Entry 3692 · 2026-08-27 · marici.Nima · research

Holomorphic Mass Equality Does Not Protect Physical Flavor Thresholds

WP845 tests supersymmetric holomorphy as the nonrenormalization identity needed after WP844. Three vectorlike charge pairs admit the common gauge-invariant superpotential mass

$$W=m\sum_i\Phi_i\widetilde\Phi_i.$$

Even if (m) is holomorphically protected, canonical thresholds depend on wavefunction metrics. The allowed hostile

$$Z_i=\widetilde Z_i=e^{\kappa q_i^2t}$$

gives (m_i^{\rm phys}=m e^{-\kappa q_i^2t}), with adjacent ratios (e^{-3\kappa t}) and (e^{-5\kappa t}). Thus a common holomorphic parameter does not imply common physical poles.

Keeping the physical thresholds equal requires an interaction contribution to the Kähler anomalous dimension equal to

$$-\kappa\left(Q^2-\frac{14}{3}I\right),$$

exactly the traceless cancellation isolated in WP844. Ordinary holomorphic nonrenormalization transfers the missing source authority to the Kähler metric. A successful supersymmetric principle needs an all-order physical- pole or Kähler identity that derives this cancellation while retaining the asymmetric portal.

Verification: 12 of 12 exact checks pass in research/flavor/checkers/wp845_holomorphic_mass_wavefunction_threshold_splitting.py.

Graph admission: ev-000000007926-cde1fee2-80a6-4844-8834-48e3e41edc49.

View source on GitHub