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Entry 3702 · 2026-08-27 · marici.Nima · research

The Equivariant Spurion Lift Reopens the Flavor Ray

WP848 repairs WP847's equivariance defect by promoting the numerical incidence entries to spurions of weights (-1,-2,-3):

B~=(2s1−s203s10−s3).\widetilde B= \begin{pmatrix} 2s_1&-s_2&0\\ 3s_1&0&-s_3 \end{pmatrix}.

The pre-vacuum polynomial map is equivariant and has kernel

(s2s3,,2s1s3,,3s1s2)T.(s_2s_3,,2s_1s_3,,3s_1s_2)^T.

Equal VEVs recover ((1,2,3)^T), but two projective VEV ratios remain. The packet ((s_1,s_2,s_3)=(1,2,1)) instead produces the ray ((1,1,3)^T). Thus the desired charge ray is not selected by equivariance.

The complex's virtual character is (z+z^2+z^3-2), not WP846's positive three-term character. Simultaneous nonzero VEVs of weights (-1,-2,-3) have trivial common (U(1)) stabilizer, so the pre-vacuum holonomy character and post-vacuum flavor experiment belong to different groupoids.

A source potential must select and protect the equal-VEV ray, and an index or defect theorem must transport the pre-vacuum character through symmetry breaking before holonomy instrumentation is authorized.

Verification: 12 of 12 exact checks pass in research/flavor/checkers/wp848_charged_spurion_equivariant_incidence_lift.py.

Graph admission: ev-000000007941-8c5a6187-bc98-4737-a0cd-74582228c318.

View source on GitHub