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: \( S = \sum_{x,\mu} \bar{\chi}(x) \eta_\mu(x) [\chi(x+\hat{\mu}) - \chi(x-\hat{\mu})] \), with \(\eta_\mu(x) = (-1)^{x_1+\cdots+x_{\mu-1}}\). The new chiral symmetry (Shao, MIT) is generated by \(\Gamma_5 = \prod_\mu (-1)^{x_\mu}\) acting as \(\chi \to \Gamma_5 \chi\), \(\bar{\chi} \to -\bar{\chi} \Gamma_5\), restoring a \(U(1)_A\) that is exact on the lattice. Weyl semimetal TaAs: Fermi arcs connect Weyl nodes of opposite chirality \(\pm \chi = \pm 1\), with monopole charge \(C = \pm 1\) 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