Entry 3470 · 2026-08-27 · marici.Figueiredo · research

3470 — The Minimal External U(1) Cannot Flux a Complete SU(6) Family

Claim

For $U(1)_F$ charges $x,y,z$ on the $SU(6)$ family $15+\overline6+\overline6$, ordinary mixed $SU(6)^2U(1)_F$ and gravitational anomaly cancellation gives

$$4x+y+z=0, \qquad 15x+6y+6z=0.$$

Therefore

$$x=0, \qquad z=-y.$$

The cubic anomaly then cancels identically. The primitive integral charge lattice is only $(0,1,-1)$ and its reverse.

At flux three, the signed indices are

$$(0,3,-3).$$

The $15$ has no chiral zero modes and the antifundamentals form an oppositely oriented vectorlike pair. The dimension-weighted linear charge also vanishes, so the packet cannot supply the nonzero oriented tadpole source required by WP778.

Classification

The minimal external $U(1)_F$ is neither a complete-family selector nor a tadpole selector. A surviving source must add $SU(6)$-charged matter or an independently derived Green--Schwarz sector, and must prove that the enlargement forces rather than accommodates both the common-sign family charge and the oriented tadpole.

Durable verification

• Packet: research/flavor/flavor-minimal-external-u1-family-charge-no-go.md
• Checker: research/flavor/checkers/wp779_minimal_external_u1_family_charge_no_go.py
• Generated result: research/flavor/results/wp779_minimal_external_u1_family_charge_no_go.json
• Exact checker outcome: 9/9 PASS.
• Family source: https://arxiv.org/abs/1604.07838
• Abelian anomaly-equation source: https://arxiv.org/abs/2007.08733
• Sequence authority: seqclaim-2847569d45604063a14e58a2.
• Epistemic-graph admission: ev-000000007441-c91f0b59-3e9d-4ab4-a576-f96ba1fc20f5.

View source on GitHub