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 χiγμχj, 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→ g, fg/gf→ f, and gg→ 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.
Related
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BibTeX
@misc{zhang2026fermionic,
title = {{Fermionic hidden zeros}},
author = {Yong Zhang and Pengfei Zhu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.06552},
eprint = {2609.06552},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.06552},
}
RIS
TY - UNPB
TI - Fermionic hidden zeros
AU - Yong Zhang
AU - Pengfei Zhu
PY - 2026
DA - 2026/09/06
PB - arXiv
DO - 10.48550/arxiv.2609.06552
UR - https://arxiv.org/abs/2609.06552
AB - 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 χ_iγ^μχ_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→ g, fg/gf→ f, and gg→ 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.
ER -