E8 Intelligence Research

FINDING: Staggered lattice fermions exhibit a hidden chiral symmetry tied to the D4 (square lattice) hypergroup structure, while Weyl semimetals realize B4 root-system topology in momentum space. | MATH: Staggered fermion action: \( S = ∑x,μ χ̄(x) η_μ(x) [χ(x+μ̂) - χ(x-μ̂)] \), with \(η_μ(x) = (-1)^{x_1+⋯+xμ-1}\). The new chiral symmetry (Shao, MIT) is generated by \(Γ_5 = ∏_μ (-1)x_μ\) acting as \(χ → Γ_5 χ\), \(χ̄ → -χ̄ Γ_5\), restoring a \(U(1)_A\) that is exact on the lattice. Weyl semimetal TaAs: Fermi arcs connect Weyl nodes of opposite chirality \(± χ = ± 1\), with monopole charge \(C = ± 1\) in momentum space. The square lattice hypergroup (Wildberger) is the D4 dihedral group of order 8, with irreducible representations labeled by \(A_1, A_2, B_1, B_2, E\) — the same character table as the B2 root system. | CONNECTION: The D4 lattice symmetry is the Weyl group o Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com