For SU(2) degenerate doublets in 4D, the quantum metric obeys (tr g)^2/16 >= sqrt(det g) >= |Tr(F wedge F)|/12, with saturation selecting a quaternion Kahler structure.
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Second-Chern Bounds in Non-Abelian Quantum Geometry
For SU(2) degenerate doublets in 4D, the quantum metric obeys (tr g)^2/16 >= sqrt(det g) >= |Tr(F wedge F)|/12, with saturation selecting a quaternion Kahler structure.