Mathematical analysis reveals a deformation-invariant Pontryagin defect on Calabi-Yau fourfolds, highlighting new constraints on flux quantization in F-theory.
We study Pontryagin integrals on Calabi-Yau fourfolds and introduce a Pontryagin defect number defined as the difference between a curvature-derived Pontryagin integral and its topological expression in terms of Chern classes. Under a fixed normalization of the Ricci-flat metric, we observe that the Pontryagin integral exhibits a constant value in the examples considered. The resulting defect quantity is deformation invariant and stable under Fourier-Mukai equivalence. We find a linear relation between the defect and certain combinations of Hodge numbers, together with a connection to primitive (2,2)-cohomology. Possible implications for flux quantization in F-theory are briefly discussed.
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Bhattacharjee et al. (2026) studied this question.
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