Fermionic hidden zeros

Abstract

We uncover and prove a general class of hidden zeros in tree-level amplitudes with massless fermions. For arbitrary even numbers and arbitrary arrangements of massless real adjoint fermions and gluons, color-ordered gauge-theory amplitudes in $D=4,6,10$ vanish on general rectangular kinematic loci supplemented by species-dependent bridge conditions. The fermion--fermion bridge is governed simply by the vector current $\chi_i\gamma^\mu\chi_j$, while mixed and gluonic bridges are fixed by the corresponding gauge-covariant contractions. A worldsheet analysis proves the result at arbitrary multiplicity and traces its universality to the local fusion channels $ff\to g$, $fg/gf\to f$, and $gg\to g$, with no new primitive bridge structures appearing at higher fermion multiplicity. The same mechanism extends to ten-dimensional amplitudes with gravitons and arbitrary even numbers of gravitinos in factorized gamma-traceless polarizations, and to single-trace Einstein-Yang-Mills amplitudes with adjoint gluinos and gravitons. These results expose a finite local structure underlying fermionic hidden zeros across gauge and gravitational amplitudes.